Visualizing uncertainty

class: center, middle, inverse, title-slide

# Visualizing uncertainty
### Daniel Anderson
### Week 7, Class 2

---

layout: true

---
class: inverse-red middle
# Reviewing Lab 3

---
class: inverse-blue
# Data viz in the wild

Ann-Marie

Murat

### Sarah Donaldson & Hyeonjin on deck

---

# Agenda 
* Framing uncertainty as relative frequencies
  + Discrete probabilities
  + Non-discrete probabilities
    + Understanding AUC calculations
--
* Understanding standard errors
  + Non-standard ways of visualizing SEs

--
* HOPs (briefly)
  + Also bootstrapping

---
# Learning objectives
1. Understand there are lots of different ways to visualize uncertainty, and the best method may often be non-standard.

2. Understand how to implement basic methods, and the resources available to you to implement more advanced methods

---
# Thinking about uncertainty
Uncertainty means exactly what it sounds like - we are not 100% sure.

* We are nearly always uncertain of future events (forecasting)
* We can also be uncertain about past events 
  + I saw a parked car at 8 AM, but the next time I looked at 2PM it was gone. What time did it leave?

--
### Quantifying uncertainty
* We quantify our uncertainty mathematically using probability
* Framing probabilities as frequencies is generally more intuitive

---
class: inverse-blue center middle
# Framing a single uncertainty

---
background-image:url("https://serialmentor.com/dataviz/visualizing_uncertainty_files/figure-html/probability-waffle-1.png")
background-size:contain

---
# How do we make these?
* Start out by making a grid

```r
grid <- expand.grid(x = 1:20, y = 1:20)
head(grid)
```

```
##   x y
## 1 1 1
## 2 2 1
## 3 3 1
## 4 4 1
## 5 5 1
## 6 6 1
```

```r
tail(grid)
```

```
##      x  y
## 395 15 20
## 396 16 20
## 397 17 20
## 398 18 20
## 399 19 20
## 400 20 20
```

---
# Look at the grid

```r
ggplot(grid, aes(x, y)) +
  geom_tile(color = "gray40",
            fill = "white") +
  theme_void()
```

![](w7p2_files/figure-html/see-grid-1.png)

---
# Create occurrence rate
* For each sequence of `x`, create a variable that has the given occurence rate

--
### How?

--
* Plenty of options, here's one

---
# Consider 10%

```r
nrow(grid)*.10 # n to sample
```

```
## [1] 40
```

```r
set.seed(86753098)
samp <- sample(seq_len(nrow(grid)), nrow(grid)*.10)
head(samp)
```

```
## [1] 318 134 180 283 177 248
```

```r
length(samp)
```

```
## [1] 40
```

---
# Create the variable

```r
grid <- grid %>% 
  rownames_to_column("row_id") %>% 
  mutate(event = ifelse(row_id %in% samp, "Yes", "No"))
head(grid)
```

```
##   row_id x y event
## 1      1 1 1    No
## 2      2 2 1    No
## 3      3 3 1    No
## 4      4 4 1    No
## 5      5 5 1   Yes
## 6      6 6 1    No
```

---
# Fill in

```r
ggplot(grid, aes(x, y)) +
  geom_tile(aes(fill = event), color = "white") +
  theme_void()
```

![](w7p2_files/figure-html/theatre1-1.png)

---
# Customize

```r
library(colorspace)
ggplot(grid, aes(x, y)) +
  geom_tile(aes(fill = event), color = "white", size = 1.4) +
  scale_fill_manual(
    name = "Event Occurred",
    values = c(
      desaturate(
        lighten("#1694E8", 0.5), 
        0.7), 
      "#1694E8"
      )
    ) +
  coord_fixed() +
  theme_void() +
  theme(legend.position = c(0.75, 0),
        legend.direction = "horizontal",
        plot.margin = margin(b = 1, unit = "cm"))
```

---
![](w7p2_files/figure-html/theatre2-eval-1.png)

---
# Chance of rain
## 80%
![](w7p2_files/figure-html/rain1-1.png)

---
# Vary grid size
### 10 x 10
![](w7p2_files/figure-html/rain2-1.png)

---
# Vary grid size
### 20 x 20

![](w7p2_files/figure-html/grid-size20-1.png)

---
# Vary grid size
### 30 x 30

![](w7p2_files/figure-html/grid-size30-1.png)

(probs too many)

---
class: inverse-red center middle
# Non-discrete probabilities

---
# Hypothetical
Blue party has 1% advantage (technically 1.02%) w/ margin of error of 1.76 points

### Who will win?

![](w7p2_files/figure-html/pdf-1.png)

---
# A bit of math
Our prior distribution was defined by `$\mu = 1.02$` and `$sd = 0.88$` (margin of error divided by two).

--
* What's the chance the end result is below zero?

---
# The hard way
Calculate the exact probability of data below zero under this distribution

```r
x <- seq(-5, 5, 0.001)
likelihood <- dnorm(x, 1.02, 0.88)
sim <- data.frame(x, likelihood)
ggplot(sim, aes(x, likelihood)) +
  geom_line(size = 1.2)
```

![](w7p2_files/figure-html/dnorm-1.png)

---
# How do we calculate this portion?

![](w7p2_files/figure-html/auc-1.png)

---
# Integrate

```r
zab <- filter(sim, x <= 0)
pracma::trapz(zab$x, zab$likelihood)
```

```
## [1] 0.123
```

---
# Easier: Simulate

```r
random_draws <- rnorm(1e5, 1.02, 0.9)
table(random_draws > 0) / 1e5
```

```
## 
## FALSE  TRUE 
##  0.13  0.87
```

---
# Discretized plot

```r
ppoints(50)
```

```
##  [1] 0.01 0.03 0.05 0.07 0.09 0.11 0.13 0.15 0.17 0.19 0.21 0.23 0.25 0.27
## [15] 0.29 0.31 0.33 0.35 0.37 0.39 0.41 0.43 0.45 0.47 0.49 0.51 0.53 0.55
## [29] 0.57 0.59 0.61 0.63 0.65 0.67 0.69 0.71 0.73 0.75 0.77 0.79 0.81 0.83
## [43] 0.85 0.87 0.89 0.91 0.93 0.95 0.97 0.99
```

```r
qnorm(ppoints(50), 1.02, 0.9)
```

```
##  [1] -1.07371 -0.67271 -0.46037 -0.30821 -0.18668 -0.08388  0.00625  0.08721
##  [9]  0.16125  0.22989  0.29422  0.35504  0.41296  0.46847  0.52195  0.57373
## [17]  0.62408  0.67321  0.72133  0.76861  0.81521  0.86126  0.90690  0.95226
## [25]  0.99744  1.04256  1.08774  1.13310  1.17874  1.22479  1.27139  1.31867
## [33]  1.36679  1.41592  1.46627  1.51805  1.57153  1.62704  1.68496  1.74578
## [41]  1.81011  1.87875  1.95279  2.03375  2.12388  2.22668  2.34821  2.50037
## [49]  2.71271  3.11371
```

---

```r
discretized <- data.frame(
  x = qnorm(ppoints(50), 1.02, 0.9)
  ) %>% 
  mutate(winner = ifelse(x <= 0, "#b1daf4", "#f8f1a9"))

head(discretized) 
```

```
##         x  winner
## 1 -1.0737 #b1daf4
## 2 -0.6727 #b1daf4
## 3 -0.4604 #b1daf4
## 4 -0.3082 #b1daf4
## 5 -0.1867 #b1daf4
## 6 -0.0839 #b1daf4
```

```r
tail(discretized)
```

```
##       x  winner
## 45 2.12 #f8f1a9
## 46 2.23 #f8f1a9
## 47 2.35 #f8f1a9
## 48 2.50 #f8f1a9
## 49 2.71 #f8f1a9
## 50 3.11 #f8f1a9
```

---

```r
ggplot(discretized, aes(x)) +
  geom_dotplot()
```

![](w7p2_files/figure-html/dotplot1-1.png)

---

```r
ggplot(discretized, aes(x)) +
  geom_dotplot(aes(fill = winner))
```

![](w7p2_files/figure-html/dotplot2-1.png)

---

```r
ggplot(discretized, aes(x)) +
  geom_dotplot(aes(fill = winner), binwidth = 0.35)
```

![](w7p2_files/figure-html/dotplot3-1.png)

---

```r
ggplot(discretized, aes(x)) +
  geom_dotplot(aes(fill = winner), binwidth = 0.35) +
  geom_vline(xintercept = 0, 
             color = "gray40", 
             linetype = "dashed", 
             size = 1.5)
```

![](w7p2_files/figure-html/dotplot4-1.png)

---

```r
ggplot(discretized, aes(x)) +
  geom_dotplot(aes(fill = winner), binwidth = 0.26) +
  geom_vline(xintercept = 0, 
             color = "gray40", 
             linetype = 2, 
             size = 3) +
  scale_fill_identity(guide = "none") +
  scale_y_continuous(name = "", 
                     breaks = NULL)
```

![](w7p2_files/figure-html/dotplot5-1.png)

---
# Probs too many though

```r
discretized2 <- data.frame(
  x = qnorm(ppoints(20), 1.02, 0.9)
  ) %>% 
  mutate(winner = ifelse(x <= 0, "#b1daf4", "#f8f1a9"))

ggplot(discretized2, aes(x)) +
  geom_dotplot(aes(fill = winner), binwidth = 0.4) +
  geom_vline(
    xintercept = 0.1, 
    color = "gray40", 
    linetype = 2, 
    size = 1.4) +
  scale_fill_identity(guide = "none") +
  scale_x_continuous(
    name = "",
    limits = c(-1, 3),
    labels = scales::percent_format(scale = 1)
  ) +
  theme_dviz_open(20, font_family = "Roboto Light") +
  scale_y_continuous(breaks = NULL,
                     name = "") +
  labs(caption = "Each ball represents 5% probability")
```

---
![](w7p2_files/figure-html/descritized2-eval-1.png)
---
class: inverse-red center middle
# Uncertainty of point estimates

---
# Quick review (hopefully a review)

* What is a standard error?

--
* Standard deviation of the sampling distribution

* What is the sampling distribution?

--
* Samples from the underlying, population-based, generative distribution

* What does this mean, exactly?

--
* Let's simulate to explore

---
# Simulation

* Imagine the "real" distribution has `$\mu = 100$` and `$\sigma = 10$`.

--
* Let's draw a sample of 10 from this distribution

```r
set.seed(123)
samp10a <- rnorm(n = 10, mean = 100, sd = 10)
samp10a
```

```
##  [1]  94.4  97.7 115.6 100.7 101.3 117.2 104.6  87.3  93.1  95.5
```

--
* Calculate the mean

```r
mean(samp10a)
```

```
## [1] 101
```

---
# Do it a second time

```r
samp10b <- rnorm(n = 10, mean = 100, sd = 10)
samp10b
```

```
##  [1] 112.2 103.6 104.0 101.1  94.4 117.9 105.0  80.3 107.0  95.3
```

```r
mean(samp10b)
```

```
## [1] 102
```

