ETC5510: Introduction to Data Analysis

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# .monash-blue.outline-text[ETC5510: Introduction to Data Analysis]

.bottom_abs.width100[

Lecturer: *Nicholas Tierney & Stuart Lee*

Department of Econometrics and Business Statistics

ETC5510.Clayton-x@monash.edu

May 2020

]

]]

---
# Recap

- Models as functions
- Linear models

---
# Overview

- Correlation
- Model basics
- Let's look at  `$R^2$` again
- Using many models
  
---
# Other Admin

## Project deadline (Next Week)

Find team members, and potential topics to study (ed quiz will be posted soon)

---
# What is correlation?

- Linear association between two variables can be described by correlation
- Ranges from -1 to +1

---
# Strong Positive correlation

As one variable increases, so does another

---
# Strong Positive correlation

As one variable increases, so does another variable

---
# Zero correlation: neither variables are related

---
# Strong negative correlation

As one variable increases, another decreases

---
# STRONG negative correlation

As one variable increases, another decreases

---
# Correlation: The animation

---
# definition of correlation

For two variables `$X, Y$`, correlation is:

`$$r=\frac{\sum_{i=1}^{n} (x_i-\bar{x})(y_i-\bar{y})}{\sqrt{\sum_{i=1}^{n}(x_i-\bar{x})^2}\sqrt{\sum_{i=1}^{n}(y_i-\bar{y})^2}} = \frac{cov(X,Y)}{s_xs_y}$$`

---
class: bg-main1

# Dance of correlation