---
# Do it a bunch of times

```r
samples <- replicate(1000, rnorm(10, mean = 100, sd = 10),
                     simplify = FALSE)
samples
```

```
## [[1]]
##  [1]  89.3  97.8  89.7  92.7  93.7  83.1 108.4 101.5  88.6 112.5
## 
## [[2]]
##  [1] 104.3  97.0 109.0 108.8 108.2 106.9 105.5  99.4  96.9  96.2
## 
## [[3]]
##  [1]  93.1  97.9  87.3 121.7 112.1  88.8  96.0  95.3 107.8  99.2
## 
## [[4]]
##  [1] 102.5  99.7  99.6 113.7  97.7 115.2  84.5 105.8 101.2 102.2
## 
## [[5]]
##  [1] 103.8  95.0  96.7  89.8  89.3 103.0 104.5 100.5 109.2 120.5
## 
## [[6]]
##  [1]  95.1  76.9 110.1  92.9  93.1 110.3  97.2  87.8 101.8  98.6
## 
## [[7]]
##  [1] 100.1 103.9  96.3 106.4  97.8 103.3 111.0 104.4  96.7 111.5
## 
## [[8]]
##  [1] 109.9 105.5 102.4  93.7 113.6  94.0 121.9 115.3  97.6  89.7
## 
## [[9]]
##  [1]  92.9 102.6  97.5  96.5  90.5  99.5  92.2  83.3  96.2 109.2
## 
## [[10]]
##  [1]  94.2 106.1  83.8  99.4 105.2 103.0 101.1  93.6  91.5  89.8
## 
## [[11]]
##  [1] 101.2  90.5  95.1  97.4 118.4  93.5 102.4 100.8  90.4  99.3
## 
## [[12]]
##  [1] 114.4 104.5 100.4  95.8  79.5 111.3  85.4 107.4 119.1  85.6
## 
## [[13]]
##  [1] 107.0  97.4  84.3  84.9  84.0  94.7  85.4 106.9 121.0  87.1
## 
## [[14]]
##  [1] 107.9 107.7 103.3  89.9  98.8  97.2 105.6  96.3 109.8  96.3
## 
## [[15]]
##  [1] 110.5  89.5  87.4 132.4  95.8 103.0 106.4  95.2 105.2 103.7
## 
## [[16]]
##  [1]  97.8 100.7  99.7 121.3  92.6  89.0 100.4 103.1 104.4  95.4
## 
## [[17]]
##  [1]  89.4 112.6  96.5  91.3  97.6  98.0 111.1 100.8 107.5  95.0
## 
## [[18]]
##  [1] 102.1  96.8 100.9  91.0  86.9 120.0 106.0  87.5  93.9  88.1
## 
## [[19]]
##  [1] 122.0 113.1  97.3 105.4  95.9  95.2  92.1  94.1 116.5  99.5
## 
## [[20]]
##  [1] 101.2 102.4 112.3  94.8  90.1 116.8  95.6  92.8  87.6  87.2
## 
## [[21]]
##  [1]  94.3 106.2 111.1 107.1  96.4 100.6  93.0  92.8 108.8  89.8
## 
## [[22]]
##  [1] 119.6  99.1 102.1  92.6  94.3  86.8  98.2 104.2 103.2  92.2
## 
## [[23]]
##  [1]  92.1  95.0 115.0  88.6  98.2 119.0  99.0  86.4  93.4 104.9
## 
## [[24]]
##  [1]  96.2  94.4  96.6 100.9 116.0  99.1 110.8 106.3  98.9  84.7
## 
## [[25]]
##  [1]  94.8  95.1 100.5 113.0 122.9 115.5  98.7  82.4  96.1 100.9
## 
## [[26]]
##  [1] 108.5 109.6 106.8  86.0 108.5  95.5 101.7 100.7 104.3 100.2
## 
## [[27]]
##  [1]  83.3 107.4 103.9  97.3 101.2 101.3 102.2 116.4  97.8 101.7
## 
## [[28]]
##  [1] 111.7 110.5 111.5  94.2 120.0 100.7 118.7  86.5 100.2 112.5
## 
## [[29]]
##  [1]  92.8  92.5  90.6  89.5  95.6 103.3  79.9 102.1 112.4 120.4
## 
## [[30]]
##  [1] 113.0 107.6  82.7  94.0  96.5 107.0  98.9  87.4 116.8 109.1
## 
## [[31]]
##  [1] 102.4 112.2  86.6 106.6  94.8 106.8  99.4 106.3 113.4 100.1
## 
## [[32]]
##  [1] 110.2  88.1  92.8 115.2 103.8  79.5  86.4  98.0 108.7  99.0
## 
## [[33]]
##  [1] 106.2 109.6 116.7 100.6  99.5  82.5 101.0  94.3  90.3  98.2
## 
## [[34]]
##  [1] 110.1  80.1  95.7 101.2  91.1 103.3 104.1  99.7  75.3 125.7
## 
## [[35]]
##  [1]  97.9 106.5 102.7 110.2 108.2  97.9 103.8  90.5 108.6  95.4
## 
## [[36]]
##  [1] 124.2  83.5  95.4 108.3 105.1  94.1  90.0 101.4  99.9  82.1
## 
## [[37]]
##  [1] 100.3 101.9 101.7  89.4 104.8 113.8 104.6  88.6  95.6 103.5
## 
## [[38]]
##  [1]  93.5  78.4 108.8  91.7  94.3 115.0  92.3 108.5  87.4  96.5
## 
## [[39]]
##  [1]  99.3  88.3  93.7  99.7 106.7  83.5  96.5 107.6  94.6 102.3
## 
## [[40]]
##  [1] 104.9 102.7 106.5  98.8  95.9  73.6  99.1 104.3 105.4  94.4
## 
## [[41]]
##  [1] 117.8 102.9 101.3 112.7  92.8  95.5 124.0 100.1 116.3  85.6
## 
## [[42]]
##  [1]  98.1 103.8 103.0  89.9 100.2  89.2 107.1 110.8  77.8 112.4
## 
## [[43]]
##  [1]  87.6 104.5 106.6  98.0  93.5 101.7 104.4 108.8  79.5  83.6
## 
## [[44]]
##  [1] 114.3 110.5 104.4 107.2 109.2  73.4 111.1  95.2 102.3  97.0
## 
## [[45]]
##  [1] 108.7  96.5 105.2  96.1  89.1 112.1 107.4 117.2 100.7 111.3
## 
## [[46]]
##  [1] 119.8  97.2  86.8  97.6  97.9 101.5 117.1  96.7 103.7  97.7
## 
## [[47]]
##  [1] 100.2 103.1 113.3 101.2 107.1 107.8 109.1  94.3 116.3  96.2
## 
## [[48]]
##  [1]  98.9 114.0 112.9  89.1  91.3  86.4 101.8 101.6 103.6 105.5
## 
## [[49]]
##  [1]  94.0  90.1 110.3 107.5  84.9  99.0  91.0  79.3 101.5  99.2
## 
## [[50]]
##  [1]  99.0 102.2 108.8 102.1  93.8  92.7  98.7 103.1  89.6  98.2
## 
## [[51]]
##  [1] 109.7  98.9  93.0  97.2 111.1 105.5 112.4 101.4 104.1  94.4
## 
## [[52]]
##  [1] 106.1  94.9  85.8 101.3 119.5 108.0 111.7 103.6  93.9  98.0
## 
## [[53]]
##  [1]  97.3  95.3 107.0  88.0 108.7 108.6  88.0 106.4 124.3  94.4
## 
## [[54]]
##  [1] 108.4  92.2 111.1 102.5 116.5  85.4  99.5  94.7  98.0  93.7
## 
## [[55]]
##  [1]  91.7 105.8  89.1 114.8  88.1 101.0 105.3 105.9  97.0 100.8
## 
## [[56]]
##  [1] 109.6  85.4  92.2 103.2  95.6 113.7 106.7 100.7  84.9 100.3
## 
## [[57]]
##  [1]  96.8  99.0  88.2 105.0  89.6  97.7 103.8  92.2 105.8  86.8
## 
## [[58]]
##  [1]  71.9 104.6 108.4  97.1 105.0  88.4  98.7  80.6 111.8 118.6
## 
## [[59]]
##  [1] 110.7  99.7  99.7  84.8 107.9  97.9  93.4  85.9  97.0  91.5
## 
## [[60]]
##  [1]  96.0  87.8 116.9  99.8 110.7  74.0  95.5  93.2  87.8 115.5
## 
## [[61]]
##  [1]  85.8 103.2 108.5 101.8  91.2 109.4 101.7  89.4  86.1 120.9
## 
## [[62]]
##  [1]  93.2  81.4 105.3 103.1  86.5  80.6  98.8 111.4 106.4  95.1
## 
## [[63]]
##  [1]  91.7 102.7 101.6 106.3  96.0 109.0  91.7  96.7 107.4 109.9
## 
## [[64]]
##  [1]  80.6 101.1 106.1  85.5 104.8  91.7 110.2 105.4 107.7 101.2
## 
## [[65]]
##  [1] 108.6 113.8 119.7  99.7  77.5 100.3 102.1  98.4 105.7 110.1
## 
## [[66]]
##  [1]  94.8  97.1 104.0  94.5 100.9  80.4  88.8  86.7  91.5  93.1
## 
## [[67]]
##  [1] 103.8 109.8  92.7  90.0  89.6  95.9  97.6 104.8  96.8  79.2
## 
## [[68]]
##  [1]  99.1 111.9 111.9  92.1  84.5 124.6  98.4  99.0 104.2  83.9
## 
## [[69]]
##  [1]  92.7  84.6  93.1 101.2  86.4 105.9 102.9  91.0 102.3 107.5
## 
## [[70]]
##  [1] 110.6  97.9  99.1  99.1 114.4 111.3 108.3  97.1 103.7 104.0
## 
## [[71]]
##  [1]  89.6  82.7 106.4  84.7 100.0 102.5 105.6 101.9  92.7 109.9
## 
## [[72]]
##  [1] 117.4 108.8  80.6 114.0  99.4 105.2 106.2  99.0  99.2 110.2
## 
## [[73]]
##  [1] 107.1 109.9 123.8 106.6 102.1  77.9 126.9  95.2 123.7 103.7
## 
## [[74]]
##  [1] 115.4  98.9 105.1 102.1  98.1  98.8 110.1  98.0  79.6  98.0
## 
## [[75]]
##  [1] 105.4 106.2 106.2  83.1 103.7 109.7 112.8  97.8  96.8 114.9
## 
## [[76]]
##  [1]  83.3  95.6 104.6  83.8 102.8 118.8 100.0  97.2 104.7  97.2
## 
## [[77]]
##  [1] 108.1 109.0 100.0  88.2  86.8  94.1 108.0  80.4  81.1  93.5
## 
## [[78]]
##  [1] 103.9  90.9 108.9 103.3  98.3 108.2 103.9  95.5 102.3 106.5
## 
## [[79]]
##  [1] 103.6  93.4 108.6 111.5 102.8 101.4  99.2 121.6 102.8  98.4
## 
## [[80]]
##  [1]  74.9  84.3  99.2 102.1 102.8 108.2  98.1 112.1  90.8  87.9
## 
## [[81]]
##  [1]  87.7 107.4  99.2 107.9  97.3  94.1  96.3  81.5  88.3  85.6
## 
## [[82]]
##  [1] 110.5  94.0 107.9 115.2  98.1 102.8  82.5  91.8 100.6 103.0
## 
## [[83]]
##  [1]  92.4 126.8  95.4 100.6 106.5  99.7  93.6 110.5 116.2  99.7
## 
## [[84]]
##  [1] 105.6  99.0 110.2  88.4 123.2  94.0  85.4  96.5 101.5 116.2
## 
## [[85]]
##  [1] 109.1 101.4  86.1  91.3  98.4 125.5  81.4 111.3  94.7 116.7
## 
## [[86]]
##  [1]  88.6 101.4  89.0 109.0 114.8 119.5 108.0 118.4 112.5  98.7
## 
## [[87]]
##  [1] 104.8  90.3  98.1 112.2 105.4 104.6  89.6  94.0  92.4 104.0
## 
## [[88]]
##  [1]  90.1 105.6  88.8 118.3 104.6  93.0 102.4  96.5 103.7 102.4
## 
## [[89]]
##  [1]  89.9  92.1 103.0 116.4 110.8  93.8 108.3  99.5 103.0 102.6
## 
## [[90]]
##  [1] 125.8  88.1 101.0  82.2 105.9 111.0 114.5  80.7 104.1 115.9
## 
## [[91]]
##  [1]  95.9  97.9  99.6 103.7 106.7 113.2  99.0 102.0 124.9 104.3
## 
## [[92]]
##  [1] 101.9  86.6 100.0  97.8  99.9  94.2  93.1  92.8  97.9 113.7
## 
## [[93]]
##  [1] 110.5  96.4  83.1  91.6  95.4 101.0  93.4 120.1  97.3  87.9
## 
## [[94]]
##  [1]  98.6  89.9 101.6 102.3 103.6  83.8 102.2 103.1  85.8 109.6
## 
## [[95]]
##  [1] 107.8 123.0 101.6 100.5 101.0 100.7  81.5  83.3  99.2  94.2
## 
## [[96]]
##  [1] 100.5  78.9  85.0  89.0 109.9  89.0  92.0 100.8  96.8 101.5
## 
## [[97]]
##  [1] 123.1  88.8  96.9  94.8 115.1  92.3  99.2 107.9  89.4 116.6
## 
## [[98]]
##  [1] 106.8  89.3 104.5  97.9 103.1  99.1 110.7  86.5  94.8  97.5
## 
## [[99]]
##  [1]  90.0  89.6  99.8  98.7  74.5 110.4 102.5 124.2 106.9  95.5
## 
## [[100]]
##  [1] 128.0 128.3  87.8 104.7  97.9 101.9 102.3  87.4 102.9 117.5
## 
## [[101]]
##  [1]  98.4  98.4 114.0 109.0  83.5 102.3 116.5 114.2 104.2 107.2
## 
## [[102]]
##  [1]  88.0 103.0  90.5  95.4 109.4  88.6 102.7 104.3 100.5 118.2
## 
## [[103]]
##  [1]  89.8 106.1  99.1  97.4 104.6  89.8  86.9  95.1 117.5 100.6
## 
## [[104]]
##  [1] 103.3  98.1 104.7  90.5 111.6 105.8  91.9 100.5 107.2 105.6
## 
## [[105]]
##  [1] 114.8  93.9 111.2 110.4  98.4  90.2  89.1 104.6  99.3 117.8
## 
## [[106]]
##  [1] 105.4  96.3  89.7  94.2 103.4  95.5 105.1  96.7  98.9  92.7
## 
## [[107]]
##  [1] 119.1 103.3 102.3  83.1 106.6  89.8  91.1 109.2  95.5  82.5
## 
## [[108]]
##  [1] 117.7  76.2 105.7 110.2  93.7 104.4 104.4 110.4 104.8  97.6
## 
## [[109]]
##  [1] 109.2 108.0  90.6  86.0 101.6  97.3  90.1 100.8  86.8 101.6
## 
## [[110]]
##  [1]  93.8 109.6 124.2  90.8 110.6 108.3  99.3  95.5 115.8  79.9
## 
## [[111]]
##  [1]  93.6  85.6 114.0  98.1  94.8 131.8  99.5  95.6 103.0  84.3
## 
## [[112]]
##  [1] 104.9  99.0 104.7  90.2  89.8  93.1  92.3 113.0 115.8  98.4
## 
## [[113]]
##  [1]  96.4  96.7 100.7 101.0 102.9  92.5  91.5 112.0  94.5 103.0
## 
## [[114]]
##  [1]  99.4  90.4 105.9 101.7 114.0 101.2  96.7 102.8  88.1  91.6
## 
## [[115]]
##  [1] 105.1  96.7  99.3  98.8  93.5  79.8 103.5 107.6  87.1 114.8
## 
## [[116]]
##  [1] 103.9 113.4  90.4 101.7  99.0 107.7  94.2  99.9  82.2  92.2
## 
## [[117]]
##  [1] 101.3  92.9  99.6  95.3 106.1 111.7  91.8  96.9 114.4  78.0
## 
## [[118]]
##  [1]  96.8 120.6 121.9 101.6  91.4 101.7  93.5 114.5  91.9 103.7
## 
## [[119]]
##  [1] 106.2  92.4 108.5  92.5 106.3 111.0  90.1 111.1  95.1 102.9
## 
## [[120]]
##  [1] 102.0  95.7 102.7  87.7  98.6 108.3  78.3  85.1  88.4  84.1
## 
## [[121]]
##  [1] 104.2  90.1  78.4  93.6  96.1 108.6  89.0 111.6 104.0 103.6
## 
## [[122]]
##  [1]  91.5 119.5  98.4  81.8  98.0  80.7  96.9  95.8 106.8 110.1
## 
## [[123]]
##  [1]  92.7 108.1 114.2  92.2  93.5 106.5 101.8 105.5 114.0 103.9
## 
## [[124]]
##  [1] 110.5 106.2 104.3 103.9 112.9  90.0  88.9 105.9  98.8 100.7
## 
## [[125]]
##  [1] 107.4 107.5  97.4  96.9 100.7 110.6 104.3 114.3  99.9 111.3
## 
## [[126]]
##  [1] 108.8 106.1 104.1  97.2  98.9 102.3 100.5 109.4  98.9  99.3
## 
## [[127]]
##  [1] 95.2 98.6 99.3 76.9 86.4 99.3 97.3 88.0 80.1 96.5
## 
## [[128]]
##  [1] 106.5 117.7  99.6 114.9 100.8 101.2 103.2  91.3  99.5 109.1
## 
## [[129]]
##  [1]  92.5  96.8  88.5 103.5 104.2 106.5  87.8 101.1  90.6 100.0
## 
## [[130]]
##  [1] 113.4  95.0 107.2  92.5  95.2 104.4  93.2  83.0 112.7 103.6
## 
## [[131]]
##  [1]  94.2  80.1 119.0 133.9 102.1 108.5 112.2  93.0  96.5  82.7
## 
## [[132]]
##  [1]  92.6 106.2  97.1  97.9  98.9  81.4 108.4  85.6  97.9  95.6
## 
## [[133]]
##  [1]  97.8 114.6  94.2  92.2  84.8  91.9  88.3 104.1  91.4 103.0
## 
## [[134]]
##  [1]  98.5  85.7  92.1 108.9 109.0 120.1 100.0  85.0  92.3 104.1
## 
## [[135]]
##  [1] 119.0 101.1 111.4 107.7  88.3  98.3 113.1 108.8 104.6 104.8
## 
## [[136]]
##  [1]  95.1  86.8 113.0  85.8  90.6 106.3  87.4  94.5  88.2 106.2
## 
## [[137]]
##  [1] 104.5 104.2 104.4 105.6 106.4  80.3  98.5 101.1 107.2  88.1
## 
## [[138]]
##  [1]  95.0  89.3 110.6 112.8 107.9  87.8 104.5 111.5 101.7  94.3
## 
## [[139]]
##  [1]  89.1  93.3 107.1  95.7 102.3 112.9 105.8 113.6  83.0  97.2
## 
## [[140]]
##  [1] 100.7 105.8  88.3 108.1 103.1 102.6 105.1  98.8 109.3 106.5
## 
## [[141]]
##  [1]  98.5 110.4 102.9 106.7  94.1 115.8 100.0 108.5  99.0  97.2
## 
## [[142]]
##  [1] 107.8  84.2 104.8 103.9  73.0 103.7  78.3 106.6  95.5  93.1
## 
## [[143]]
##  [1]  99.9 113.7  93.6 105.6 103.4  88.2  82.6  80.1 105.5  99.7
## 
## [[144]]
##  [1] 119 106 108 113  95 105 109 114 108 104
## 
## [[145]]
##  [1]  91.3 107.3 105.0 106.3 104.2  98.0  99.2 106.9 101.7  91.7
## 
## [[146]]
##  [1]  97.1  86.8  90.3  98.6  82.0  83.1 111.0  94.2  81.5  98.9
## 
## [[147]]
##  [1] 113.2 106.6 104.4 111.8  92.3 107.3  94.1 100.0 122.1 109.7
## 
## [[148]]
##  [1] 107.7  88.9  92.1 122.8  89.1 102.1 108.9 110.2 110.9  98.4
## 
## [[149]]
##  [1]  91.8  96.9  91.0 106.3 111.2 121.3 103.7  91.3 110.2 109.0
## 
## [[150]]
##  [1]  97.6  84.4 107.6 111.3  97.0 105.4  97.2 106.8  98.8  96.6
## 
## [[151]]
##  [1] 101.1  97.2  94.1  96.8  99.9 102.1 115.3  86.4  98.0 106.3
## 
## [[152]]
##  [1] 117.6 104.3  99.9  96.9 104.1 109.9  98.2 101.6 102.2 107.3
## 
## [[153]]
##  [1] 111.1 102.8  99.2 113.9 101.6 115.8  99.4 106.1  84.5  98.9
## 
## [[154]]
##  [1]  99.8  92.4  89.6 109.5 109.1  87.0 104.2  88.9  89.5 105.3
## 
## [[155]]
##  [1]  93.1 109.9 100.4 105.4  94.8  88.5 109.1 102.4  97.6 100.7
## 
## [[156]]
##  [1] 113.3  93.0  92.5  93.8  84.2 108.2 101.9 102.1  99.6  94.9
## 
## [[157]]
##  [1]  91.8 108.5  85.7 104.4  92.1 102.8  92.6  94.8 117.7 106.7
## 
## [[158]]
##  [1]  78.6 101.3  95.5  88.6 102.1 101.3  96.7 119.7  77.5 108.4
## 
## [[159]]
##  [1]  97.1 106.6  95.5  94.1  82.9  97.9 124.8 109.9 116.8 109.1
## 
## [[160]]
##  [1] 111.4 109.0 104.8  94.2  94.7  84.0  99.9 109.0 110.3 101.0
## 
## [[161]]
##  [1]  94.5 132.9 107.4 114.2  96.6  99.6 104.5 116.8  96.9 108.5
## 
## [[162]]
##  [1]  79.1  94.9  87.1 111.1  98.4  96.1 113.7 111.2  91.0 104.3
## 
## [[163]]
##  [1]  87.7  95.2 116.2 114.5 111.1  94.3  81.2  88.2 109.5  97.1
## 
## [[164]]
##  [1]  78.4  98.2 114.1 106.4  91.8  84.5  91.7 100.3 108.9  80.6
## 
## [[165]]
##  [1] 110.2 100.1 105.7  83.5  93.3  95.5 110.4 110.3 104.4 116.0
## 
## [[166]]
##  [1]  94.8 110.1  99.6  93.3 109.2 113.8 108.8  94.9  95.3 113.8
## 
## [[167]]
##  [1] 103.5 108.3  96.6 112.6  91.9 106.3  91.8  75.4  86.6 101.4
## 
## [[168]]
##  [1] 108.8  82.5  87.5 117.6  95.7 105.1  94.7  97.0 100.9 100.1
## 
## [[169]]
##  [1]  98.1  95.3  69.5 118.7 117.9  89.0  98.3 113.8 110.0 112.8
## 
## [[170]]
##  [1]  89.3 125.8  88.7 107.5 101.4  96.0  96.2  90.1 116.2 100.9
## 
## [[171]]
##  [1] 102.6 102.1  96.2  88.7 102.5  79.1  85.8  89.2  89.2 101.1
## 
## [[172]]
##  [1] 116.0  84.8 104.3 109.0  90.1  99.5 108.2  97.4  97.8 103.1
## 
## [[173]]
##  [1]  99.4  94.4  98.6 118.8 108.7  90.9  87.6  96.4 113.3 102.9
## 
## [[174]]
##  [1]  93.0 108.8  98.7  88.8 104.6 115.2 104.3 101.9  93.4 105.7
## 
## [[175]]
##  [1]  89.3  83.5  99.6  99.7 123.7  87.8 101.7 108.1 110.5  99.9
## 
## [[176]]
##  [1]  92.6  99.3 119.4 104.8  79.6 114.2 105.4  99.7  99.8  98.5
## 
## [[177]]
##  [1] 102.6  95.0 102.8  90.7 102.0 111.1 105.1 110.3  89.1 100.5
## 
## [[178]]
##  [1] 106.2  89.3 115.7  89.7 101.6 101.5 101.2  97.9 104.5  89.7
## 
## [[179]]
##  [1]  87.1  93.5  99.4 112.6 115.9 103.2 103.8  97.6 100.5  86.0
## 
## [[180]]
##  [1] 102.9  94.6 103.3  96.5  93.4  97.8  96.3 110.9 102.1 104.3
## 
## [[181]]
##  [1]  87.6 115.0 101.6  91.4 103.1 108.7  86.2 116.9  98.4 111.2
## 
## [[182]]
##  [1] 100.7  96.7  81.7  89.0  99.6 108.3  81.2 113.8 114.0  88.6
## 
## [[183]]
##  [1] 104.7  89.7  98.7 109.3 108.7  91.5  96.1  90.2 103.4  84.4
## 
## [[184]]
##  [1]  73.7 114.7 122.7  95.4 107.6  99.9 114.7 105.5 102.0  82.0
## 
## [[185]]
##  [1] 110.8  96.5  86.0  98.0  98.7 110.6  88.3  94.4 114.9 113.6
## 
## [[186]]
##  [1] 111.6 116.6 102.0  94.2 105.6 110.6 124.1  80.4 102.7 106.5
## 
## [[187]]
##  [1]  99.5  84.4 107.4  92.2 105.1 109.1 112.8  84.4 110.8  92.4
## 
## [[188]]
##  [1]  87.1 113.1 111.5  97.6 107.6  91.4  98.5  99.1  97.2 107.3
## 
## [[189]]
##  [1] 115.4  95.4  99.7 116.4  96.7  74.0 105.1  91.1  90.0 114.2
## 
## [[190]]
##  [1] 124.5  89.6 110.3  99.1 101.4 112.2 102.1  91.5  95.3 106.9
## 
## [[191]]
##  [1]  76.6 111.0  84.3 100.2  98.1 112.9 101.9 101.0 107.0  91.7
## 
## [[192]]
##  [1]  98.0 111.8 106.8  87.2 106.4  86.2  94.0 112.1  77.5  82.2
## 
## [[193]]
##  [1] 113.0  91.9 112.4  98.3 104.3 108.1  93.5  97.0  95.8 128.2
## 
## [[194]]
##  [1] 101.3 104.7  96.6  97.6 113.8  96.6 100.2 103.8  95.7 119.6
## 
## [[195]]
##  [1]  85.7 120.1  96.5 113.6  80.0 109.6 108.8  87.3  92.3 101.9
## 
## [[196]]
##  [1] 111.4  92.3  97.8 115.7  88.7 109.5 104.5  88.9  93.3 107.8
## 
## [[197]]
##  [1] 102.5 114.3  94.0  82.9 110.5  93.9 101.2 117.2  97.5 115.5
## 
## [[198]]
##  [1]  89.0 109.3 102.5  92.6  87.2 100.8 102.6 102.8 105.4  95.4
## 
## [[199]]
##  [1]  94.9 102.4  94.6 112.2 101.7  93.8  81.9  93.6 120.5  94.4
## 
## [[200]]
##  [1]  91.6 106.5 104.4 107.5  97.2 111.2  88.3  99.5  93.0 106.8
## 
## [[201]]
##  [1] 101.3 111.1 120.6 101.4  94.7  91.8  97.4  99.3 119.9  88.7
## 
## [[202]]
##  [1]  89.1  95.9 105.9 108.2  90.9 101.3  99.6 112.0 110.9  96.9
## 
## [[203]]
##  [1] 100.5 106.5  83.5  96.9 105.7  94.8  99.4  99.8  92.8  90.1
## 
## [[204]]
##  [1]  98.0  96.5 108.3 115.3  99.9 104.0  99.3 106.0 102.2 102.4
## 
## [[205]]
##  [1] 111.1  90.1 114.5 103.5 101.8  94.4  98.4 103.7  79.4  94.0
## 
## [[206]]
##  [1] 105.9  97.1  92.0  93.6 102.4  83.7 108.7  78.3  95.0  92.1
## 
## [[207]]
##  [1]  87.5  89.2 102.5  98.8  97.0  76.8  86.8  98.7  91.2  92.0
## 
## [[208]]
##  [1] 110.5 101.8  89.6  95.3  97.2  93.2  90.4  99.5 107.4 102.3
## 
## [[209]]
##  [1]  98.0 103.9 107.9  98.6 104.6  88.5  97.5  95.8 102.0 103.6
## 
## [[210]]
##  [1]  98.8  92.3  90.7 102.8 113.6  92.1  96.2 103.3  94.5 101.2
## 
## [[211]]
##  [1]  99.5  92.2 108.3 108.5 110.2 112.7  94.9  95.4 102.6 106.3
## 
## [[212]]
##  [1]  96.6  95.8  93.8 114.8  74.9  98.3 100.4  89.4 103.9  80.3
## 
## [[213]]
##  [1] 109.5  83.4  78.0  92.4 101.6  93.5  94.4 103.3  89.4  99.1
## 
## [[214]]
##  [1] 105.0 116.3 104.8 117.1 104.5 100.0  77.4  87.8  96.8 107.1
## 
## [[215]]
##  [1]  96.8 105.4  89.4  97.3 102.2  96.4 101.1  93.3 103.7  99.2
## 
## [[216]]
##  [1]  99.5  80.5  93.3  85.1  83.9  95.1  98.4 102.8 110.9 104.4
## 
## [[217]]
##  [1] 110.1  94.7  96.9 110.9 100.0  83.2  91.5 110.1  93.9 103.3
## 
## [[218]]
##  [1] 100.1  95.0  96.5 103.9 102.1 112.3  98.0  90.8 101.7 107.1
## 
## [[219]]
##  [1] 122.8  95.4  96.7 108.8 112.8  93.4 106.6  94.3  90.4 106.2
## 
## [[220]]
##  [1] 101.1 103.9  94.2 117.9 106.7  96.3 107.0  87.9  98.6 114.0
## 
## [[221]]
##  [1]  98.1 109.1  97.8  77.0  91.2 102.2 114.5  94.1 102.8  90.4
## 
## [[222]]
##  [1]  89.8  92.2 113.7 109.4 105.9 111.2  95.8 107.6 102.1  89.5
## 
## [[223]]
##  [1]  91.7 100.5 102.1  96.8  90.0  79.1 104.3  97.0 105.5  84.5
## 
## [[224]]
##  [1]  87.5  98.9  85.9  80.2 107.8 109.0  89.7  97.3  88.7 103.2
## 
## [[225]]
##  [1]  99.7  91.3  92.3  89.4 104.4 105.7 103.8  91.6  82.1 105.3
## 
## [[226]]
##  [1]  98.2  99.6 110.3  91.1 111.4  95.9  92.9  97.9 103.9  97.9
## 
## [[227]]
##  [1]  91.0  97.2  74.6  94.9 104.6  98.3 106.9 104.9 106.5 106.6
## 
## [[228]]
##  [1]  82.6 100.0 116.3  95.2 104.5 101.4 105.6  97.3  93.5 100.7
## 
## [[229]]
##  [1] 102.1  98.1 100.3 104.1  92.2 111.4 122.0 114.8  95.5  81.8
## 
## [[230]]
##  [1] 100.5 108.8 107.8  87.7  88.9 101.3 106.3 108.7 108.2  90.3
## 
## [[231]]
##  [1]  86.9  79.9 105.0 108.3 103.4  89.4 115.7  96.3 117.8 105.5
## 
## [[232]]
##  [1] 111.9 103.3  99.4  89.9  94.4  99.5 102.8  99.7  98.2 101.8
## 
## [[233]]
##  [1]  94.8  94.6  85.4 108.5 100.5  99.2  92.6  97.5  89.1  89.5
## 
## [[234]]
##  [1]  80.8 109.8 101.3  88.8 111.6 106.2 107.4  97.7  95.8  99.0
## 
## [[235]]
##  [1] 104.0 108.0 115.9  94.9  89.8 101.0 130.2  95.7 111.5  97.6
## 
## [[236]]
##  [1]  95.2  92.9  97.9 116.4 103.0 104.9 108.4 120.7 107.8  85.7
## 
## [[237]]
##  [1]  89.7  84.1  71.5 112.9  95.1 103.9 111.8  94.9  98.7 103.5
## 
## [[238]]
##  [1] 102.3  92.3 107.3 105.5  97.1  87.8 106.3 114.3 113.8 108.7
## 
## [[239]]
##  [1]  95.2  94.7  94.1  95.9 107.1 102.6  81.4  81.4  99.8 101.5
## 
## [[240]]
##  [1]  76.9  91.8 100.3 114.6  79.9  87.4  89.2 101.8 103.3  96.8
## 
## [[241]]
##  [1]  83.9  93.7  94.4  98.0 116.2  93.2 100.8  92.9  87.6 106.4
## 
## [[242]]
##  [1]  89.5 127.4 100.9 100.6  99.3 118.4 106.6  97.5  88.3  89.6
## 
## [[243]]
##  [1]  92.2 112.1  98.1  92.4 107.9 113.5  93.1  95.6 103.5 100.0
## 
## [[244]]
##  [1] 104.1 117.1  99.4  97.2 104.9  99.5 106.3  97.8 104.4  84.4
## 
## [[245]]
##  [1] 100.1  94.8  88.1  95.9 103.7 100.9 106.9 109.4 108.3  96.8
## 
## [[246]]
##  [1]  86.7  97.2 111.7  98.8  83.6 104.9 102.8  96.0 101.7 113.7
## 
## [[247]]
##  [1] 113.0  95.4 100.1  85.5  92.7 120.1 115.0  97.7  93.1  86.3
## 
## [[248]]
##  [1] 121.3 101.1  94.1 110.8  89.0 107.3 114.4  97.9 114.5 106.4
## 
## [[249]]
##  [1]  93.2 105.7  93.0  94.7 107.7  95.2  99.8 110.2  87.9 116.0
## 
## [[250]]
##  [1] 120.4 106.1 104.2  95.0 104.9  95.0 102.9  93.1 107.9 106.9
## 
## [[251]]
##  [1] 112.4 119.8  93.5 109.7  85.7  95.4 109.5  92.6 103.5  91.0
## 
## [[252]]
##  [1]  96.3  99.6  93.9  80.5 102.4 104.7 101.4  95.1 109.0 110.8
## 
## [[253]]
##  [1]  76.3 111.2  82.2  96.6  88.9  93.7 113.2 105.3 104.9  79.2
## 
## [[254]]
##  [1] 102.0 106.3 108.6  90.3 109.4  86.0 117.4  92.0 107.7 103.2
## 
## [[255]]
##  [1]  89.4 111.4 100.3 108.2 102.2 108.7 100.2 111.2  96.5 105.3
## 
## [[256]]
##  [1] 103.8 108.4  93.8 101.8  94.2 109.1  93.6 117.3 107.9  99.9
## 
## [[257]]
##  [1] 112.1  99.2 105.6 105.3 104.2  94.0  87.5  83.2  95.4 106.8
## 
## [[258]]
##  [1]  97.6  88.0 121.6 107.0 119.5 112.1  93.9  95.9  85.6 107.4
## 
## [[259]]
##  [1] 116.2  90.8  88.0 108.8  84.8 119.2 105.7  82.9 103.5 101.1
## 
## [[260]]
##  [1]  75.3  99.6  94.1  91.1 102.4 108.5 117.3  73.7 107.4  90.5
## 
## [[261]]
##  [1] 111.6 103.5 114.4  85.2 104.9 103.0 110.5  97.7 111.4  95.6
## 
## [[262]]
##  [1]  95.7 100.3  89.3  95.4 111.1 116.5 111.1  95.8 103.2 101.0
## 
## [[263]]
##  [1]  87.4 102.6  91.8  89.4 107.3  92.9  98.6  90.3 100.6 104.9
## 
## [[264]]
##  [1] 105.0  89.2 112.6 114.9 103.7 101.6 100.8 102.6 103.8 101.4
## 
## [[265]]
##  [1] 106.5  96.6 111.3  99.6  82.4  99.0 104.5 112.3 100.6  80.6
## 
## [[266]]
##  [1] 100.0  88.0  90.2  89.7  92.0 111.4  91.7  95.6 101.8 108.9
## 
## [[267]]
##  [1]  93.3  91.7  94.8  88.3 109.2  78.2  94.7  85.6  80.4 100.3
## 
## [[268]]
##  [1] 115.4 116.3  94.4  93.0  94.6 107.1  74.4 102.5  95.9  92.6
## 
## [[269]]
##  [1]  79.9  97.9  83.5  99.8  91.1 100.5 104.6  95.0  89.8  93.9
## 
## [[270]]
##  [1]  93.3  85.1  92.2  98.1  97.8 103.3 112.9 103.3 114.8  93.5
## 
## [[271]]
##  [1] 113.5 105.9  88.1 104.0  87.6 109.5  94.6  97.6  93.2  91.5
## 
## [[272]]
##  [1] 117.0 109.9 106.8 100.7 107.4 106.6 116.0 108.5  97.9  97.9
## 
## [[273]]
##  [1]  95.3  96.4  97.6 112.2  76.7  93.0  98.7  87.2 116.2  97.7
## 
## [[274]]
##  [1]  88.8  91.1 108.7 118.7  98.8 101.1  90.5 113.2 107.2  76.7
## 
## [[275]]
##  [1]  93.5  97.7  88.9  97.3  88.7 103.6 103.4 108.1 104.2 115.9
## 
## [[276]]
##  [1]  96.1  78.5 100.3 106.5  96.0 114.0 110.9 105.4 100.7  94.5
## 
## [[277]]
##  [1]  98.2 104.7 109.7  97.0  92.7 124.8 105.2  91.0 109.3 100.6
## 
## [[278]]
##  [1] 108.3 100.5  99.4 100.9 104.1  93.9  93.4  98.2 101.7  96.8
## 
## [[279]]
##  [1] 103.2  89.0  85.7 118.9 104.0  96.0  97.2 107.9  97.9 101.9
## 
## [[280]]
##  [1]  97.4  95.0 106.0 101.4 113.0  88.7  98.6  97.9  89.3 110.0
## 
## [[281]]
##  [1]  98.9  86.1  94.1  88.9 110.4 125.4  93.3  99.1 102.8 127.1
## 
## [[282]]
##  [1]  76.7  94.9  88.0  97.7  97.2  92.7 118.3 102.6 123.9 108.2
## 
## [[283]]
##  [1]  87.3  92.5 102.7  94.2 103.5 107.3 104.2  98.7  93.6  87.1
## 
## [[284]]
##  [1] 103.4 109.2  99.2 107.5 122.3 119.3  95.1 105.5  93.0 106.9
## 
## [[285]]
##  [1]  99.4 102.8  91.4 112.1  99.2  95.5  99.2 100.8 116.4  88.9
## 
## [[286]]
##  [1] 124.6  92.3 101.7  79.4  93.5 107.3 105.1 104.1  95.3  81.6
## 
## [[287]]
##  [1]  89.3  97.7 106.2 108.4  97.0  98.5  98.4 100.6 115.4  92.7
## 
## [[288]]
##  [1]  98.0 100.8  86.6  90.8 102.0 104.3 111.4  95.3 114.5  91.4
## 
## [[289]]
##  [1]  84.0  80.5 111.0 103.0  98.7  97.1 115.9 112.0  90.0  86.1
## 
## [[290]]
##  [1] 110.9 105.6  94.9 104.0  79.8  93.3 104.4  99.3  87.2 110.2
## 
## [[291]]
##  [1] 111.6  90.6  98.1 107.3 108.6  94.7  91.2 103.5  80.8  90.5
## 
## [[292]]
##  [1] 107.7  83.0  88.0  97.6  97.0  82.5 105.1  89.8  98.4  98.0
## 
## [[293]]
##  [1] 107.0  99.3  98.7 116.5 103.7 106.2 104.7 105.7 113.4  99.4
## 
## [[294]]
##  [1] 102.4 119.7  94.7 112.9  93.9 117.1  93.3  91.9 110.4 109.6
## 
## [[295]]
##  [1] 105.5 102.7 102.4 120.5  85.7  90.1  87.2 109.6  97.5  98.7
## 
## [[296]]
##  [1] 117.8  94.2 120.2  85.9 113.2 103.2  96.1  98.3 113.4 117.0
## 
## [[297]]
##  [1]  83.2 134.2 125.8  94.7  99.4  93.4  99.1 107.4 101.0 101.9
## 
## [[298]]
##  [1] 114.8  78.0  95.1 101.4  92.2 110.6  95.5  95.7 111.9 108.3
## 
## [[299]]
##  [1]  98.5  96.7  85.5  93.0 126.0  99.6 109.1  98.2 106.1  99.5
## 
## [[300]]
##  [1] 113.6  95.0  82.9 109.0  97.6 114.6 101.2 114.5 103.5  96.5
## 
## [[301]]
##  [1] 107.3  95.4 116.8 101.5  79.7  95.3  83.7  78.2 100.6 106.5
## 
## [[302]]
##  [1]  92.4  86.7  94.0  84.5 107.0 105.7  84.0  93.8 110.5  98.3
## 
## [[303]]
##  [1] 100.1 104.2 106.3 112.1 107.7  86.2  96.4 103.0  98.9  78.2
## 
## [[304]]
##  [1]  92.4 110.1 101.6  85.3 102.2  98.4 106.7 121.1  84.8  94.9
## 
## [[305]]
##  [1]  98.6  78.6  99.7  94.1 122.4  70.8 114.9 110.1 107.4 101.5
## 
## [[306]]
##  [1]  92.9 111.1  91.1 106.9 104.0 110.8  94.0  94.2 103.0 103.1
## 
## [[307]]
##  [1] 113.7 104.9 101.4 108.4  94.6 110.9  89.8 103.4  82.9 102.5
## 
## [[308]]
##  [1]  84.3  97.7  82.4  93.6  92.2 105.5  94.2  92.3 112.2 116.7
## 
## [[309]]
##  [1] 110.9  85.1 112.8  87.7  99.3 107.3  97.9  98.5 101.3 104.3
## 
## [[310]]
##  [1] 104.1  82.7  98.2 102.9 105.9  96.8  93.0  86.3  92.7  98.8
## 
## [[311]]
##  [1]  93.6 105.9 103.7  83.9 103.2 105.4  97.4  99.7  95.7  97.1
## 
## [[312]]
##  [1]  89.9 104.3  87.8  94.1  90.9  91.3  96.3  95.1  93.0  97.5
## 
## [[313]]
##  [1]  84.2 101.1 106.3  87.2  85.9 122.3 102.4 100.5  98.0 104.9
## 
## [[314]]
##  [1] 100.4  94.5  95.7  96.6  96.8  92.5 110.7 100.9  92.3 105.9
## 
## [[315]]
##  [1] 103.5  98.6 104.0  90.9  98.0  90.0  88.2  96.7 101.7  90.9
## 
## [[316]]
##  [1]  98.2  81.7  95.5 111.7  88.5  88.1  97.8 105.3 112.4 126.5
## 
## [[317]]
##  [1] 108.0 106.7 120.3  97.0  97.9 102.5  85.8  81.6 118.1  94.3
## 
## [[318]]
##  [1]  95.4  90.1 101.4 105.9  97.7 100.1 109.5  99.9  94.4  99.4
## 
## [[319]]
##  [1]  91.6 101.0  91.0 113.9  75.1 104.0  95.1 119.9  97.7 104.8
## 
## [[320]]
##  [1] 104 102 105 120 109 102 118 106 107 112
## 
## [[321]]
##  [1] 101.6 107.3  97.3 101.2 100.4  93.6 120.3  94.4  96.4 113.2
## 
## [[322]]
##  [1]  99.8 111.7  93.9  99.9  97.5  90.3  97.0  93.4 108.6  97.1
## 
## [[323]]
##  [1]  99.2  91.7 102.2  83.9  70.5 118.8 107.6 106.3  77.6 106.8
## 
## [[324]]
##  [1] 105.2  99.2 108.3 111.2  98.8 119.5 109.9 112.2  96.8  98.7
## 
## [[325]]
##  [1]  90.8 104.1 102.6 100.9  93.2  97.7 119.9  90.7  95.9  86.0
## 
## [[326]]
##  [1]  87.6  97.1  96.1  93.8  92.3  98.0 111.3  96.4  87.2  89.3
## 
## [[327]]
##  [1]  80.0  82.9  92.5  90.2  88.5 119.9 117.5 125.6 107.8  98.4
## 
## [[328]]
##  [1]  89.6  89.0  95.0 112.8 106.7 108.9  98.1  84.5 103.3  97.9
## 
## [[329]]
##  [1]  97.0 121.8 108.7  97.7  81.0  97.1 109.9 103.7 102.7 110.5
## 
## [[330]]
##  [1]  98.3  96.5  97.5 107.3  97.3 107.6  87.7  87.3 101.3 107.6
## 
## [[331]]
##  [1]  95.9  94.2  71.6 103.7  91.0 104.0 114.3  95.0 107.0  98.5
## 
## [[332]]
##  [1] 103.7  88.4 104.2 113.0 118.0  88.1 105.3  94.9 105.2  98.2
## 
## [[333]]
##  [1]  97.5 106.8 107.5 102.8 104.6 103.8 102.8 100.9 109.2 107.1
## 
## [[334]]
##  [1] 107.9 111.1 105.5  98.5  89.1  95.1  91.3  97.0  94.7  98.0
## 
## [[335]]
##  [1]  89.8  93.8 103.6 102.1  96.0 110.1  83.6 104.8 115.7  95.9
## 
## [[336]]
##  [1] 103.9  94.4  99.8 108.2  90.9  94.5 105.3 104.2 108.1 112.5
## 
## [[337]]
##  [1] 107.7  89.2 101.5  96.0  99.9 109.2 102.8 101.6  98.8 104.0
## 
## [[338]]
##  [1]  88.2  95.8 116.2 106.2  90.4  87.7  90.4 105.8 104.3  94.3
## 
## [[339]]
##  [1]  96.3 109.8  96.9  99.4 103.5  98.2  92.6  95.9  89.2 104.7
## 
## [[340]]
##  [1] 113.3 102.4 108.1  93.5  98.6  98.6  85.7 100.9 104.8 106.8
## 
## [[341]]
##  [1] 113.2  85.3 106.2 107.2  97.9 106.0  85.9 102.1  68.7 103.1
## 
## [[342]]
##  [1] 116.0 115.4  73.4 105.4  96.5  99.7  77.8 103.9  94.7 103.7
## 
## [[343]]
##  [1]  98.1  89.7 103.3 106.0 100.5 105.7  95.4 112.8  96.4  94.2
## 
## [[344]]
##  [1] 110.4 111.1 106.8 102.2 115.9  89.9 111.4 117.1 100.5 105.9
## 
## [[345]]
##  [1] 106.1 111.9  91.4 109.0  82.9 120.8  94.3  96.8 102.6  87.5
## 
## [[346]]
##  [1]  97.4 100.6  96.6 120.3  82.1  98.9 111.8  91.6  98.6 119.4
## 
## [[347]]
##  [1]  81.3  92.0  88.0 106.3  91.3 104.7  93.5  98.5 108.6 101.4
## 
## [[348]]
##  [1]  80.6  94.6 107.1 118.6  88.9  97.7  99.2  92.7  86.2 118.4
## 
## [[349]]
##  [1] 114.8  85.9  81.2  97.2 104.3  98.7 111.3  97.5  88.3 115.2
## 
## [[350]]
##  [1]  97.7  97.2  97.4 100.6  76.8 106.8 107.2 106.3  95.9 101.0
## 
## [[351]]
##  [1]  85.7 103.6  91.8 113.2  90.7  79.4 101.7  83.7  90.7 108.0
## 
## [[352]]
##  [1] 118.7  97.4 109.7  86.2 117.3  99.9  92.2 104.0  91.9 100.5
## 
## [[353]]
##  [1] 101.0 111.7  94.3  96.2 101.2 109.0 119.0 115.8 109.6  81.0
## 
## [[354]]
##  [1] 109.5 107.5  93.0  94.4  86.3  99.9 100.9  82.5  84.2 101.7
## 
## [[355]]
##  [1]  89.7  97.0 110.1  95.7 101.3 106.2  88.8 112.4 109.2 112.7
## 
## [[356]]
##  [1]  95.7  85.4 105.1 106.2 125.4 117.2  95.4  89.9 106.2 119.9
## 
## [[357]]
##  [1]  88.2  92.2 117.5 118.4 101.9  83.8  94.6 111.7 121.5  99.8
## 
## [[358]]
##  [1]  93.7 103.1 101.4  90.9 105.9 113.9 100.1 106.3 102.5 104.6
## 
## [[359]]
##  [1]  97.9 112.0 102.3  95.0 106.3 109.6  99.3  73.2 116.4  92.5
## 
## [[360]]
##  [1]  96.5 116.2  81.0  88.9  92.5  86.9 111.0 112.6 105.0  95.6
## 
## [[361]]
##  [1]  95.8  94.3  94.8 104.8 109.1  95.4 103.2  76.1 100.8  91.2
## 
## [[362]]
##  [1] 111.0 111.9  78.0 109.2  94.3  98.4 109.0 106.9  91.8 103.2
## 
## [[363]]
##  [1]  95.3 112.5  84.3 108.2 113.9  73.9 106.5  96.4 101.1  97.3
## 
## [[364]]
##  [1] 106.9 109.3 105.9  98.9  95.8  98.6  97.7 102.1  91.8 105.8
## 
## [[365]]
##  [1]  90.0  85.2 102.6 104.2 110.3 107.3 102.2 106.9  90.2  88.6
## 
## [[366]]
##  [1]  87.8 100.4 106.6 109.1 114.8 103.3  98.7  93.4 102.5  99.4
## 
## [[367]]
##  [1]  96.7  93.2  89.9  90.2 114.7 102.5  95.7  84.2 101.9  95.0
## 
## [[368]]
##  [1]  99.1  97.9 107.8  99.3  98.2 123.7 110.9 101.3  92.7 111.8
## 
## [[369]]
##  [1]  90.7  99.5 108.5  95.9  96.3 104.4 101.4  97.5  97.9 102.5
## 
## [[370]]
##  [1] 104.7 112.9  95.8 113.2  85.3  93.5  86.5 103.1 104.2  86.3
## 
## [[371]]
##  [1] 100.5  90.9 104.9  84.5 108.6  99.6  89.6  99.2  97.3  96.4
## 
## [[372]]
##  [1]  85.0  94.1  98.3  85.2 103.0 113.7 107.8  92.0  93.4  95.3
## 
## [[373]]
##  [1] 106.1  99.6  90.5  84.9 105.6  89.6 105.0 100.7 107.2 110.9
## 
## [[374]]
##  [1]  85.8 110.2 106.9  96.9  99.8 104.9 106.6  82.9 114.6  85.9
## 
## [[375]]
##  [1]  79.2 109.5  84.9  97.8  86.5  82.1  95.6 106.5 103.2  93.6
## 
## [[376]]
##  [1]  99.8  99.0  99.8  95.5 103.6  89.2 103.8  96.6  96.6 107.1
## 
## [[377]]
##  [1]  95.7  90.1  88.0 106.7  76.7  95.8 101.8  86.3 100.1 106.7
## 
## [[378]]
##  [1]  81.8  91.1 117.6  93.5  90.3  91.4  95.7 101.9  93.0 102.0
## 
## [[379]]
##  [1] 107.0 103.4 107.5  92.0  98.8 106.6 100.5 102.1 100.5 101.8
## 
## [[380]]
##  [1]  99.8  89.0 101.7  95.4 114.4  94.7 101.5  80.3  93.4  91.7
## 
## [[381]]
##  [1] 112.3  98.5 101.4 103.0  94.7 103.0 115.1 106.2 107.1  91.7
## 
## [[382]]
##  [1] 101.8 102.9  93.4 101.2 119.7  90.3 105.5  89.3 103.5  89.6
## 
## [[383]]
##  [1] 105.9  87.3 100.2 113.4  97.8  98.9 114.0 120.4 124.8  96.1
## 
## [[384]]
##  [1]  89.4 106.5 104.4 112.9 101.5 101.6 115.1 101.6 106.8 104.8
## 
## [[385]]
##  [1]  99.6  94.7  96.6  80.5 112.8  84.0  94.1  96.3 112.1 100.6
## 
## [[386]]
##  [1] 109.4  97.1 116.7 104.9 105.5 108.8  85.2  99.9 102.1  92.3
## 
## [[387]]
##  [1] 100.1  92.8 102.2  82.2 102.8  93.6 109.4  80.3 100.4  97.8
## 
## [[388]]
##  [1] 109.4  84.2  94.5 107.1 106.1 103.6 102.9  83.3 108.5 102.2
## 
## [[389]]
##  [1]  81.9  98.3 109.5 107.0  93.7 109.1  96.0 103.8 109.3 103.9
## 
## [[390]]
##  [1]  93.5 108.2 114.8  90.7  98.2 110.0  91.5  82.8  95.1 110.7
## 
## [[391]]
##  [1]  86.4  97.5 109.6 100.5 105.7 116.2 109.0 105.9 104.9  88.4
## 
## [[392]]
##  [1] 108.4 105.4 104.0 100.6  87.3 101.5 112.5  93.9  82.0 118.4
## 
## [[393]]
##  [1]  94.4 111.4 106.2 116.6  99.6  97.0 117.3 121.6 103.2 101.7
## 
## [[394]]
##  [1] 107.4  93.3 105.0  90.1  97.0 107.9  92.4 108.5 105.0 114.3
## 
## [[395]]
##  [1] 121.7  94.2 103.9 115.6 102.0  93.5  90.0 114.0 126.0  89.5
## 
## [[396]]
##  [1] 101.1  84.3 100.7  96.9  99.9 128.9  86.0 104.3 118.3  93.9
## 
## [[397]]
##  [1]  91.8 100.5 113.0  96.6  89.7 100.7  79.8  85.2 110.9 104.6
## 
## [[398]]
##  [1]  78.3 106.2  77.0  95.5 103.0  85.7 112.7 112.1  93.3 111.2
## 
## [[399]]
##  [1] 102.0 106.5 106.7  87.2  79.7 122.1 102.3 103.8  88.1 111.3
## 
## [[400]]
##  [1] 118.4 115.3  79.8  89.6 101.0 107.0  94.6  91.4 102.3  90.6
## 
## [[401]]
##  [1] 120.4  81.7 105.1  80.0  95.1 114.8 111.2  86.0  85.2 100.6
## 
## [[402]]
##  [1]  90.5 104.1  90.2  83.9  95.7  87.8 110.9  96.7  99.6 113.8
## 
## [[403]]
##  [1] 118.6  99.5 103.3 113.1  98.3  89.6 109.9  84.8  97.5  96.0
## 
## [[404]]
##  [1]  94.8  72.5  94.1 112.7  95.3  93.8  93.3  91.3 101.5 105.9
## 
## [[405]]
##  [1] 114.5  84.3 104.0  98.5 102.9  89.7 100.5  88.5 106.6  90.5
## 
## [[406]]
##  [1] 100.6  78.7 103.3 111.1 107.7 110.5  86.4  98.3  99.3 107.2
## 
## [[407]]
##  [1]  98.3  98.0 116.8 110.9  82.4  96.2  90.1 129.7  95.1 111.5
## 
## [[408]]
##  [1] 101.0 101.1 105.0  98.6 108.3 105.6  83.1  94.4  94.8  94.9
## 
## [[409]]
##  [1] 110.7 114.9  90.8 105.4  88.3  94.4 103.0  98.1  93.2  87.4
## 
## [[410]]
##  [1]  96.9 100.5 105.6  91.2 105.9  88.4  94.5 104.5  93.1  92.2
## 
## [[411]]
##  [1]  99.5 100.4 109.3  97.7  83.0  93.4  93.7  90.7 103.2 125.0
## 
## [[412]]
##  [1] 107.9  98.5 105.0 114.4  96.9 106.6 105.6  98.8 100.6 106.5
## 
## [[413]]
##  [1]  99.7  96.6  94.1 102.9  99.4  96.3 101.8  92.3  92.0 113.7
## 
## [[414]]
##  [1]  91.2 103.2  90.3  97.7 103.9  89.9 106.0 102.2  96.8 102.5
## 
## [[415]]
##  [1] 100.8  91.6  86.0 101.1  90.0  99.6  83.5  90.7 102.7 110.5
## 
## [[416]]
##  [1] 101.7  90.1  95.8 110.9 105.2 107.9 110.0 103.8 111.1  90.3
## 
## [[417]]
##  [1] 103.0  96.6 102.0 113.3 105.0  93.7  96.5  90.5  99.1  95.0
## 
## [[418]]
##  [1] 107.9  95.1 107.1 107.2  95.6 114.3 100.3  93.5 100.7  90.1
## 
## [[419]]
##  [1] 106.5  91.0 112.9  79.3  88.9  96.6  93.0 113.5  99.4 103.5
## 
## [[420]]
##  [1] 107.1 101.5 109.6 104.4 107.0  85.1  88.7  77.7  97.5 114.3
## 
## [[421]]
##  [1]  90.2 103.2 104.4 102.4  97.2  93.8  93.6 100.2 113.0  92.1
## 
## [[422]]
##  [1]  98.8 101.0 107.9  97.7 106.4  85.0 107.2 101.0  89.0  76.7
## 
## [[423]]
##  [1]  96.3 106.7 103.2  96.4 100.5 101.6  92.5 100.5 101.1  92.8
## 
## [[424]]
##  [1] 102.0 103.1 105.3 107.1 104.1 103.0  99.0 104.5  87.3 106.5
## 
## [[425]]
##  [1]  94.7 123.4  94.0  71.1 113.7  94.0 105.9 102.3 111.0  91.0
## 
## [[426]]
##  [1]  88.1 110.6  90.4  84.7 107.8  99.3 122.8 103.4  96.5  93.7
## 
## [[427]]
##  [1] 116.8  87.9 106.2 105.6  94.3 115.4  92.5  99.8 103.9 123.2
## 
## [[428]]
##  [1] 106.2 117.3  92.7  82.5 108.9  83.7  86.6 106.1  99.4 108.5
## 
## [[429]]
##  [1] 114.3 109.1 103.8 105.5 101.4 117.1 100.5 108.1  90.6 100.4
## 
## [[430]]
##  [1]  80.0 101.4  85.1  98.7  97.6 109.7  93.6  93.4  80.3 106.2
## 
## [[431]]
##  [1] 110.9  97.7 114.8  95.9  90.0 102.3 106.9  85.1  83.6 100.5
## 
## [[432]]
##  [1] 104.8  76.6  82.9 103.1 108.9  96.2 112.0  93.9  98.3 113.5
## 
## [[433]]
##  [1]  99.2 100.3  91.0 100.7  93.6  82.0  90.3  97.6 101.6 110.7
## 
## [[434]]
##  [1] 100.4  98.7 111.1 124.2  99.1 111.8 104.9  99.2  80.8  90.3
## 
## [[435]]
##  [1]  94.4  88.9  88.4  95.9 109.5  90.8 101.2  98.0 107.9 100.4
## 
## [[436]]
##  [1]  98.3  94.2 108.9 111.4 100.2 132.7 100.0 129.2  98.7  84.3
## 
## [[437]]
##  [1]  85.8  91.3 114.8 117.0 104.0 103.1  94.6  93.2  92.8  91.3
## 
## [[438]]
##  [1]  94.6  93.8 105.3 107.7 116.0  75.5 105.0  96.8  97.3  83.6
## 
## [[439]]
##  [1]  99.7  92.2 103.6  88.9 134.5  92.2  97.2  87.7  96.7 121.3
## 
## [[440]]
##  [1]  96.1 106.1  90.6 115.4 104.7  92.8 102.3  96.1 105.1  91.9
## 
## [[441]]
##  [1] 105 116 113 103 103 104 109 104 106 106
## 
## [[442]]
##  [1] 102.3 107.2 100.6 110.1  95.7 101.9 100.3  89.3 112.0  88.4
## 
## [[443]]
##  [1] 113.1  89.3  90.2 108.6  99.2  81.5 115.0  75.1  93.1  84.8
## 
## [[444]]
##  [1]  94.3 100.9  96.7  94.2  98.4 102.7  91.4  79.3  90.7  81.0
## 
## [[445]]
##  [1] 106.4 118.7  88.5  91.1  91.2 107.9 100.3 104.9 107.7 102.5
## 
## [[446]]
##  [1] 104.5  88.4  99.4  93.8  87.0  88.3 109.4  87.0  96.0 109.8
## 
## [[447]]
##  [1] 103.3 106.5 103.3  98.5  78.0  93.9  86.2  96.2 120.5 101.4
## 
## [[448]]
##  [1]  92.8 108.9 104.9  99.2  97.7  98.5  99.3 106.2 101.3  93.7
## 
## [[449]]
##  [1] 108.3  93.0 113.1  90.2 107.5 112.6 112.2  98.9 106.9  78.6
## 
## [[450]]
##  [1] 104.4  98.9 106.0 101.1 112.9  98.3 107.3  98.9 106.6  87.7
## 
## [[451]]
##  [1] 106.1  96.1 103.9  91.2 105.4 129.9 115.4 109.8  93.8 103.2
## 
## [[452]]
##  [1]  98.4  80.1  97.6  96.8  99.1  94.7 106.5 119.2 111.6 106.6
## 
## [[453]]
##  [1] 100.6 100.8 111.6 112.8  94.1 109.5  88.2  88.1 116.0 100.4
## 
## [[454]]
##  [1] 100.3 109.8  98.0  91.5 101.4  82.9  95.3  98.4  85.6 101.8
## 
## [[455]]
##  [1]  92.7 111.1  97.2  89.1 102.4  99.5 100.4 102.2  96.1  96.7
## 
## [[456]]
##  [1] 106.5 116.3  80.7  98.6 109.8  88.2 111.7  96.2 107.1 114.7
## 
## [[457]]
##  [1] 109.0 112.1  77.9  87.3 105.8  90.9  94.5 113.8 101.2 100.5
## 
## [[458]]
##  [1]  97.5  84.0  81.2  97.8 103.5  86.8  81.9 112.8 105.1 104.8
## 
## [[459]]
##  [1] 109.2 105.5  89.4 112.5  87.2  95.2 103.3 102.8 105.9 108.8
## 
## [[460]]
##  [1]  91.9  87.1  88.3 105.7  95.4 104.1 111.8  93.3 109.2  93.6
## 
## [[461]]
##  [1] 106.2 100.3  91.5 109.5 107.2  91.3 100.4 125.2  92.5  98.3
## 
## [[462]]
##  [1] 114.0  88.9 123.8  93.3  94.8  99.6 110.7 132.4 104.8 106.2
## 
## [[463]]
##  [1]  86.3 101.4  76.4  97.4 114.6  98.0  99.4 100.4  98.8 101.0
## 
## [[464]]
##  [1]  84.9  95.2  96.6 105.7 102.1  92.4 108.5 112.3  87.2 101.8
## 
## [[465]]
##  [1]  92.5  93.9 104.2 108.4 103.8  94.7 111.3 110.3  90.1 103.1
## 
## [[466]]
##  [1]  88.4 114.7 102.7 110.7 103.9  98.9 107.5  89.0  85.7  93.7
## 
## [[467]]
##  [1] 102.6  95.9  95.3 109.2  95.0 109.7  92.3  97.4  91.7  95.7
## 
## [[468]]
##  [1]  88.4 104.5 111.8 102.8 117.1  83.6  92.5 105.2 106.3 103.3
## 
## [[469]]
##  [1] 117.5 116.8  85.4  95.8  85.7  89.7 102.5 103.5  92.2 103.0
## 
## [[470]]
##  [1]  92.7 102.5 101.1  97.2  90.4  95.3 104.9  95.1  96.7  89.3
## 
## [[471]]
##  [1]  95.7  99.8  92.7  96.2  89.0 107.5 122.1  95.7 104.7 115.8
## 
## [[472]]
##  [1]  96.2  96.1 106.5  90.5  98.3  94.5  90.3 104.2  98.6 121.7
## 
## [[473]]
##  [1]  71.6 106.5  91.8  97.1  89.1 105.8 113.6 104.9  90.9 116.1
## 
## [[474]]
##  [1]  98.4 101.8  99.5  97.8 100.8  89.7 111.5 106.5 100.8 109.5
## 
## [[475]]
##  [1]  87.8 110.9 102.1 105.0  95.4  92.2  94.5 110.4 110.9 115.5
## 
## [[476]]
##  [1]  99.4  92.4 114.7  84.5  98.4 106.0  88.4  84.4 104.9 116.2
## 
## [[477]]
##  [1]  92.9  93.1  90.6 114.8  92.9  91.6  92.0  94.1  94.0 106.1
## 
## [[478]]
##  [1] 103.0 104.7  93.7 107.2  69.6 111.3 102.0  95.9 104.8  87.8
## 
## [[479]]
##  [1]  93.7 101.1  84.4  99.6  99.6  97.2  87.1 111.7  85.1  85.2
## 
## [[480]]
##  [1]  94.2 115.5 101.1 102.6  97.8 102.7 106.3 107.1 113.7  92.2
## 
## [[481]]
##  [1]  98.4 104.1 108.3  96.7 106.5  94.5  96.6 110.1  81.2 102.2
## 
## [[482]]
##  [1] 109.3  96.6 106.2  92.9 101.7 100.1  99.7  87.2  98.4  91.9
## 
## [[483]]
##  [1]  96.4 110.2  94.3  99.7 101.0  98.1 108.1  99.6 101.5  91.1
## 
## [[484]]
##  [1]  96.2  93.5 104.7 111.5  95.4  77.8  91.5  90.7 111.8 101.4
## 
## [[485]]
##  [1] 115.6 104.0  84.5 104.9  92.5 100.0  99.0  98.6  96.7 119.2
## 
## [[486]]
##  [1] 115.1  91.1 102.0 111.5 111.0  91.0 114.1  93.0 101.3 101.7
## 
## [[487]]
##  [1]  80.8  98.7  79.0  80.3 103.2 103.4 109.7 103.8  93.3  92.0
## 
## [[488]]
##  [1] 108.0 114.5 108.0 102.2  99.3 116.3  75.1 109.9  98.3  88.7
## 
## [[489]]
##  [1] 108.4  90.2 103.4 101.9 101.4  81.5 101.6  95.1  93.0  88.2
## 
## [[490]]
##  [1]  88.6  91.5 112.5 107.0 102.7 117.2 116.1 109.0  88.2 114.3
## 
## [[491]]
##  [1]  98.0  97.6 102.4 100.6  95.1 106.8  95.2  94.4  97.5  92.4
## 
## [[492]]
##  [1] 101.5  99.0  97.0 104.6  81.8 102.5 109.0 108.8 122.3  93.6
## 
## [[493]]
##  [1]  90.2 103.3  83.1 112.1  89.5 104.4  96.6  76.2 102.6  89.0
## 
## [[494]]
##  [1] 109.2  75.5  98.7  89.5 111.3  92.7 109.4  95.3 101.3 114.6
## 
## [[495]]
##  [1]  93.2 118.2 109.9 112.8  77.5  98.3  85.3 107.6 112.2  93.8
## 
## [[496]]
##  [1]  94.9  83.8 107.9 114.6  83.0  81.9 111.4 113.5 103.7 102.4
## 
## [[497]]
##  [1]  93.8 103.4  95.5 120.4  95.5  68.6 105.0  87.4 108.2  84.5
## 
## [[498]]
##  [1]  97.4 103.9  98.0  80.5  85.7  91.5 116.2  98.7 112.8 101.8
## 
## [[499]]
##  [1]  95.1 111.3  88.5 114.8 109.2 103.4 105.7 102.0  95.5  96.6
## 
## [[500]]
##  [1]  94.0 112.4 106.0  98.9  88.6 103.2  89.9  91.5 120.4  86.0
## 
## [[501]]
##  [1]  91.2  94.2  94.0  88.7  98.1  89.6 113.4 101.2 108.6  85.9
## 
## [[502]]
##  [1]  99.9 105.5 101.0 100.2  89.7  93.7  96.0  92.0 107.6 117.6
## 
## [[503]]
##  [1] 113.2 104.2  98.8 105.8  92.1 102.6 101.7  76.5 119.0  86.7
## 
## [[504]]
##  [1]  73.7 100.0 101.1  99.9 101.4  88.2 105.9 113.8  91.6 103.1
## 
## [[505]]
##  [1]  97.3  99.4 109.8 102.8 119.3  96.7 114.8  95.4  97.7  96.7
## 
## [[506]]
##  [1] 102.9 104.7 101.5 106.0  92.2  97.6 106.5 110.4 103.4 107.1
## 
## [[507]]
##  [1] 108.4 106.1  97.8  98.4 106.2  95.4  98.7  99.1  84.1 103.3
## 
## [[508]]
##  [1] 105.7  99.4 117.9  98.2 105.8 105.3 107.8 104.2  98.1 105.6
## 
## [[509]]
##  [1] 102.5 102.4 107.2 107.7  99.9  96.1 113.3 100.5  96.2  90.5
## 
## [[510]]
##  [1] 102.7 103.9  88.6  86.5 101.8  91.8 113.5  88.9  84.5  99.3
## 
## [[511]]
##  [1] 104.7 101.6  98.8 103.8  92.3 102.3  91.7  92.0 101.1 104.1
## 
## [[512]]
##  [1]  91.3  84.5  89.7  80.0 101.3 105.8 118.0  91.1  95.3  98.9
## 
## [[513]]
##  [1] 102.4  92.0 109.3  96.2 109.9  83.7  98.4 103.5  95.1  95.2
## 
## [[514]]
##  [1]  93.6 101.0 112.6  89.8  99.0  95.2 114.1 119.3 105.0 100.7
## 
## [[515]]
##  [1] 113.7  95.4  99.4 110.5 101.1  95.2 101.8  95.5 118.7  96.2
## 
## [[516]]
##  [1] 109.4 100.0 113.3 109.3  93.5 102.8  98.5 105.0  99.5 104.7
## 
## [[517]]
##  [1]  98.8 109.6 103.1  86.8  99.8  96.6 111.2  88.5  79.6 104.7
## 
## [[518]]
##  [1] 109.4 104.5 113.5 109.0  90.7 109.3  94.1 111.1 109.9  99.5
## 
## [[519]]
##  [1] 110.7  97.3 110.1  76.9  89.5 101.5  94.9  73.3  91.6 116.1
## 
## [[520]]
##  [1]  87.9 101.7  95.1 100.2  98.2  98.6  98.8  78.2 100.0 101.3
## 
## [[521]]
##  [1] 104.1 113.7 100.4 102.7  85.7 101.0  84.4 120.0  96.4 103.5
## 
## [[522]]
##  [1] 104.4  86.9 104.7  89.3 104.6  93.8  93.2 104.1 103.7  97.5
## 
## [[523]]
##  [1]  92.6 101.9  99.5 109.6  93.7  98.8 122.7  87.2 103.2 104.1
## 
## [[524]]
##  [1]  95.5  92.9  85.4  85.8  97.4 112.5 100.5 115.5  94.0 105.8
## 
## [[525]]
##  [1] 101.2 103.6 102.1 107.8  99.9 109.7 104.9  99.9  98.9  87.2
## 
## [[526]]
##  [1]  93.5  97.4 109.4 107.9  91.9  95.2 117.4  85.9 101.8 102.8
## 
## [[527]]
##  [1]  95.0  86.3  96.1 126.9  98.9  97.8 101.8  88.3 107.5 107.2
## 
## [[528]]
##  [1]  96.5 100.6  94.9 106.9  83.4  97.8 106.2 116.9  90.9  88.8
## 
## [[529]]
##  [1]  98.9  99.4 107.6  98.9  94.3 118.9  96.7 108.8 107.4  95.6
## 
## [[530]]
##  [1] 116.6  88.4  90.6 111.7  84.4 106.4 102.0 107.4 107.8  93.3
## 
## [[531]]
##  [1]  93.2 108.1 108.9  88.9  87.7  89.3  99.9  99.8 123.3 105.4
## 
## [[532]]
##  [1]  98.5  94.7  94.6  93.8  89.1 101.7  68.1  88.3 109.9 101.5
## 
## [[533]]
##  [1] 105.5  94.1 114.1  97.0 105.9 100.1 104.8  95.6 112.4  94.8
## 
## [[534]]
##  [1] 128.6  98.4 101.3  93.8 107.3 101.9 106.4 107.1  92.3 108.3
## 
## [[535]]
##  [1]  88.1 101.5 109.1  84.1  95.6  96.0  79.4  98.0 114.1  85.9
## 
## [[536]]
##  [1]  89.0  96.1  99.4 101.0 101.9  97.2 123.6  95.5  86.6  84.4
## 
## [[537]]
##  [1]  98.0  94.6 110.5  98.1 100.8  83.8  97.6  97.3  86.0  90.9
## 
## [[538]]
##  [1]  91.3 108.3 105.6 106.9 114.1  96.8 111.8  97.3 111.6  87.5
## 
## [[539]]
##  [1]  94.0 109.1 116.6  99.6  96.7 106.3  98.8 100.1 102.5 110.9
## 
## [[540]]
##  [1]  89.3  95.6 106.0  78.6 113.0  93.5  89.6 101.7 122.3  93.3
## 
## [[541]]
##  [1]  85.1  98.7 111.7  97.2 106.0 111.6  82.9 106.0  94.8  99.4
## 
## [[542]]
##  [1] 122.5 102.5 108.1  90.1 104.3  98.8  97.7 105.6  85.0 113.9
## 
## [[543]]
##  [1] 122.8  95.6 105.2 120.5  91.2 100.5 123.1  90.7 109.6 104.7
## 
## [[544]]
##  [1]  96.4 103.6  96.7 107.6  94.9  82.4 108.1 111.3 101.1  91.7
## 
## [[545]]
##  [1]  95.2  86.8  86.1 111.3  79.4 105.6  96.2  86.7  97.7  98.1
## 
## [[546]]
##  [1] 112.0 124.0 118.2 116.3 116.2 109.3  95.5 101.7  84.7  92.2
## 
## [[547]]
##  [1]  91.3  89.1 114.1 105.0 102.6  99.9 109.9 108.8  91.0  80.0
## 
## [[548]]
##  [1]  88.2  95.1 100.0 115.0 106.3 106.9 108.1  98.7  89.3  91.0
## 
## [[549]]
##  [1]  86.4  87.1  84.8 108.6  87.9 106.2 123.5  98.0  98.2 108.4
## 
## [[550]]
##  [1]  99.9  92.4  85.8 100.9  95.7 103.9 102.8 113.0 106.0 111.4
## 
## [[551]]
##  [1] 100.7 108.2  97.5  98.5 100.7  88.9  87.9  97.1  86.0 101.0
## 
## [[552]]
##  [1] 108.0  91.2 100.5  84.6 109.3  96.4 115.3 100.4 118.6 103.3
## 
## [[553]]
##  [1]  98.1 110.1 105.3  94.4 107.0 106.3 103.7  96.4  99.5 108.8
## 
## [[554]]
##  [1] 111.2 103.0  91.9 107.5 101.5 111.4  84.0  92.6 105.3  86.5
## 
## [[555]]
##  [1] 127.5  91.5 104.5  82.7 122.1 107.3  94.9 102.6  92.9  82.8
## 
## [[556]]
##  [1]  89.1  90.9 111.4 104.7  96.3  97.4 110.7  90.0 106.0  90.7
## 
## [[557]]
##  [1] 107.2 112.6  95.6 104.6  77.9 103.2 103.1 104.3 112.2  90.5
## 
## [[558]]
##  [1] 114.0  90.4  83.7 122.1 108.2 107.6 106.3  97.9 110.1 114.4
## 
## [[559]]
##  [1]  84.4  88.6  92.8 105.3  76.6  98.4  85.5  96.5  83.9 111.7
## 
## [[560]]
##  [1]  97.2  98.1 114.9  91.4  84.5  93.8  93.5 103.5  96.8  85.9
## 
## [[561]]
##  [1]  98.2 106.0  86.6 110.0 107.1 115.0  96.7 104.2  91.3  97.4
## 
## [[562]]
##  [1]  89.5 110.8  85.5 106.1  93.2  89.5 114.6 101.1 103.3 101.9
## 
## [[563]]
##  [1] 106.5 114.7 100.6 112.2  76.5 106.3 104.2 101.8 101.3  95.4
## 
## [[564]]
##  [1]  93.8 111.0  98.1 111.8  96.1  89.9 114.5  99.0 112.2  87.7
## 
## [[565]]
##  [1] 103.6  96.8 119.5 113.1 105.6  94.9 109.8 107.2  85.5 111.9
## 
## [[566]]
##  [1] 108.6  98.1 123.1 109.5  94.9 109.3 104.1  98.3  67.4  95.7
## 
## [[567]]
##  [1] 100.2 107.2 103.5 102.3 115.1  99.5  89.4  95.0  98.2  94.3
## 
## [[568]]
##  [1]  81.4 106.0 107.9  92.6 104.4  96.8  97.0 106.0 104.2  94.2
## 
## [[569]]
##  [1]  92.7 105.4  90.0  93.0 113.8 101.6  95.6  88.2 107.2  94.5
## 
## [[570]]
##  [1] 101.0 111.9  97.8 110.3  88.5  82.4 103.3 111.9  94.7  97.4
## 
## [[571]]
##  [1] 109.3  95.5  88.8  91.7  98.3  84.5 108.1 105.7 108.4 115.5
## 
## [[572]]
##  [1] 109.9 114.5  96.5 111.6  86.5 106.1 116.6 120.6 102.9 107.6
## 
## [[573]]
##  [1]  89.2  84.7  99.9 102.9  98.7  92.0  87.8 109.4 110.1  98.4
## 
## [[574]]
##  [1] 116.8 100.2 109.8  93.3 106.1 106.6 102.9 110.9  98.7  79.9
## 
## [[575]]
##  [1]  96.6 107.6  81.3  82.8 100.2 101.2 112.2  99.4 105.1 102.7
## 
## [[576]]
##  [1] 107.4 109.2  86.7  93.2 109.2  78.3  74.3 101.4 100.3  96.5
## 
## [[577]]
##  [1] 108.5 111.9 109.9  98.2  99.7 103.0  78.7  90.0 108.0 102.5
## 
## [[578]]
##  [1]  87.0 112.9 104.9  94.0 100.1 100.7  97.0  98.2  98.5 106.6
## 
## [[579]]
##  [1] 110.0 105.5 117.5 106.2 103.2 108.4  98.6 107.3 120.1  97.9
## 
## [[580]]
##  [1] 110.3 100.2  92.5 111.3 104.6  96.8 117.6  81.4  99.4  97.9
## 
## [[581]]
##  [1]  98.7 101.2 118.6  79.2 110.4  92.4 109.4  95.5 108.6  97.8
## 
## [[582]]
##  [1]  93.9  87.7  90.0  96.4  99.6 105.1  99.2 112.3  87.6 105.5
## 
## [[583]]
##  [1] 109.2 105.1  98.7  94.9  85.9  84.6 107.0  96.8  84.9 105.2
## 
## [[584]]
##  [1] 107.9  78.5 118.4 112.4  87.3  92.0 102.1 103.6  88.1  93.6
## 
## [[585]]
##  [1] 130.8 109.4 113.9  92.1  96.9  86.5 103.6  99.5 123.1  96.8
## 
## [[586]]
##  [1] 100.1  90.6 102.3  92.2  89.6  99.0  91.0  91.4 105.1 110.9
## 
## [[587]]
##  [1] 108.7  99.9 100.9  92.4 103.0 110.0  90.3 110.0  93.5 104.3
## 
## [[588]]
##  [1]  86.1 101.7 113.1  99.2  84.2 116.3  91.8  90.2  93.8  90.0
## 
## [[589]]
##  [1] 102.0 103.3  96.4 108.2 104.5  87.2 106.6  87.0  99.2  97.3
## 
## [[590]]
##  [1]  92.0 111.3 100.3 105.2  99.5  91.2 105.8  92.0 108.5 124.2
## 
## [[591]]
##  [1] 103.4 106.7 104.4 112.5  87.5  90.4 100.7  99.4  88.5  82.5
## 
## [[592]]
##  [1]  95.3 116.5 122.4 108.4  83.8 107.5  94.6 101.3 106.8 116.6
## 
## [[593]]
##  [1] 101.3  93.0 107.6 108.2 109.0 111.4 102.9  90.6 101.3  82.4
## 
## [[594]]
##  [1] 111.5 105.1 107.0 101.6  76.1  93.9 109.4  97.3 108.4  90.6
## 
## [[595]]
##  [1] 102.6  94.5  93.5  98.1 117.1 101.7 102.2 115.9  97.1 105.2
## 
## [[596]]
##  [1]  92.8 108.5  86.5  99.4 111.3 113.4  99.1  76.1 116.5  93.8
## 
## [[597]]
##  [1] 107.2  83.0  95.5 116.3 103.4 103.4 109.0  86.4 100.3 104.7
## 
## [[598]]
##  [1] 111.3  91.9 102.3 106.7 137.2 115.9  76.3 100.2 101.9 108.2
## 
## [[599]]
##  [1]  93.0 110.0  93.1  99.0 106.0  93.9 100.8 115.8  95.4  88.4
## 
## [[600]]
##  [1] 107.2  92.2  97.3 105.1 104.6 111.8  93.2  96.8  93.4  98.4
## 
## [[601]]
##  [1] 119.9  99.4  99.7 105.1  87.8 109.5  99.4  93.0 103.7  98.2
## 
## [[602]]
##  [1]  98.5  98.9 115.5  94.5 109.5 101.6  97.2  93.6  96.3  97.2
## 
## [[603]]
##  [1] 110.9  92.2 116.4  98.3  93.5  92.9 101.9 117.5  97.8  99.0
## 
## [[604]]
##  [1] 102.1 100.6  92.6 109.9  87.7  90.2  95.8  97.2 110.5  93.8
## 
## [[605]]
##  [1]  98.2  96.7 116.0 114.5  89.4 104.4  87.0  91.7  94.2  91.5
## 
## [[606]]
##  [1] 102.3  96.9 103.1 112.3 111.7  79.3  97.5 104.8 111.6  94.3
## 
## [[607]]
##  [1] 101.3 116.3 102.0 118.8  77.8 120.3  76.3 111.3 110.6  96.2
## 
## [[608]]
##  [1]  96.7 103.6 101.7 102.4 113.1 102.3  79.4 104.2  96.8 108.4
## 
## [[609]]
##  [1]  91.3  97.5  84.6  85.2  82.6 100.2  72.6 112.5  93.5 100.1
## 
## [[610]]
##  [1] 112.0 103.0 104.2  93.6  87.1 106.4  98.0 100.0  91.8  94.4
## 
## [[611]]
##  [1]  77.1  83.5  84.3  98.2  89.3 103.9 100.4  95.0  83.9  93.3
## 
## [[612]]
##  [1] 108.9 104.8  96.9  77.6  95.1  70.8 117.7 100.3 112.6  98.3
## 
## [[613]]
##  [1] 120.8  91.0 108.4  99.9 107.3  86.7 122.4 103.0  95.0  88.1
## 
## [[614]]
##  [1]  84.7  81.8  82.8 100.4 111.2 103.5  80.7 100.9 115.0 110.1
## 
## [[615]]
##  [1] 118.4 104.2  67.1 106.4 102.1  82.8  98.7  93.3  95.6 104.7
## 
## [[616]]
##  [1]  94.1  93.5  85.4 101.7 105.5 105.7 111.9  76.3 100.3  86.7
## 
## [[617]]
##  [1] 106.1 100.8  89.3  96.2 114.0  94.6  82.8 110.9 111.7  93.9
## 
## [[618]]
##  [1] 116.5  98.3  87.3  96.9 102.5 105.6 103.9 112.4 102.3 105.2
## 
## [[619]]
##  [1] 110.3  98.3  92.1  97.2  86.7 100.5 105.0  89.5  91.3  88.9
## 
## [[620]]
##  [1]  99.6 114.2  93.7  93.7  99.7  90.2 110.1  97.0 111.3 106.4
## 
## [[621]]
##  [1] 107.9  85.2  83.2 100.6  96.4  96.6  99.0 116.0  95.4  93.8
## 
## [[622]]
##  [1] 116.3 102.2 102.4  87.0 107.5 111.7 107.1  88.5 114.5  97.0
## 
## [[623]]
##  [1] 118.4 104.6 104.2 120.1 112.1 104.6  92.1 109.0 107.7  94.9
## 
## [[624]]
##  [1]  97.8  97.2  83.6 106.8  85.1 103.5  84.5 109.6 108.2 118.7
## 
## [[625]]
##  [1]  88.1 109.5  97.8 102.2  95.9 104.2  88.9  91.0 108.2  71.1
## 
## [[626]]
##  [1]  97.3  95.6 107.5 104.3  86.5 114.8 110.6 114.4  90.3 119.0
## 
## [[627]]
##  [1] 112.1 111.6  87.9  99.3 101.9  86.3  98.0 107.8 103.1 102.4
## 
## [[628]]
##  [1] 114.5  92.5 107.9 110.7  86.9  80.1 109.6  97.5 124.0 103.2
## 
## [[629]]
##  [1]  99.7  82.7  91.9  86.2 128.5  87.2 106.2 113.4  96.8 101.4
## 
## [[630]]
##  [1]  89.2  99.9  96.4  92.5 106.0  91.7  84.5 108.2 102.0  83.8
## 
## [[631]]
##  [1]  93.0 108.5  90.0 107.7  96.7  85.8 104.7  75.1  93.5  99.1
## 
## [[632]]
##  [1] 102.5 102.6 101.1 113.8 117.1 118.3  86.9  91.9  87.4  95.8
## 
## [[633]]
##  [1] 103.1 101.9  97.7  98.4  95.8  91.4  92.7  91.7  94.9  86.1
## 
## [[634]]
##  [1] 112.3 119.5  86.9 112.6 101.1 100.3 100.6 104.6 101.0  91.4
## 
## [[635]]
##  [1] 101.4 108.7  97.6  87.8  83.5 106.2  99.4  94.1 102.3  93.0
## 
## [[636]]
##  [1]  99.2 102.9  79.6  90.2  86.8  87.6 115.5 111.8 107.6  96.3
## 
## [[637]]
##  [1] 111.8  87.8  80.0  69.7 102.3 100.4  92.1 104.9 100.4  97.0
## 
## [[638]]
##  [1] 112.7 114.4 110.4 106.0  90.0  97.5  99.6 101.5 111.2  85.8
## 
## [[639]]
##  [1]  86.4  99.4  85.3 111.2  98.3  73.1  97.6 102.1  92.3  87.3
## 
## [[640]]
##  [1] 100.1 112.2  95.2 111.1 114.0  87.4 108.7  98.9 102.5 117.6
## 
## [[641]]
##  [1] 109.8  95.2  85.0 103.6 105.3 112.1 114.3 102.2 101.7 104.4
## 
## [[642]]
##  [1] 110.8 101.7  96.1  89.5 100.1  99.8 100.0  96.1  94.1 109.3
## 
## [[643]]
##  [1]  98.6 115.6  92.2  81.6  98.4 109.1  98.5  84.2  94.2  99.6
## 
## [[644]]
##  [1] 113.0 111.2 108.1 104.7  91.9 108.1 112.2 107.4 111.8 103.0
## 
## [[645]]
##  [1] 110.2 114.0  90.3 115.2 107.6 107.1 100.7  90.4  87.5 103.0
## 
## [[646]]
##  [1]  98.6 110.7  99.8  96.3 115.1  97.3  93.3 106.7 115.0  90.2
## 
## [[647]]
##  [1]  97.3  96.5 100.3 103.3 107.3 110.5  92.7  99.9 107.9  94.1
## 
## [[648]]
##  [1] 104.6 117.4  86.6 107.2  99.3  90.0 102.6  99.5  89.8 100.2
## 
## [[649]]
##  [1] 105.8  98.0 118.0 115.6  92.5 113.8 112.6  93.5 115.7 116.7
## 
## [[650]]
##  [1] 106.3 108.9  89.9 118.6  94.1  96.4 105.1 101.0 116.8  92.7
## 
## [[651]]
##  [1]  94.6 102.6 105.6 129.3  87.0 111.2 108.9 111.0  87.3 103.6
## 
## [[652]]
##  [1]  95.0  82.5  91.0  89.6 116.4  92.9 109.0 106.1  92.1 105.4
## 
## [[653]]
##  [1] 105.6  88.5 107.3  99.9  97.6  91.1  98.3  89.2  99.8  98.7
## 
## [[654]]
##  [1]  97.5 111.1  93.8  98.7 108.6 113.2  99.0 100.7 111.0 103.2
## 
## [[655]]
##  [1] 103.3  97.4 101.0 100.1 105.8  98.5  96.9  99.3  95.4 115.5
## 
## [[656]]
##  [1]  89.4 112.1  99.9  79.8  94.6 111.6  87.1 101.3  87.7 100.8
## 
## [[657]]
##  [1] 110.2  97.9 109.6 107.3 112.1 113.3 110.0 103.9 100.6 101.4
## 
## [[658]]
##  [1] 103.6  91.0  94.1  95.0  94.8  97.2  99.4  92.1  77.7 120.2
## 
## [[659]]
##  [1]  91.8 110.2  93.8 105.0  98.6 106.0  81.5 102.4  98.5 113.9
## 
## [[660]]
##  [1]  96.7  96.1  81.6 101.6 106.2  97.7  94.2 103.6  88.0 103.1
## 
## [[661]]
##  [1] 110.1  98.4  96.1  96.5 104.9  87.3  91.6  85.1  97.3  99.6
## 
## [[662]]
##  [1] 100.9  98.3  81.7  87.2  97.0 102.8 101.9  89.5 110.2 100.5
## 
## [[663]]
##  [1]  96.5 102.7 108.5 106.0  96.0  88.2 108.6  89.5  93.1 111.5
## 
## [[664]]
##  [1]  94.7  97.4 104.7 113.4  90.2 107.4  99.7 114.2 109.6  99.5
## 
## [[665]]
##  [1]  92.5  87.0  89.9  95.6  87.9  98.6  94.6 119.8 111.0 105.1
## 
## [[666]]
##  [1]  94.4 120.2  97.2  99.6  80.7 110.9  99.5  89.8  99.9 110.8
## 
## [[667]]
##  [1] 100.8 103.0 110.6  90.8  97.5 106.9  86.0 112.0  89.2 102.7
## 
## [[668]]
##  [1] 101.8  94.1 102.2  98.1 108.9  86.5 113.0  97.5  92.6  89.4
## 
## [[669]]
##  [1] 110.8  84.6 101.4  94.0  92.3  98.4 100.6  96.3  92.5 107.3
## 
## [[670]]
##  [1] 106.6 116.5  90.1  89.9  91.8  88.5 119.8  74.9  85.9  92.4
## 
## [[671]]
##  [1]  97.6  98.5 110.1 112.8  89.6 102.3  83.1 108.9  91.3 104.4
## 
## [[672]]
##  [1]  90.1 100.2  99.9  89.3 103.8 132.8 100.2  95.8  94.8  96.4
## 
## [[673]]
##  [1] 101.7  91.3 115.2 106.0 109.2 113.8  89.1  90.6 103.3  95.2
## 
## [[674]]
##  [1] 105.1  99.3 107.1  83.9 107.0  81.5  99.8 104.7  92.1 115.0
## 
## [[675]]
##  [1] 102.2  83.9 115.6 103.1  97.2 107.2  87.5 100.0 102.8  70.8
## 
## [[676]]
##  [1]  95.9  93.1 103.6 111.1 101.5  92.0  99.2  89.9  89.9  75.0
## 
## [[677]]
##  [1]  97.4 105.9 102.7  89.5  95.3 111.3 107.4 105.4  96.8  99.5
## 
## [[678]]
##  [1]  88.9 100.4 104.0 100.5 102.1  76.0 102.9  96.7  87.4  97.0
## 
## [[679]]
##  [1] 101.9  90.4 100.2  88.2  89.2 118.1 107.7  84.2  97.6 101.3
## 
## [[680]]
##  [1]  96.9 111.0 122.6  94.2 108.4 111.2 104.1 104.7 112.3 101.2
## 
## [[681]]
##  [1]  80.2 104.5  87.1  93.9  97.6  78.8  98.2 108.9  93.8  85.1
## 
## [[682]]
##  [1]  97.0  94.3 103.1  93.8  93.0 103.6 105.0 111.5 110.7  93.4
## 
## [[683]]
##  [1] 109.1  86.8 101.6  80.1 104.0  89.3  99.3 102.7  85.0 109.0
## 
## [[684]]
##  [1] 111.0 102.8  87.6  85.2  85.0  95.5  98.9 103.5 108.0  94.8
## 
## [[685]]
##  [1] 111.0  96.3  85.0 107.1 105.6 101.2 104.9 114.3  96.7 110.1
## 
## [[686]]
##  [1]  94.5 113.8  98.3  97.7 106.2 106.1 114.4 104.7 110.1 106.8
## 
## [[687]]
##  [1]  95.2 112.7  90.3 110.2  91.0 109.8  98.9 100.4 119.3  92.4
## 
## [[688]]
##  [1] 110.5  93.2 100.2  98.8 119.4 112.7 100.8 101.3 100.8  86.2
## 
## [[689]]
##  [1]  83.2  98.1  97.9  92.7  91.1  99.5 117.8  96.5 111.3  97.5
## 
## [[690]]
##  [1] 103.1 121.7 102.9  93.5  82.9  94.9 110.0  95.3 108.2  97.6
## 
## [[691]]
##  [1]  86.0  81.0  89.9 100.1  95.0  92.1 100.9  89.1 109.7  94.0
## 
## [[692]]
##  [1]  98.3  91.0 105.5 103.7  95.6  80.3 101.6 104.3 104.9 110.5
## 
## [[693]]
##  [1]  91.8  92.6  87.2 108.6  95.4  92.0  99.5  98.1  93.6 119.7
## 
## [[694]]
##  [1]  92.6 111.4 106.0 118.2 101.1 100.1  93.8  88.0  97.0  94.1
## 
## [[695]]
##  [1]  94.8 103.7  95.5  65.9  97.9 101.9  99.3 102.0  95.5 109.5
## 
## [[696]]
##  [1]  96.6  95.4 109.2 111.9  95.8  98.7  92.9 101.3 117.4 108.8
## 
## [[697]]
##  [1] 106.5 104.7  97.9  83.3 107.5 101.4  94.8 113.1 108.5 112.1
## 
## [[698]]
##  [1] 107.5  92.4  97.5  80.9  98.0  82.2 101.1 101.5  93.8  99.8
## 
## [[699]]
##  [1]  83.8 103.8 119.0 106.0 117.3  98.5  97.3 111.5 105.1 108.0
## 
## [[700]]
##  [1]  98.6  99.5 102.5 100.4 107.9  96.3  90.8 114.8  92.6 102.9
## 
## [[701]]
##  [1]  81.4  93.6 124.2 100.9 108.2 105.4  85.8 108.6  89.8 107.1
## 
## [[702]]
##  [1]  87.9  99.7 105.3  96.7  98.6 105.7 107.2 115.2 128.2  98.9
## 
## [[703]]
##  [1] 113.3 106.9 100.7  99.5  90.0 109.9 110.4  95.0  88.0 100.3
## 
## [[704]]
##  [1] 111.2 117.4  94.4  98.8 117.1  96.0  89.9 103.5 123.8  92.5
## 
## [[705]]
##  [1]  95.3  99.0 100.6  96.1 104.8  93.4  98.7 106.8 101.3 106.9
## 
## [[706]]
##  [1]  86.1  91.7  98.5  84.3 101.9 109.2  98.7  83.6  97.5  87.0
## 
## [[707]]
##  [1]  97.3  86.0  79.6 108.5 102.6  88.4  85.9  87.7  94.6 112.0
## 
## [[708]]
##  [1] 103.8  90.4 109.8  86.1 116.8  97.5 114.3  89.8  99.7  94.9
## 
## [[709]]
##  [1] 103.4  90.3  87.8  90.5 117.7 102.4 110.3  92.4  98.9  99.1
## 
## [[710]]
##  [1]  97.2  98.6 103.0  92.1 107.7 118.0  99.4 105.2 102.1  99.6
## 
## [[711]]
##  [1] 104.5  99.4  91.3  99.1 112.2 105.7 104.0  98.9 105.5  79.7
## 
## [[712]]
##  [1]  99.3  85.0  95.9  86.0 112.7  93.1  95.1 112.4 108.1  96.6
## 
## [[713]]
##  [1]  79.8 108.4  96.3  92.9  94.6  88.8  85.8  89.9 110.8  89.5
## 
## [[714]]
##  [1]  96.8 105.2 104.5  80.5 114.6 101.8 110.0  90.6  95.5  97.3
## 
## [[715]]
##  [1] 106.5  87.8  95.2 106.3 110.9  90.9 114.1  98.7  98.1 106.7
## 
## [[716]]
##  [1] 108.8  92.4 108.6  90.5 108.4  94.7  92.1 110.6 104.7  87.8
## 
## [[717]]
##  [1] 108.7  97.3 105.7 104.6  90.3  98.9  99.8  95.7  80.1  94.9
## 
## [[718]]
##  [1] 104.9 109.7 111.5 107.1  98.0  96.5  94.2 109.4  94.0 102.0
## 
## [[719]]
##  [1] 109.3 103.6 101.9  95.8  88.3  97.2  91.4 101.4 100.3  96.6
## 
## [[720]]
##  [1] 105.8 114.5 100.6 105.4  89.7  99.0 100.3 104.6 103.8 101.7
## 
## [[721]]
##  [1] 103.9  91.1 101.9  83.7 109.1 106.8  99.5 116.9  94.5 112.7
## 
## [[722]]
##  [1] 107.0 121.9 112.7 107.6 105.8 105.3 108.6 107.6 112.0  98.6
## 
## [[723]]
##  [1] 117.7  99.7  86.9 112.8  85.8 100.4  91.5 113.1 106.7  93.2
## 
## [[724]]
##  [1] 110.7 102.2 107.0 109.1  94.9 102.7  74.7  96.5 108.5 110.2
## 
## [[725]]
##  [1] 105.9 102.5 107.5  90.7  93.3  90.9 103.5 100.6 103.9 103.9
## 
## [[726]]
##  [1] 111.6 117.4  86.9 104.3  93.9 114.1 107.0 111.9  87.6 100.8
## 
## [[727]]
##  [1] 116.1  91.3  90.0  98.6  93.3 108.3  95.8  97.9  86.5 103.5
## 
## [[728]]
##  [1] 106.7  87.2 114.5  90.7 104.6 101.7  91.3  94.5 109.5  99.3
## 
## [[729]]
##  [1]  98.4 109.3 103.8  97.6 101.9  86.7 102.6 121.9  97.8  94.4
## 
## [[730]]
##  [1] 113.7 108.3 114.2 105.9 104.1 106.9  91.4 102.7 104.4 118.7
## 
## [[731]]
##  [1] 108.6 116.4 100.6  91.6  91.9  87.1  82.0  96.2  95.2 114.2
## 
## [[732]]
##  [1]  83.7 101.6  95.7 106.6 107.7  91.6  98.3  97.8  89.5 101.2
## 
## [[733]]
##  [1]  96.4  93.5  89.8 100.6 100.8  93.6 116.0  88.4  98.1  92.7
## 
## [[734]]
##  [1] 108.6 111.2  75.4  94.2  81.0 118.4 101.4 104.4 100.2  84.4
## 
## [[735]]
##  [1]  84.2 108.8 103.6  92.7  85.7 106.9  90.9  97.0 107.9  91.2
## 
## [[736]]
##  [1]  86.8 119.3  94.8 117.9  95.3 104.3 105.2  88.2  92.6 118.7
## 
## [[737]]
##  [1]  99.8 110.6  83.6 109.3  97.0  98.2  94.6  99.3 101.9  82.7
## 
## [[738]]
##  [1]  92.0 104.5  98.8 101.0  97.0 112.2 100.0  99.2 106.9 123.0
## 
## [[739]]
##  [1] 105.4 111.6  91.7 100.7  95.1 108.9 101.4 106.4 126.8  93.4
## 
## [[740]]
##  [1] 105.5  89.7  92.7 111.1  99.2 103.5  92.8  98.7  90.1 105.9
## 
## [[741]]
##  [1]  90.8  96.8  95.7 101.6  96.0  87.0 102.8 107.6 116.7  85.5
## 
## [[742]]
##  [1] 114.3  89.8  98.1  87.9 115.3 101.4  99.6 104.4 128.6  93.4
## 
## [[743]]
##  [1] 104.5 101.0 101.7 111.2 102.0  99.2 103.2  92.9 118.8 118.6
## 
## [[744]]
##  [1]  92.0  81.1 119.5 104.9  85.9  91.9  89.7 101.3  97.2 113.7
## 
## [[745]]
##  [1] 118.6 109.1  99.8 111.2  92.5  93.5 100.2  98.1  92.2 103.7
## 
## [[746]]
##  [1]  93.8 111.3  96.5  96.4  99.4 113.6 106.1 103.6 110.3  89.2
## 
## [[747]]
##  [1] 111.5 100.1  85.6  94.1  96.3 115.2  80.0  96.5  90.4 102.7
## 
## [[748]]
##  [1] 100.2 110.6 109.9 107.1 118.0  89.2  95.1 109.6  94.2  87.5
## 
## [[749]]
##  [1] 103.5 108.1  94.8  73.1  89.0  87.4  93.6  96.1 109.9  85.8
## 
## [[750]]
##  [1]  93.9  92.6 114.3  85.1  84.5 110.4 100.3  94.2  92.8  74.2
## 
## [[751]]
##  [1] 102.7  98.6 111.0  95.2 110.1 102.5 107.4  82.0 109.9 107.8
## 
## [[752]]
##  [1] 113.1  99.4  89.2  98.6 107.5 108.8 113.3  99.3 115.8  92.1
## 
## [[753]]
##  [1]  73.2 102.3  99.6  87.0 101.4  87.6  91.6 114.0  69.4 103.2
## 
## [[754]]
##  [1]  95.4  93.8 101.3  95.2  94.7  86.1 116.0 109.1  87.3  96.9
## 
## [[755]]
##  [1] 106.6  94.4 100.4 101.2 116.3  92.2 107.7  94.1  97.2  99.5
## 
## [[756]]
##  [1] 103.1 101.1  95.2  99.9 102.5 104.2  86.6  97.8 118.0  94.3
## 
## [[757]]
##  [1] 100.5 110.0  87.8  86.8 111.7 106.3  89.0 114.8 110.1 117.5
## 
## [[758]]
##  [1]  87.9 110.4 101.0  80.9  91.5 107.4 107.7  85.3 100.1  81.4
## 
## [[759]]
##  [1] 108.9 104.9 117.5  97.4 105.0  93.1  90.2 109.8 109.2 103.3
## 
## [[760]]
##  [1] 104.6 103.2 104.1 101.9  86.8  80.0  86.8 112.5  88.8 106.0
## 
## [[761]]
##  [1] 108.0 101.8 103.2 106.5 115.8 100.0  96.9  93.8 109.4 101.0
## 
## [[762]]
##  [1] 110.9  86.5  95.4  97.5 105.1 106.5  97.8 102.3  88.4 120.3
## 
## [[763]]
##  [1]  97.4  99.0  96.5  90.1 108.7  81.8  96.8 101.2  85.3 110.7
## 
## [[764]]
##  [1]  95.2 106.6  81.8  97.2 100.7  86.5 109.2 102.7  99.1 101.8
## 
## [[765]]
##  [1]  99.5 106.7 101.8 115.4  95.8 108.7 101.4 121.6 100.3 101.3
## 
## [[766]]
##  [1]  96.5  79.1  80.3  98.6 100.9  93.1 106.2 113.6 117.1  78.2
## 
## [[767]]
##  [1] 108.1 109.5 106.9 111.3  98.5  97.1 110.2  93.2 108.9  92.0
## 
## [[768]]
##  [1]  94.1  93.0 108.8  99.4 105.4 123.8  90.1 113.3 106.2 100.2
## 
## [[769]]
##  [1]  88.2 128.5  83.4  92.4 111.3  84.5 104.4  84.3 104.5 121.8
## 
## [[770]]
##  [1] 102.0 104.8 107.3  92.0  90.4  94.7 103.6  89.3  99.2 108.0
## 
## [[771]]
##  [1]  94.5  99.4 101.7  83.9  98.3  88.0  97.5 105.1 106.3  91.1
## 
## [[772]]
##  [1]  88.0 117.8  80.8  88.9  96.8  99.3  93.7  86.5  99.1  87.2
## 
## [[773]]
##  [1]  95.0 104.2 110.3 111.0 109.1  97.2  82.4  84.4 106.9  77.1
## 
## [[774]]
##  [1] 107.4 100.2 119.1  99.9  78.6 108.2 110.9  95.9  97.1 104.0
## 
## [[775]]
##  [1] 102.6  99.9 100.6 119.8 111.0 120.5  96.0  95.9  96.9 107.2
## 
## [[776]]
##  [1] 117.8 104.2  96.8 103.1  96.6  98.1  90.3 101.4  95.8  89.8
## 
## [[777]]
##  [1] 100.1 104.8  98.4  97.5  97.6 109.9 107.3  99.7  90.9 100.5
## 
## [[778]]
##  [1]  87.3 111.0 103.7 114.9 110.9 104.6  95.3  98.8  88.1  98.0
## 
## [[779]]
##  [1] 111.6 101.7 101.6  95.7 113.2 105.3  91.5 102.9 111.1  97.4
## 
## [[780]]
##  [1] 100.4  96.5 112.9 101.2 126.3  80.2  99.5 108.9  97.4 120.7
## 
## [[781]]
##  [1]  99.9  89.7  95.6  97.7 101.1 101.6 114.9  93.1  95.4  99.9
## 
## [[782]]
##  [1]  88.5 102.1 102.8  88.0  87.5  99.3  93.2 107.2  94.4  99.2
## 
## [[783]]
##  [1] 104.4  92.3 109.2 103.1 122.6  96.8  80.3 111.7 100.1 116.1
## 
## [[784]]
##  [1]  90.3 126.4 114.2  98.0 111.2  99.2 119.9  94.0 101.7  89.7
## 
## [[785]]
##  [1]  99.1  91.0 117.4  96.8  94.0 111.2  82.7 110.6  92.9 101.9
## 
## [[786]]
##  [1]  86.6 106.2 109.7 103.5  93.4 105.9  97.7 101.8  95.7 124.4
## 
## [[787]]
##  [1]  82.4 106.3 119.1  91.5  82.9  87.8 101.1 114.2 106.8 101.7
## 
## [[788]]
##  [1]  89.9  92.5 100.7 100.7  98.4  81.5 102.5  97.7  84.2  82.6
## 
## [[789]]
##  [1] 101.6  91.0  81.7  99.0 104.9 110.3  90.1  99.7 111.3  85.1
## 
## [[790]]
##  [1] 111.4 118.2  92.6  98.6  61.5  80.2 113.0  70.9 101.0  89.2
## 
## [[791]]
##  [1]  97.7  93.8  98.1  98.5 104.3  97.1 111.0  89.5  99.5  79.0
## 
## [[792]]
##  [1] 104.9 101.5 107.9  86.1  94.6  87.9  99.2  91.8  97.0 111.2
## 
## [[793]]
##  [1] 118.4  80.7  86.4 111.8 100.8  90.1 107.0  88.4  98.6 103.7
## 
## [[794]]
##  [1] 107.9 106.8 105.5 104.1 109.7  96.5  89.1 104.1 103.7 109.9
## 
## [[795]]
##  [1]  90.0 103.5  95.5 106.5 111.4 108.5  89.8  91.3  93.9 104.4
## 
## [[796]]
##  [1]  92.9 102.1 111.1 105.4 112.5 100.9 102.6  90.2 106.3  82.6
## 
## [[797]]
##  [1]  86.4 103.6  90.8 103.7  87.0 100.3  83.1 104.7  82.4 102.7
## 
## [[798]]
##  [1] 100.1 109.3 123.7  82.1  96.4  93.4  93.2  87.1 104.8 102.2
## 
## [[799]]
##  [1] 105.1 118.1  83.0 102.9  97.3  96.2  93.1  98.1 109.4  91.8
## 
## [[800]]
##  [1]  96.9 104.2 104.5 117.5  97.0  98.2  82.2 113.1 107.3 109.9
## 
## [[801]]
##  [1]  90.0 115.2  93.1 115.1  99.6 105.8 101.5  91.6  98.4  94.7
## 
## [[802]]
##  [1]  89.8  98.6  91.1  99.8 101.8 107.2  91.5 106.7 100.0  96.4
## 
## [[803]]
##  [1] 111.2 102.5  92.1  87.3 103.4  92.4 118.1 105.4  72.6  89.8
## 
## [[804]]
##  [1]  87.5  89.8  83.5 105.2 103.8 104.3 111.2  99.6 114.4  88.7
## 
## [[805]]
##  [1]  93.1  92.2  96.2  91.0 106.4  98.7 111.1  84.7  84.7  93.2
## 
## [[806]]
##  [1]  91.3  84.8 103.9 106.7 113.2 105.1 104.3 113.0  96.1 101.3
## 
## [[807]]
##  [1] 102.9 123.7 104.3  92.1 104.7  88.5  88.8 112.1  88.3  84.3
## 
## [[808]]
##  [1]  95.3  93.7 103.1  97.6 126.5 113.3  80.1 103.2  95.9 107.8
## 
## [[809]]
##  [1]  89.8  94.8 100.7 104.1  83.5  96.1  79.6 105.4  93.3 113.8
## 
## [[810]]
##  [1] 111.8  92.2 103.5 111.7 104.6  88.9  80.3 102.5  92.8 113.7
## 
## [[811]]
##  [1]  91.8 106.5 109.4 108.0  83.1  85.3  95.1 110.4 112.4 118.6
## 
## [[812]]
##  [1]  90.7  93.5  99.8 112.5  80.9  87.8 117.5 107.8  78.6 110.7
## 
## [[813]]
##  [1] 103.9  93.0  99.9 106.4 103.5 108.0 115.4 103.9  85.2 100.6
## 
## [[814]]
##  [1]  76.2  97.6  92.0  90.7  93.8 138.5  90.0  90.9  96.2  96.2
## 
## [[815]]
##  [1] 134.0  99.7  98.5  95.3 111.3  97.9 104.7 101.1  84.4  91.9
## 
## [[816]]
##  [1] 100.0 112.0 103.1 101.3  91.9 109.3 109.5  96.8 107.7  97.6
## 
## [[817]]
##  [1] 102.1 108.3 105.6  92.5 103.8  94.7  98.1  91.0  99.8 108.7
## 
## [[818]]
##  [1]  96.9 107.2  99.0 105.6  84.5 107.1  93.5  95.6 102.6 104.9
## 
## [[819]]
##  [1]  95.0  89.7  93.1  87.3 111.2 103.8  99.9  89.6 108.6 101.9
## 
## [[820]]
##  [1]  82.7  96.1  96.8  96.8 100.3 103.9 112.0  98.9  93.7  88.1
## 
## [[821]]
##  [1] 103.4  95.7 106.1  91.3  97.0  87.4 105.5  98.0 128.0  95.6
## 
## [[822]]
##  [1]  91.9 119.6 119.3 115.3 103.2 107.4 109.3 111.3  93.3  92.1
## 
## [[823]]
##  [1] 110.9  88.3 103.9  92.7 120.5 109.7 105.3 102.0  91.9  95.2
## 
## [[824]]
##  [1] 101 102 103  74 104 106 111 116 109 110
## 
## [[825]]
##  [1]  95.8  94.5  91.4 116.3  79.5 102.6 100.4 104.4 108.4  86.4
## 
## [[826]]
##  [1] 108.0 104.0  99.4  95.5 103.9  92.5 104.0 100.1  83.4 117.3
## 
## [[827]]
##  [1] 120.9 110.6  95.9  94.1 110.9 109.4 111.0  97.3 111.5 117.8
## 
## [[828]]
##  [1] 101.7 101.9 100.4  88.2  88.4  94.2 104.6 102.6 112.2  91.1
## 
## [[829]]
##  [1]  98.9  95.3 102.0 106.3 116.9 116.6 118.5 106.2 118.0  88.9
## 
## [[830]]
##  [1] 101.5 114.5  97.1 104.8 107.6  97.9 112.5 105.4  92.1 111.8
## 
## [[831]]
##  [1]  87.7 109.4  92.0 106.1 104.4 111.8 104.2 108.5  92.9  99.1
## 
## [[832]]
##  [1] 110.6  91.6  89.8  98.4  98.8 100.0 123.2  85.0  90.8  91.8
## 
## [[833]]
##  [1] 114.5 112.5  90.7  89.3  96.7  80.1 104.9  99.2  82.8  97.6
## 
## [[834]]
##  [1]  99.5 108.4  99.5  92.9  93.6 113.5  97.0 103.0 104.1 104.4
## 
## [[835]]
##  [1]  85.0 106.9 111.9 120.6  86.8  88.6 104.4  94.9 112.5  84.9
## 
## [[836]]
##  [1] 103.7 103.9 108.8 109.0 101.1  83.4 103.3 103.8  81.5 111.2
## 
## [[837]]
##  [1] 101.1  88.8 102.7 109.6 105.8  95.9 123.6  98.1 103.3 104.8
## 
## [[838]]
##  [1] 109.5 108.5  99.8  98.7  89.2 104.2 107.1  95.8 108.5 100.6
## 
## [[839]]
##  [1] 105.2  92.6 110.7  87.1 121.0  98.2  86.0  89.6  80.0  98.0
## 
## [[840]]
##  [1] 101.9  93.6  98.3  87.0 110.2  98.3 102.9 121.2 109.8  88.1
## 
## [[841]]
##  [1] 111.2  83.3 128.7 114.8  84.4  91.6 115.5  88.4 124.0 113.3
## 
## [[842]]
##  [1] 108.4  95.5 116.7 101.8 110.8  94.3 108.1  90.3  94.6  98.2
## 
## [[843]]
##  [1] 112.0 101.8  95.5  89.5  92.6 103.1 103.6  97.1  93.3  79.3
## 
## [[844]]
##  [1] 103.8  96.3  99.5  98.6  79.5  99.1 118.0 118.5  85.0 100.3
## 
## [[845]]
##  [1]  79.2  94.1 117.4 108.3  96.6  96.0  99.2  88.2 101.0  91.6
## 
## [[846]]
##  [1]  86.5  91.8 110.5  89.5  90.4  76.8 105.4 100.9  96.1 109.1
## 
## [[847]]
##  [1] 100.2 105.8  95.8  93.7 111.0 108.3 109.1 104.2  98.8  91.3
## 
## [[848]]
##  [1] 119.8 101.5  96.6 117.7 116.9  93.3 100.0  97.1 109.6  96.9
## 
## [[849]]
##  [1] 102.7 100.4 100.0  90.2 101.4 104.6 100.4  96.3 105.7 101.2
## 
## [[850]]
##  [1] 108.3  89.8 119.5  89.6  95.1 107.5 103.9  85.1  93.7 107.3
## 
## [[851]]
##  [1] 121.5 117.1 119.5 111.4 104.9  97.2 106.7  93.9  80.0 112.1
## 
## [[852]]
##  [1]  94.8 107.3  82.7  65.3  98.9  85.5  96.3 103.4  94.6 100.3
## 
## [[853]]
##  [1]  92.8  89.0  97.6 110.1  89.0 108.8  94.6  86.7 106.3 107.3
## 
## [[854]]
##  [1] 111.7 105.9  99.6 115.2  95.6  99.1  96.7 107.5  96.2 106.5
## 
## [[855]]
##  [1]  85.7  92.2 102.9 101.9  93.0 113.9 108.2 100.9 103.0  97.3
## 
## [[856]]
##  [1] 112.2 103.7  80.0 100.3  99.5  89.8  96.3 117.2 125.4 110.9
## 
## [[857]]
##  [1]  95.6 109.9 107.0 117.6  93.5 108.9 126.2  79.0 108.8 113.2
## 
## [[858]]
##  [1] 104.9 105.7  92.5  92.6  89.7  82.8 104.3 101.1  99.7 101.6
## 
## [[859]]
##  [1]  95.9 117.7 103.6  99.8  89.4  90.2  92.5 104.7 109.2  94.3
## 
## [[860]]
##  [1]  91.6  92.7  89.2 101.1 112.2  73.9  99.2 113.1  92.1  98.9
## 
## [[861]]
##  [1] 107.9 103.7 103.3  77.1  95.9  98.1 110.6 103.2 107.6 108.5
## 
## [[862]]
##  [1]  85.5 105.4 105.1  87.1  79.1 102.4 104.6  93.1 110.2  86.3
## 
## [[863]]
##  [1] 119 106 115 108 103 104 113 111 103 121
## 
## [[864]]
##  [1]  89.5  87.0 124.6  92.1 115.9 108.2  95.7 100.1  96.0 101.0
## 
## [[865]]
##  [1]  95.0  89.3 106.9  97.1  98.1  96.5 103.5  90.2 103.3  94.8
## 
## [[866]]
##  [1]  97.7  95.1 100.6 104.4  91.4  94.3  98.7  84.0  98.8 116.5
## 
## [[867]]
##  [1]  96.4  99.6  89.0  96.7 105.2 107.9 101.6  97.7  88.2  99.9
## 
## [[868]]
##  [1] 103.1  96.2 109.5 102.3  90.5  96.3  93.7  87.3  88.7  96.5
## 
## [[869]]
##  [1]  92.6 101.5  80.9  86.3 113.7  96.4 102.6 108.0  99.3 112.3
## 
## [[870]]
##  [1] 108.2 120.5 109.0 119.3 100.3  88.4 110.7  96.9 104.8 117.4
## 
## [[871]]
##  [1] 108.0  85.0 115.1 107.4  99.0  93.3  99.6  87.1  77.6  92.2
## 
## [[872]]
##  [1]  99.6  87.7  77.6 105.9  92.2 100.5  75.9 108.0  90.8 112.0
## 
## [[873]]
##  [1] 100.7 102.1 103.0  98.9 106.5 119.1 103.1  98.7  97.9  88.1
## 
## [[874]]
##  [1] 101.8  85.9  89.1 114.1  84.7 121.3 107.0 117.6 104.5  98.1
## 
## [[875]]
##  [1] 116.9 100.2  95.8  94.2  94.5 104.5 103.9 100.6  81.7  88.8
## 
## [[876]]
##  [1]  77.4  87.8 118.5 115.2  92.7 112.5  98.6  98.2 110.5  98.7
## 
## [[877]]
##  [1] 112.1 102.9  90.2 104.1  99.6  94.8  97.9 100.1 106.3 100.7
## 
## [[878]]
##  [1] 102.1  87.3  98.1  98.9  96.4  96.0 100.1 100.0 104.8 114.4
## 
## [[879]]
##  [1]  97.8  97.3 121.1  95.9  94.5 105.1  98.6 104.8 107.7 128.0
## 
## [[880]]
##  [1] 112.3 109.4 103.1  96.0 100.5  89.7 108.1 106.3 112.9  90.0
## 
## [[881]]
##  [1]  97.4  90.3  97.9 102.1 108.3 103.0  93.8  99.1  90.4 104.1
## 
## [[882]]
##  [1] 105.7  87.5 107.7 109.3 106.5 108.8  90.6  91.1 113.3 107.3
## 
## [[883]]
##  [1]  96.9 106.0 118.1 101.9  96.0  94.2  88.5 102.1 105.1 101.7
## 
## [[884]]
##  [1] 103.5  98.5 104.7  91.7  97.8  99.6 113.2  79.4 122.7  93.0
## 
## [[885]]
##  [1] 110.8  97.3  97.1  98.7  75.6 128.8 102.6 106.7  94.1  92.8
## 
## [[886]]
##  [1] 113.5 107.9 111.2  96.8  86.6  93.9 116.6  84.3 117.7  95.1
## 
## [[887]]
##  [1]  84.3  88.6 103.5  97.1  74.1  96.3 115.7  96.6 115.5  93.2
## 
## [[888]]
##  [1] 107.4  96.5 109.1  81.5 102.0 113.6  91.6 116.6  96.0  94.4
## 
## [[889]]
##  [1]  88.9 105.7  88.9  85.9  97.5  82.6  91.1 119.5 100.5 108.6
## 
## [[890]]
##  [1]  83.8  78.2 109.6 101.0 116.2 110.4  77.8 112.0  89.8  99.1
## 
## [[891]]
##  [1] 102.6  93.2  92.3 100.1 102.7  84.0 117.7 113.5  96.7  83.1
## 
## [[892]]
##  [1] 110.2 120.2  88.8 101.6  85.4  95.0 106.3  85.5  89.0  96.5
## 
## [[893]]
##  [1]  94.6 100.2  98.8  80.4  87.2 101.5 104.7 114.5 105.9  99.8
## 
## [[894]]
##  [1] 106.1  89.0  77.1  97.6  97.1  91.8  77.6  86.3 114.9  88.8
## 
## [[895]]
##  [1]  99.8  96.6 116.9 101.4 120.3 110.5  84.5 101.1 104.6  93.7
## 
## [[896]]
##  [1]  96.1 100.3  80.7  78.6  92.8 104.4 111.3  75.7  97.8  90.9
## 
## [[897]]
##  [1]  94.1 109.9 120.1  96.7 100.5  82.5 127.5  99.7 107.1 104.6
## 
## [[898]]
##  [1]  87.4 101.6  86.8 101.0 103.1  90.3  86.3 100.6 101.0 101.1
## 
## [[899]]
##  [1] 119.3  93.8  94.4  90.1 127.3  92.8 113.3  87.8 114.0 103.3
## 
## [[900]]
##  [1]  91.8 103.1 111.3 109.3 102.2  95.8  83.5  90.2  88.9 106.1
## 
## [[901]]
##  [1]  95.7 104.9 107.7 108.9 118.4  96.0  96.8  93.1 113.2  95.8
## 
## [[902]]
##  [1]  99.4  93.9  97.4 103.0  90.6 109.4  88.3 108.5  93.2  90.9
## 
## [[903]]
##  [1] 111.6  99.9 102.1 114.1 107.7  99.2  90.5 102.6  96.3 108.3
## 
## [[904]]
##  [1]  88.8  93.1 128.6 113.4  89.3  94.9  98.9  92.5 108.8 102.5
## 
## [[905]]
##  [1] 115.9  98.9 108.9 103.4  85.9  86.0 100.8  82.3  90.7 106.8
## 
## [[906]]
##  [1] 106.9  95.4 100.5  88.3  98.9 109.0 112.7  87.4  96.5  98.5
## 
## [[907]]
##  [1] 101.6  87.4 101.6 105.1 116.0  88.5 105.6  96.8  83.0 119.7
## 
## [[908]]
##  [1]  89.9  93.1  97.0 103.0 101.3  84.8  92.7 106.4  90.9 102.2
## 
## [[909]]
##  [1] 101.0 109.3 106.2 103.6 110.2 103.3  91.8  96.6  93.2  92.5
## 
## [[910]]
##  [1] 112.1 110.0 103.6 100.1  99.9  94.9 104.9  86.4  88.3 106.6
## 
## [[911]]
##  [1]  91.7 107.7 100.9 102.3  97.8  95.2 117.0  96.1 124.6 102.5
## 
## [[912]]
##  [1] 100.4 105.7 107.3  84.1  98.7 101.9  87.1  88.8  94.3 105.4
## 
## [[913]]
##  [1]  95.2  90.9  85.1  82.3 107.1 108.0  87.1  89.5 100.7 120.4
## 
## [[914]]
##  [1] 117.6  96.4  92.6 118.5 114.9  83.5  88.3 107.3  98.4  74.3
## 
## [[915]]
##  [1] 101.2 116.0 100.2 108.9  91.4  99.0 109.5  98.5  99.4 101.8
## 
## [[916]]
##  [1]  89.9  91.8  95.6  90.2 111.4  91.2  98.8 113.5  95.7  92.7
## 
## [[917]]
##  [1] 102.2 100.3 102.0  90.6  93.2 106.0  73.6 112.2 102.8  84.9
## 
## [[918]]
##  [1]  81.0  90.6 110.8 103.7  97.4 102.3 112.6  98.9  98.0  96.5
## 
## [[919]]
##  [1]  98.0  80.3  98.5 123.0  98.7 106.6  96.3 115.0 107.0  99.2
## 
## [[920]]
##  [1]  96.5  95.4  92.0 105.5 102.4 110.9  94.3  84.8  80.4  75.8
## 
## [[921]]
##  [1] 107.6  99.9 107.0 108.9  93.8 116.3 120.7 101.6  97.6 106.1
## 
## [[922]]
##  [1] 109.0 113.3 107.3  98.8 103.6  96.0  90.8  85.2  85.8  96.0
## 
## [[923]]
##  [1] 105.4 109.9 101.3  97.6  82.1  97.5  91.3  86.8  89.1  95.8
## 
## [[924]]
##  [1]  96.4 111.5 122.1 104.8  98.9 117.7 105.8 102.4 112.2  84.2
## 
## [[925]]
##  [1] 104.0 100.0 109.2  91.8  94.4 110.5 103.5  92.2  91.6  92.3
## 
## [[926]]
##  [1] 103.2 107.6  87.2 106.2 104.0 102.3 102.0  93.7  79.3  93.4
## 
## [[927]]
##  [1]  85.6 100.7  82.5 102.4 123.4 111.8 109.9  97.9  93.3  85.7
## 
## [[928]]
##  [1] 106.1 107.7 108.4  93.5  96.3  85.1  99.8  90.7  86.1  88.4
## 
## [[929]]
##  [1]  98.8 102.2 108.7  80.4 115.5  91.0 103.3 109.8  91.3  90.5
## 
## [[930]]
##  [1] 102.2  88.0  95.9  90.4 102.7 107.1 110.6  96.8  99.1  99.2
## 
## [[931]]
##  [1]  99.5  97.9  92.4 101.9  94.0  99.7  99.1  87.3 111.6 101.9
## 
## [[932]]
##  [1]  96.4 105.1  89.4 118.8 105.0  97.1 111.3 101.7  94.1  86.0
## 
## [[933]]
##  [1]  99.6 106.2 103.3  86.0 104.2  94.5 100.1 112.5 103.3 105.3
## 
## [[934]]
##  [1]  91.7 102.2  85.5 108.6  92.4  87.9  91.4 106.5 101.9  79.6
## 
## [[935]]
##  [1]  78.2  96.0  91.1 100.4  94.5  95.7 102.9 106.5  95.9 104.6
## 
## [[936]]
##  [1]  81.8  92.6 102.8  96.2 106.3  88.5 107.9 107.8 101.8  99.3
## 
## [[937]]
##  [1] 108.9  97.8 102.9  88.7  93.1 103.9  94.0  96.8 110.8 101.7
## 
## [[938]]
##  [1] 105.0 110.1  97.4  96.8 110.4  83.0 103.8 101.1 115.8  98.2
## 
## [[939]]
##  [1] 102.0  87.2  96.5  89.0 106.0 100.8  96.6 102.6 113.6  93.4
## 
## [[940]]
##  [1] 105.2 100.3  89.4  83.9 112.6 115.4 112.3  90.2  96.4 119.4
## 
## [[941]]
##  [1] 107.5 106.6 118.3  88.7  95.2  94.7  95.8  89.1 100.9  98.0
## 
## [[942]]
##  [1]  90.7 118.5 100.6  76.0  96.8  74.4  97.6 103.8  94.5  99.7
## 
## [[943]]
##  [1] 103.3  96.2 113.8 118.8 108.1 109.7 123.4  98.7 101.7  84.5
## 
## [[944]]
##  [1]  99.4  94.6  98.6 101.3  98.7  97.2  75.2 112.2 106.3  82.0
## 
## [[945]]
##  [1] 100.3 114.3 117.8 124.6  94.4 109.5 114.2  92.3 105.8 103.0
## 
## [[946]]
##  [1] 112.8 102.6  97.5 104.9  89.3 106.6  96.4 104.6 102.3 102.8
## 
## [[947]]
##  [1]  92.8  98.9  95.6 106.0 120.2 105.6  87.8  88.3 100.3 110.0
## 
## [[948]]
##  [1] 114.2  88.9 101.0 101.3  98.9  87.6 106.3  80.9 106.9  84.2
## 
## [[949]]
##  [1]  96.6  98.5  93.3  94.3 104.7 113.0 100.4  94.1  93.3 107.2
## 
## [[950]]
##  [1]  95.4  84.5 100.4 109.1 104.6 117.1 124.7 106.2  98.2 112.7
## 
## [[951]]
##  [1] 107.5 121.2 103.5  98.4 108.4 102.2 104.1 113.5  87.3  94.0
## 
## [[952]]
##  [1]  92.8  90.9 100.6  95.2 106.8 112.9  93.2 104.1 103.2  90.7
## 
## [[953]]
##  [1] 102.6  92.1  89.4  81.7 117.1  98.7  96.7 114.3 121.3  92.8
## 
## [[954]]
##  [1]  87.8  99.2  85.5  93.8  99.0  94.8 116.8 102.3 101.2 116.7
## 
## [[955]]
##  [1] 115.1  96.8 100.1  90.4  93.1  85.5 106.5  97.7 105.6  97.9
## 
## [[956]]
##  [1]  85.4  89.4 107.5  92.4  85.8  83.8  94.1 103.5  96.5  94.7
## 
## [[957]]
##  [1]  99.3 100.8 109.4 100.6  98.7  96.3  89.9  98.7  86.5 114.7
## 
## [[958]]
##  [1] 102.0  80.8  87.3 107.0  77.1 106.9 103.0  92.8  94.2  87.0
## 
## [[959]]
##  [1]  88.2  96.2  85.3  97.0  94.4 101.5 105.0 102.6 106.1 101.6
## 
## [[960]]
##  [1]  93.6  97.7 113.6 116.0 104.6  89.6 103.3 112.2  89.0 111.1
## 
## [[961]]
##  [1]  84.6  98.0 113.4 100.4 106.8  98.8  92.1 113.2 103.5  95.1
## 
## [[962]]
##  [1]  87.4 103.1  96.1 107.2 110.0 118.5 100.1 101.6  96.0  92.9
## 
## [[963]]
##  [1]  76.4  88.0 106.4 116.5  86.1 107.5  95.7 107.9 117.4  90.4
## 
## [[964]]
##  [1]  79.2  97.0 106.9 109.5 104.9  98.7 130.7 109.6  96.2 101.8
## 
## [[965]]
##  [1] 108.1 104.6  99.8 101.9 104.8  94.1  97.5 108.0  95.8 106.3
## 
## [[966]]
##  [1]  88.9 109.1 112.7  95.4  84.2 103.0 102.4  84.4 106.0  79.7
## 
## [[967]]
##  [1]  92.3 116.5 107.8 101.1  71.6 100.8  89.3 100.4 101.3 104.6
## 
## [[968]]
##  [1]  97.0  98.5  95.1 101.3  93.5 106.1  90.4  86.9  99.1  95.4
## 
## [[969]]
##  [1] 104.5  84.7 102.6 109.8  91.1 107.8 108.3 105.9  89.0  96.9
## 
## [[970]]
##  [1] 103.2  85.6  91.5 104.8 110.7 103.3  95.0  93.7 119.3  96.6
## 
## [[971]]
##  [1] 106.9  88.7  89.9  96.0 103.6 108.6 100.1 104.7  99.0 103.4
## 
## [[972]]
##  [1]  85.6 100.6  97.9  98.2  93.8 117.3  91.6  97.2  91.6  97.3
## 
## [[973]]
##  [1] 104.7  77.7  98.2  97.1  88.6  98.4 102.7 102.6  95.0 123.1
## 
## [[974]]
##  [1]  96.7  84.0  94.5 109.6  92.5  99.3  96.0  93.1 113.2  81.5
## 
## [[975]]
##  [1]  99.8  98.3 114.3  99.4 110.3 102.4  91.6 103.8  89.0  88.1
## 
## [[976]]
##  [1] 112.1 102.1  84.2  93.9 106.1 102.8  95.6  90.5  97.3 109.1
## 
## [[977]]
##  [1]  94.3 109.6 106.5  97.4  81.8  91.7 106.5 118.2 108.3  90.1
## 
## [[978]]
##  [1] 102.4  96.1  94.4  89.0  92.3 108.4 118.8 106.4  88.3  92.9
## 
## [[979]]
##  [1] 121.1  95.4  92.1  95.4 123.9 103.6  97.1 110.9  86.0  98.8
## 
## [[980]]
##  [1] 107.0  88.8  95.1 104.2  86.1  79.8  97.1 120.4  92.0  86.2
## 
## [[981]]
##  [1]  98.8 112.3  90.6 106.2  97.2  80.3  99.4 103.4  97.8 101.3
## 
## [[982]]
##  [1]  91.3  93.0  98.6 113.2  86.5  92.1  99.6  87.6  86.6  97.1
## 
## [[983]]
##  [1]  95.0 105.5  96.1  85.3 124.6  95.1 123.9  90.6 105.4  93.5
## 
## [[984]]
##  [1] 110.7  93.7  99.8 105.4  96.7  92.9  98.0  81.4  98.0  94.8
## 
## [[985]]
##  [1] 100.2  83.8 106.2  99.4  89.3 112.8  98.6  82.8 115.5  94.2
## 
## [[986]]
##  [1] 101.9 116.2 106.5 100.6 102.6  94.8 108.9 102.1  93.7  94.6
## 
## [[987]]
##  [1] 105.3  90.5 107.1 108.4  90.3 112.0  96.5 114.6 104.3  85.2
## 
## [[988]]
##  [1] 107.2  91.9  95.5 103.8 110.4  95.2 101.3  84.4  78.8  81.2
## 
## [[989]]
##  [1]  91.9 110.2  90.6  90.3  97.1  89.1 105.9 102.0 106.9  90.7
## 
## [[990]]
##  [1]  99.1 100.1 104.1 101.2  92.7 107.3 103.6  98.8  95.7 107.8
## 
## [[991]]
##  [1] 117.5 114.7  95.4  98.9  95.3 101.8  96.7 116.7  96.5  95.6
## 
## [[992]]
##  [1]  98.8  98.1 106.9 105.3  84.2  93.4  95.7 109.4  99.8 105.0
## 
## [[993]]
##  [1]  99.2  95.6 106.6 123.3 100.1  66.0  90.4  97.7  84.4 103.2
## 
## [[994]]
##  [1]  94.2 107.0 109.4  81.9 105.6 109.7  93.2  90.7  80.6 109.6
## 
## [[995]]
##  [1] 120.8  98.8 111.1 112.3 101.0 100.4 120.5  95.5  88.2 112.4
## 
## [[996]]
##  [1]  94.0  85.2  96.6  91.6  90.1 122.7 100.1 105.6  78.9 101.0
## 
## [[997]]
##  [1]  82.0 104.7 107.3  95.7  94.6 113.2  89.1 103.1 104.9 107.4
## 
## [[998]]
##  [1]  98.8 101.6  90.2 109.4  94.1  89.8  96.3  92.4 110.8  93.6
## 
## [[999]]
##  [1] 123.7  98.3 109.3  94.3 102.3 111.3 113.8  97.7  84.0  97.0
## 
## [[1000]]
##  [1]  97.2  99.7 110.9  89.9  83.7 107.7  99.7 103.6  86.7  93.0
```

---
# Calculate all means

```r
map_dbl(samples, mean) %>% 
  head()
```

```
## [1]  95.8 103.2  99.9 102.2 101.2  96.4
```

--
* What's the `$sd$` of these means? That's the standard error.

```r
map_dbl(samples, mean) %>% 
  sd()
```

```
## [1] 3.14
```

---
# Sample size
Let's re-do this, pulling a sample of 100 each time.

```r
samples2 <- replicate(1000, rnorm(100, mean = 100, sd = 10),
                      simplify = FALSE) 
map_dbl(samples2, mean) %>% 
  sd()
```

```
## [1] 0.973
```

---
# Visualize the sampling distributions

```r
sample_means <- tibble(
  iter = rep(1:1000, 2),
  sample = rep(c(10, 100), each = 1000),
  mean = c(map_dbl(samples, mean),
           map_dbl(samples2, mean))
)
sample_means
```

```
## # A tibble: 2,000 x 3
##    iter sample      mean
##   <int>  <dbl>     <dbl>
## 1     1     10  95.75441
## 2     2     10 103.2204 
## 3     3     10  99.91284
## 4     4     10 102.2169 
## 5     5     10 101.2308 
## 6     6     10  96.37082
## # … with 1,994 more rows
```

---

```r
ggplot(sample_means, aes(mean)) +
  geom_density(aes(fill = factor(sample)), alpha = 0.3)
```

![](w7p2_files/figure-html/sampling_dist_vis-1.png)

---
# Fit a model

```r
m <- lm(cty ~ displ + class, mpg)
summary(m)
```

```
## 
## Call:
## lm(formula = cty ~ displ + class, data = mpg)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -5.269 -1.150 -0.016  1.034 12.978 
## 
## Coefficients:
##                 Estimate Std. Error t value Pr(>|t|)    
## (Intercept)       28.777      1.473   19.54  < 2e-16 ***
## displ             -2.172      0.175  -12.43  < 2e-16 ***
## classcompact      -3.599      1.252   -2.87   0.0044 ** 
## classmidsize      -3.676      1.206   -3.05   0.0026 ** 
## classminivan      -5.595      1.306   -4.28  2.7e-05 ***
## classpickup       -6.182      1.121   -5.51  9.6e-08 ***
## classsubcompact   -2.629      1.237   -2.13   0.0346 *  
## classsuv          -5.599      1.087   -5.15  5.7e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.25 on 226 degrees of freedom
## Multiple R-squared:  0.729,	Adjusted R-squared:  0.721 
## F-statistic: 86.9 on 7 and 226 DF,  p-value: <2e-16
```

---
# Visualize with standard errors

```r
tidied_m <- broom::tidy(m, conf.int = TRUE)

tidied_m
```

```
## # A tibble: 8 x 7
##   term          estimate std.error  statistic      p.value  conf.low
##   <chr>            <dbl>     <dbl>      <dbl>        <dbl>     <dbl>
## 1 (Intercept)  28.77682  1.472892   19.53763  1.905873e-50 25.87446 
## 2 displ        -2.171562 0.1746638 -12.43281  2.197130e-27 -2.515740
## 3 classcompact -3.599125 1.252190   -2.874265 4.436052e- 3 -6.066585
## 4 classmidsize -3.675526 1.206253   -3.047061 2.585762e- 3 -6.052466
## 5 classminivan -5.595070 1.305993   -4.284151 2.714490e- 5 -8.168550
## 6 classpickup  -6.182466 1.121448   -5.512931 9.600087e- 8 -8.392297
## # … with 2 more rows, and 1 more variable: conf.high <dbl>
```

---

```r
ggplot(tidied_m, aes(term, estimate)) +
  geom_hline(yintercept = 0,
             color = "cornflowerblue",
             linetype = 2) +
  geom_errorbar(aes(ymin = conf.low, ymax = conf.high)) +
  geom_point() +
  coord_flip()
```

![](w7p2_files/figure-html/broom_viz1-1.png)

---
# Multiple error bars

```r
library(colorspace)
ggplot(tidied_m, aes(term, estimate)) +
  geom_hline(yintercept = 0,
             color = "cornflowerblue",
             linetype = 2) +
  geom_errorbar(aes(ymin = estimate + qnorm(.025)*std.error, 
                    ymax = estimate + qnorm(.975)*std.error),
                color = lighten("#4375D3", .6),
                width = 0.2,
                size = 0.8) + # 95% CI
  geom_errorbar(aes(ymin = estimate + qnorm(.05)*std.error, 
                    ymax = estimate + qnorm(.95)*std.error),
                color = lighten("#4375D3", .3),
                width = 0.2,
                size = 1.2) + # 90% CI
  geom_errorbar(aes(ymin = estimate + qnorm(.1)*std.error, 
                    ymax = estimate + qnorm(.9)*std.error),
                color = "#4375D3",
                width = 0.2,
                size = 1.6) + # 80% CI
  geom_point() +
  coord_flip()
```

---
![](w7p2_files/figure-html/multiple-error-eval-1.png)

---
# Add levels to legend
Include the color spec in `aes()`

```r
p <- ggplot(tidied_m, aes(term, estimate)) +
  geom_hline(yintercept = 0,
             color = "cornflowerblue",
             linetype = 2) +
  geom_errorbar(aes(ymin = estimate + qnorm(.025)*std.error, 
                    ymax = estimate + qnorm(.975)*std.error,
*                   color = "95%"),
                width = 0.2,
                size = 0.8) + 
  geom_errorbar(aes(ymin = estimate + qnorm(.05)*std.error, 
                    ymax = estimate + qnorm(.95)*std.error,
*                   color = "90%"),
                width = 0.2,
                size = 1.2) + 
  geom_errorbar(aes(ymin = estimate + qnorm(.1)*std.error, 
                    ymax = estimate + qnorm(.9)*std.error,
*                   color = "80%"),
                width = 0.2,
                size = 1.6) 
```

---

```r
p
```

![](w7p2_files/figure-html/show-p-1.png)

---

```r
p + 
  scale_color_manual("Confidence Interval",
                     values = c("#4375D3",
                                lighten("#4375D3", .3),
                                lighten("#4375D3", .6))) +
  geom_point() +
  coord_flip()
```

---
![](w7p2_files/figure-html/add_legend-eval-1.png)

---
# Density stripes

```r
#devtools::install_github("wilkelab/ungeviz")
library(ungeviz)
ggplot(tidied_m, aes(estimate, term)) +
  stat_confidence_density(aes(moe = std.error),
                          fill = "#4375D3",
                          height = 0.6) +
  xlim(-10, 35) +
  geom_point()
```

![](w7p2_files/figure-html/density-stripes-1.png)

---
# Actual densities

```r
library(ggridges)
ggplot(tidied_m, aes(estimate, term)) +
  stat_confidence_density(aes(moe = std.error, 
                              height = stat(density)),
                          geom = "ridgeline",
                          confidence = 0.95,
                          min_height = 0.001,
                          alpha = 0.7,
                          fill = "#4375D3") +
  xlim(-10, 35) 
```

![](w7p2_files/figure-html/densities-1.png)

---
class: inverse-blue center middle
# HOPs
### Hypothetical Outcome Plots (and related plots)

---
# Standard regression plot

```r
ggplot(mtcars, aes(disp, mpg)) +
  geom_point() +
  geom_smooth()
```

![](w7p2_files/figure-html/loess1-1.png)

---
# Alternative

![](w7p2_files/figure-html/bootstrap1-1.png)

---
# How?
### Bootstrapping

```r
row_samps <- replicate(100,
                       sample(seq_len(nrow(mtcars)), 
                              nrow(mtcars), 
                              replace = TRUE),
                       simplify = FALSE)
row_samps
```

```
## [[1]]
##  [1] 31  6 32 12  1 14  2 11 20 10 26 10 22 30 25 25  5 31 19 13 19 20 17  1
## [25]  4 12 12 25 20 21 16 23
## 
## [[2]]
##  [1] 11 23 14  1 24 20 10 30 27 24 22 23 25  1 18 18 25  8  8 16 25 19 31 13
## [25] 11 10 21  6 14 14 12 24
## 
## [[3]]
##  [1] 27 29 22  5  6  8 14 16  7 13 17 13 21 10  7 21  7 20 30 30  5 10  9  8
## [25]  4 15 16 21 27 23 19  7
## 
## [[4]]
##  [1] 16  7  8 28  3 17 13 26  8 30  3 32 20 10  2  6 19 21 11  6 16  9 17  4
## [25] 25  4 27 29 19 21  1 16
## 
## [[5]]
##  [1]  6 13 29  8  2 14 11  3 27  3 28 31 32  3  6 16  6 18 27  2 10 15 30 12
## [25] 20 26 19  7 16 31 20  3
## 
## [[6]]
##  [1]  7  8 30 22  9 13 23  9 20  7 13 20 30  1 30 23  6 16  8 32 22 10 28 27
## [25]  5  2 24  5 10 30  3  6
## 
## [[7]]
##  [1] 27 20  2 12 26  7 13 23 25 22 18  8 30 17  1 13 28 22 13  9  9 20 22  8
## [25] 13 27 29  2 23 21 21 25
## 
## [[8]]
##  [1] 12  3 19 18 17 22 10 28 31 12 17 18 20 22 23  2 15 15  4 32 17 15 25 24
## [25]  3  5 15  3 16 31 17 22
## 
## [[9]]
##  [1] 24  9 23 29 24 13 25 20 23 20 27  4 24 25 17  7 20 14 27 11  3 27  7 24
## [25] 21  7 18 26 32 31 30 18
## 
## [[10]]
##  [1]  6 11 21  5  7 11  9 29 15  3 26  2  1  2 18 28  1  2  5  1 16  3 10  8
## [25] 14  3 13  2 30 24 28 15
## 
## [[11]]
##  [1] 16 27 18  4 22 14 19 26 32 19  2 28 13 23 12 14 10 24  7  7 13 17 32 19
## [25]  9  1 27 15 30 23 11  2
## 
## [[12]]
##  [1] 22  4 24  3 29 28 26 12 29 32 32 23 10 16  2 13 14  6  1  7  1  3 17 31
## [25] 21 15 31 20  8 17 19 16
## 
## [[13]]
##  [1] 22 28 31 28 14 23 14 26  8 22 19  8 18  8  9 19  9  8 20 30  4 15 30  6
## [25] 32 32  8 10 18 12  5  5
## 
## [[14]]
##  [1] 26 11 12  7 18 10 29  1  1  6 27 19 10 30 29  5  4 28 32 31 13 25 25 32
## [25]  7 15 16 16 28 11 16  2
## 
## [[15]]
##  [1] 23 17 16  6  9 12 10 19 17 26  1  7  7 22 24  3  6 20  8 18  9  6 17  3
## [25]  1 10 22  6 19 24  4 19
## 
## [[16]]
##  [1] 30  1 27  7 19 13 29 16  8 23 18 13  4 29  1 32  2  2  8 24 13 12 30 19
## [25] 17  1  4 23 13 24 14  9
## 
## [[17]]
##  [1]  8  9 31 10 12 15 26 11 22 22 25 28  2 15 11 31 12 29 21 15  4  1 28 22
## [25] 20 17 22 24 12 24 13  6
## 
## [[18]]
##  [1] 15 17 25 32  6  4 29 32 20 24 29  4 18 16 16  9 22 18 10  3  9 23  5  4
## [25] 18 30 16  1 29 28 24  6
## 
## [[19]]
##  [1]  8  1 19  2  7  7 24 23 17 17 27 10 14 25 13 12  2 10 18 13  5 22  3  5
## [25] 28 31 29 20 12 16 31 31
## 
## [[20]]
##  [1] 29 10 28 10  5 12  4  3  3 26 26 12  4 25  1  9 23 22 11 15 10 28 29 30
## [25]  4 15  7 25 21 27 24 13
## 
## [[21]]
##  [1]  8  1 28 22 30 13 24 32 23 31 25 16  5 22  9 18 22 16 24 32 13 29 13 16
## [25] 17 22 11 10 10 20  1  2
## 
## [[22]]
##  [1] 14  1 21  3 30 29 26 20  4 12 27  5 11 20 29  1  4 19 15 16 29 10  8 23
## [25] 17 19  5  1 19 28 13 21
## 
## [[23]]
##  [1] 30 19 21  6 32 16  7 10 15 29 29  1  5 23 31 23 16 15 27  2  6 20 20 26
## [25] 13 10 14 15 27  9 30 16
## 
## [[24]]
##  [1]  4  2 23  3  1 27 11  8  6 32 28 12  6 21  4 19 30 14 20 13 25 18  4 32
## [25]  5  8 16 21 27  1 10  9
## 
## [[25]]
##  [1]  6 31 21  3  1 26 18 29 26 27  2 16 14 21  1 32  1 11 24 11  4 11 11 20
## [25] 29 16 19  3 27  1 15 31
## 
## [[26]]
##  [1] 11 12  3 30 17 21 28 19 11  3 26 32  9  9 21 32  2 28 30  9 11 26  7  4
## [25] 24  1  4 14 26 17  7 26
## 
## [[27]]
##  [1] 31  3  2  6 26 10  6 15 16  5  6 13 16  5 12 29  1 28 17 11 17 21 14 26
## [25]  5 31  7  4 31  4  1 26
## 
## [[28]]
##  [1] 25  9 32  6 18  7 11 23 12 10 23 30 19 29  6  5 13 12  3 26 13  2 31 12
## [25] 32 32  6 17  2 23 23  2
## 
## [[29]]
##  [1] 28  2  2 30 14 22 24 14 23 14  4 29  5 22 22  1 32  1 19  5 13 14  7 18
## [25] 14  4 23  2 20 21 13  3
## 
## [[30]]
##  [1] 23 30 29 18 23 11 10 13  8 21 31 24 18 16  3 11 23 15  1  9 32  2 21 13
## [25]  5 10  4  4  1 27 13  8
## 
## [[31]]
##  [1] 21 23 13 15 11 25 12 27  2 31 21  8 29 11 27 17 29 14 25  8 27 31 21 30
## [25]  7 26 32 31  2 11 14 30
## 
## [[32]]
##  [1] 11  3 11 32 18 27 13 28  4 11 25 12  7  3 11 16  7 22 13  5  4 24 32 26
## [25] 31 17  5 21 12 31 14 32
## 
## [[33]]
##  [1] 16 21 23 17  5  5 22 12 27 32 14  1 17 12  4 21  1 19 12 32 27  4 25  4
## [25]  2  7 13 19 14  3 12 19
## 
## [[34]]
##  [1]  7 12 32 28 20 32  3 13 32  6 32 12 10  8 27  4  5 10 18 16 14  7 22 19
## [25] 17  9 11 26  8  7 26 32
## 
## [[35]]
##  [1] 24  8 10 16 31 19 11  1 21 11  2 10  1 31 21 24 19 12  7 10  5 17  6 11
## [25] 31 18  5 22 10 14 22 20
## 
## [[36]]
##  [1] 13 31 13  9 16  7  7 21 22 25 24  8 20 31 22 21 10  9  1 26 25 32 12 22
## [25]  2 14  7  4 31 12 32 27
## 
## [[37]]
##  [1] 14 14  9 20 19 27  4 17 13 12  4 20 25 14 10 12 23  4 15  3  4 27 19 23
## [25]  7  7 21  2 23  1  8 29
## 
## [[38]]
##  [1] 12 26 21  5  7 18 30 20 15 21 32 19 24 19 32  8  3  3  3 26 21 25 31 23
## [25] 32 24 18 30 16  6 11  1
## 
## [[39]]
##  [1] 13 18 21 17 27 22 24  1 18 17  8 11 17 27 25 10 22 23  8 12 11  8  9 32
## [25] 30 14 16 32 22  1 14  6
## 
## [[40]]
##  [1] 19 16 30 12 26  3 19  3 20  7  7  3  7 25 25 12 14 10 15 30 23 13 25  7
## [25] 23  8 12  6 17  1 14  2
## 
## [[41]]
##  [1] 26 19 19  3 32 10  3 23  2 14  1  6  8 30 28 31 13 16  5  2 31 31  5 13
## [25] 10  7 14 12 17 16  8 26
## 
## [[42]]
##  [1] 19  7 21  6  2 30 17 14 20 16 23 13 30 32 15 28 28 28 26 28 25 26 25 21
## [25] 20 28  5 16 32  3 14 18
## 
## [[43]]
##  [1] 20  3 26  9 10  6 13  2  1 28  5 32 19 21  2 11  8 19  2 20 27 15 25 26
## [25]  5 18  8 30 27 14  2  3
## 
## [[44]]
##  [1]  4 12 11  3 18 17 10 26 21 28 14 10  8 28 13 27  7 21  4 25 25 12 27  2
## [25] 15  1  3 16 13 17  7 17
## 
## [[45]]
##  [1]  9  3 28 18 28 29 23 20 28  8 26 30 31  6 21 28  7 22 27  8 26 27  4  6
## [25]  1  8 11 12 32 15 19  1
## 
## [[46]]
##  [1] 24 15  5  3 11  8 23 32 28 17 19 16 31 20 29 22 20  1  1 28 32  6 25 25
## [25] 25 19  8 12  3 11  2 21
## 
## [[47]]
##  [1] 22 32 30 10 27  2  1 20  9  3 21 19 28 19  5  8 14 27 26  1 27 19 29 11
## [25] 27 31 11 19  9 28 22 23
## 
## [[48]]
##  [1] 28  4 24  9  6 16 10  3  3 22  9 16 30 31 14 29 13  2 22  1 23  9 31 31
## [25]  3 22 12  1 26 29 17 10
## 
## [[49]]
##  [1] 24 24 31 32  2  4 31  4 11 20 15 12  7 14  3 20  2 17 21  5 18  1 13 31
## [25]  5  3 19 22 32  2 27 14
## 
## [[50]]
##  [1] 32 15 17 30 30 30  8  5 14  6 21  4 26  5 12  2  9 15 14 19 27 13 23  3
## [25] 16 27  3 24  7  4 22 30
## 
## [[51]]
##  [1]  6 21 31 26 25 13 16 14 31  6 10 30 23 32 24 24 31 11 13 10 20 21 28 25
## [25] 14 26 15  7 10 17 31 23
## 
## [[52]]
##  [1] 11 19 21  7 12  2 23 16  8  3 12 23 12  5 23 22 12 28 17 28  4  6  9  1
## [25] 11  2  4  3 14 15  8  1
## 
## [[53]]
##  [1]  5 14 23  8 22 25 23 27  8 18 19 11  1 27 26  6 17 12 14 13 13  9 28 14
## [25]  4  2 18 24  5  6 22 19
## 
## [[54]]
##  [1] 32 13 21 14  5 31 18 18 30 31 23 10  9 26 28  6 18 13 22 31 11  9 24 24
## [25] 32  4  8 13 11  1  1 27
## 
## [[55]]
##  [1] 14 18 19  2 19  5 10 25 17 22  6  8 28 28 14 19 12 20 15 28 30  6 30  3
## [25]  3  4 17 23  7 16  9  1
## 
## [[56]]
##  [1]  8 12 12 10 30 25  7  8 32 20  7  7  5 23  8 20 29 16  9  3 25  9 20 24
## [25] 30 16 29  8 30 14  5 25
## 
## [[57]]
##  [1] 21 17  5  9 30  8 31 23  9 27  3 10 26 20 31 20 28  2 16 24  2 20 19 26
## [25] 20 30  5 23 17 23 30  6
## 
## [[58]]
##  [1] 29  5  7 27 15  8 22  5  4  9 28  6 22 26 14 11 29 21 25 12 27  2  1 25
## [25] 32  7 21  9 25  2  8 16
## 
## [[59]]
##  [1]  4 24  8  8 18 21  5 18 14 30 25  1 16  5 31  4 31  6 32 28 22 13  1 23
## [25] 16 20 17 18 27 14  6 29
## 
## [[60]]
##  [1] 13 13  6 29 30 23 24 29  5 22  6 17 31 31  8  5 17 31 13 29 17 20 24 14
## [25]  7 22 17  4 14 32 26 29
## 
## [[61]]
##  [1]  9  6 26  8  2 14 18 12 19 10  1 27 22  7 22  3  6  1 11  1 14 29 31 15
## [25]  6  2  2  8 11  6 22 25
## 
## [[62]]
##  [1] 28  6 24 17 32 29 16 20 25 28 12 24 24 27  2  6  2 23 32 28 16  1 17  9
## [25] 18 20 21  4 27 14 28  2
## 
## [[63]]
##  [1]  5  5 14 20 26 15  7 18 18  9 12 21 18 16  9  3 13  8 27  2 32 14 13 10
## [25] 28 27 26  4  5 12  8 23
## 
## [[64]]
##  [1]  4 17  2 20 30 32 24  1 16 14 24 13  1  5 26 17  9  2 22  3 31 11 28 18
## [25] 16 20 21 28  1  1 21 17
## 
## [[65]]
##  [1] 30 20  2  5 28  2 32 24  8 27 28 30 30 23  4 30 30 18 20 30 12  1 11  4
## [25]  5 15 10  4 25 29 20 14
## 
## [[66]]
##  [1] 10 10 14  2 20 25 13 18 20 11 11 16 10 13 12 32  4 24 16 29 26 16 15 17
## [25] 24  8 32 20 32  2 16 13
## 
## [[67]]
##  [1] 31 19 12 28 11 17 16 15 22 29 18  8 32  7  2  3 13 20  1 16 28  6 14 25
## [25]  6 24 21 20 19 22  9 17
## 
## [[68]]
##  [1] 23 11 28  9  9 19 21  3 11  3 26  5  4 26 16 14 12 24 28 22 18 22 10  2
## [25]  4 17  5 15  5 13 19  1
## 
## [[69]]
##  [1] 21 25 27 19  5 32  3 22  2 14 31 20 11 10 30 21 12 19 13  6  2 12 21 19
## [25]  8  4 16 26 15 32 11  4
## 
## [[70]]
##  [1] 27 11 28 20 31 27 15 30 13  5  9 15 25 24 10 16 32 11 22  6 20 17 11 29
## [25] 25 18 12  1 16  8 23  2
## 
## [[71]]
##  [1] 24 31 13 30 30 20 22 13 13  4 28 22  4 31  3  2 12 28 31  1  3 31  9 32
## [25] 12 20 26  3 13  6 13 22
## 
## [[72]]
##  [1] 15  2 14 10  3  4  9 17 25 20 11 20 32  4 14 16 31 28 27 17 30 10 25 13
## [25] 23 15 14 29  1  8 10 31
## 
## [[73]]
##  [1] 13 27 15  9 31 28 28 24  4 19  3 17 31  8 18 27  6 32 21 10 21 26  2 20
## [25]  3  3 20 21  8 12 13  1
## 
## [[74]]
##  [1]  3 32 25 26 30 24 20  5 15 18 14 32 16  5  2  3 32 15  5  5 18  9  5 28
## [25] 25 20 25 16 20  5 12 16
## 
## [[75]]
##  [1] 25 29 27 17 32  9 30  4 26 27  4 25 24 16 26 12  4 23  7 25  8 14 12 18
## [25] 10  2 10  8 22 18 30  8
## 
## [[76]]
##  [1]  4  6  3  6 15 21 21 30 14 28 15  5 20 25  2 11 24 10 12 16 27 28 22 20
## [25] 31 32  4 19 23  1 29 24
## 
## [[77]]
##  [1] 25 24 20 10 11 14 15 22 23  5 16  7 30  9 19  5 20 20 19 19 12 20  6 22
## [25] 17  4  4 31  2 19  9  2
## 
## [[78]]
##  [1]  7 25 23 27 32 12  5 31 15  2 30  9 21  4 23 24 13  2 18  8 27  6 10 29
## [25] 12  5  3 12 29 19 31 22
## 
## [[79]]
##  [1] 13 23 12  7 13  2  8  3 27 10 18 18  5 17 12 20 11 10  2 10  5 10 26 27
## [25]  8 30  1 13  3 17 22  9
## 
## [[80]]
##  [1] 14 12 13  4 23 19 30  4 10  7 20 32 10  5  8 27 18  6 15 19 30 22  6 26
## [25] 21  5  2  2  3 13 26 29
## 
## [[81]]
##  [1] 16 16 26 22  7 17  2 16  9 14 32 27 22 29 25  6 28 32  4  7 17  2 25 26
## [25] 17 21 21 16  6 28 21  2
## 
## [[82]]
##  [1] 26 19  8 17 20 22 23  9  3  6  3 25  8 27 15 16 15 21 16 11  5 27 16 22
## [25] 12  7 20  5 18 10 13 17
## 
## [[83]]
##  [1] 20 31 30 20 23 32 11  5 21 32 21 12 32 23  3  7 22 31 16  6 30 10  9 31
## [25]  1 28 24 11 28 15 31 22
## 
## [[84]]
##  [1] 17  3 16 27 24 30 10 14 11 28 26 17 26  4 24 27 25 10 25 32 17  2 11 10
## [25]  9 10  2 11 19 11 11 10
## 
## [[85]]
##  [1] 13 23  2  9 13 20 26 30 18  3  9 24 12 15 25 24  5 31 18 11  4 28 16 19
## [25] 23 30  6  7 24 30 23 15
## 
## [[86]]
##  [1] 13 22  3 22  7 12  2 21 17  8 24  8  2 15 19 25 11 22 14 30 12 22 25 15
## [25] 16 32 25  7 15 24 30 32
## 
## [[87]]
##  [1]  5 10 14 20  3 20 32 25 22 28 24 16  5 17 18 12  7 17 14  8 23  5 28  2
## [25] 13  7 13 12 28  2  9 15
## 
## [[88]]
##  [1]  3  7 13 20  2  5 20  8  1 29  3 26 32 12 26 22 17 10 10 17 23 25 23  2
## [25] 10  3 11 14 11 28  2 16
## 
## [[89]]
##  [1] 16 19 23 18 12  5 22 10 17 24 23  9 15 12 32  8 29 16  1 13 27 20 13 31
## [25]  3 25 16 15 14  8 23 27
## 
## [[90]]
##  [1] 13  3 31 29  3 18 30 21  6  8 30 17 11  4  4  4  2  3 30 21 17  2  7  8
## [25]  5 15  6 16 19  2  9  3
## 
## [[91]]
##  [1] 21 20 14 22 13  5 10 22 23 21 23  2 30 21 26 20 11 16 31 29 24  9 16 32
## [25] 24  9  2 16 28  9 31 31
## 
## [[92]]
##  [1]  3 32  3 13 26  3 12  2 16 14 31 25 31  5 11  1  9  9 24 31 16  6 14 26
## [25] 24 14 17 25 11  5  9 25
## 
## [[93]]
##  [1] 14 16  4 11 28 29 29 31 30 15  7 17 27 17 31 11  1 11 14  1 20 32  9 20
## [25] 15 10 15 21 14 21  7  1
## 
## [[94]]
##  [1]  3  4 31  3  5  6 27 12 27 16 10 27 13  3 28  1 10  6 28 30  5  2 23 17
## [25] 12 23 29  4 29 15 10 31
## 
## [[95]]
##  [1]  7 13 11 18 14 22  3  4 31 30 14 11 20 22  9  3 26 17  1 17 19 12 22 28
## [25] 12  5  7 13 12 23 32 12
## 
## [[96]]
##  [1] 18 20 10 23 14 17 15  6 27  6  4 25 16 10 21 30  4 26 21 25 23 27 22 24
## [25] 10  8 20  5 10 13 30 10
## 
## [[97]]
##  [1]  2  2  4 25 30 29  9 18  7 31 16 23 26  6  4 13  9  4 19 25  1 21 25  8
## [25] 10 30  6 16  3 13 29 27
## 
## [[98]]
##  [1] 14 14  5 17 20 24 23  8  7 24 19 13 29  2 25 18 27 19 15 13 18  7  6 25
## [25]  7 27 12 14 14  4 29 11
## 
## [[99]]
##  [1] 22 28  7 25  1 15  3 15 15 25  6  2  5 25  2  4  4 30 18 32 24  8 23  4
## [25] 30 29 24 13  1 10 21 26
## 
## [[100]]
##  [1] 30 16  7 14 15 19 10  2  2 30  7 31 26  7  8 31 14  8 18  2 15 15  6 11
## [25] 21 20 16 25 26  2  5 28
```

---
# Extract samples

```r
d_samps <- map_df(row_samps, ~mtcars[.x, ], .id = "sample")
head(d_samps)
```

```
##                   sample  mpg cyl disp  hp drat   wt qsec vs am gear carb
## Maserati Bora...1      1 15.0   8  301 335 3.54 3.57 14.6  0  1    5    8
## Valiant...2            1 18.1   6  225 105 2.76 3.46 20.2  1  0    3    1
## Volvo 142E...3         1 21.4   4  121 109 4.11 2.78 18.6  1  1    4    2
## Merc 450SE...4         1 16.4   8  276 180 3.07 4.07 17.4  0  0    3    3
## Mazda RX4...5          1 21.0   6  160 110 3.90 2.62 16.5  0  1    4    4
## Merc 450SLC...6        1 15.2   8  276 180 3.07 3.78 18.0  0  0    3    3
```

```r
tail(d_samps)
```

```
##                              sample  mpg cyl  disp  hp drat   wt qsec vs am
## Lincoln Continental.1...3195    100 10.4   8 460.0 215 3.00 5.42 17.8  0  0
## Pontiac Firebird...3196         100 19.2   8 400.0 175 3.08 3.85 17.1  0  0
## Fiat X1-9.1...3197              100 27.3   4  79.0  66 4.08 1.94 18.9  1  1
## Mazda RX4 Wag.3...3198          100 21.0   6 160.0 110 3.90 2.88 17.0  0  1
## Hornet Sportabout...3199        100 18.7   8 360.0 175 3.15 3.44 17.0  0  0
## Lotus Europa...3200             100 30.4   4  95.1 113 3.77 1.51 16.9  1  1
##                              gear carb
## Lincoln Continental.1...3195    3    4
## Pontiac Firebird...3196         3    2
## Fiat X1-9.1...3197              4    1
## Mazda RX4 Wag.3...3198          4    4
## Hornet Sportabout...3199        3    2
## Lotus Europa...3200             5    2
```

---
# Plot both data sources

```r
ggplot(mtcars, aes(disp, mpg)) +
  geom_point() +
  stat_smooth(aes(group = sample),
              data = d_samps,
              geom = "line",
              color = "#4375D3",
              fullrange = TRUE,
              size = 0.1)
```

---
![](w7p2_files/figure-html/bootstrap2c-eval-1.png)

---
# Note, they match up

```r
ggplot(mtcars, aes(disp, mpg)) +
  geom_point() +
  geom_smooth(color = "magenta") +
  stat_smooth(aes(group = sample),
              data = d_samps,
              geom = "line",
              color = "#4375D3",
              fullrange = TRUE,
              size = 0.1)
```

---
![](w7p2_files/figure-html/bootstrap2d-eval-1.png)

---
# HOPs
Hops animate the process, so you can't settle on one "truth"

![](img/loess_hop.gif)

---
# How?
`gganimate::transition_states`

```r
library(gganimate)
ggplot(mtcars, aes(disp, mpg)) +
  geom_point() +
  stat_smooth(data = d_samps,
              geom = "line",
              size = 2,
              color = "#4375D3",
              fullrange = TRUE) +
  transition_states(sample, 
                    transition_length = 0.5,
                    state_length = 0.5) +
   ease_aes('linear') # Smoother transitions
```

---
# Another example
Canada has the highest average rating for their chocolate bars in the world, according to a recent study. But the sample size is also smaller than other countries, like the US.

How certain are we that Canada's chocolate is better? Compare the ratings of a randomly chosen Canadian chocolate bar to a randomly chosen US Chocolate bar.

---
class: middle

![](https://github.com/wilkelab/ungeviz/raw/master/man/figures/README-cacao-samples-anim-1.gif)

---
# Another example
## From Dr. Kay again

---
# Conclusions
* Lots of tools at your disposal (perhaps so many it can be difficult to choose)
* Do try to communicate uncertainty whenever possible

--
* I'd recommend checking out [Clause Wilke's talk](https://resources.rstudio.com/rstudio-conf-2019/visualizing-uncertainty-with-hypothetical-outcomes-plots) from `rstudio::conf(2019L)`, where he talks about the [ungeviz](https://github.com/wilkelab/ungeviz) package.

---
class: inverse-green middle

# Next time
## Tables and Fonts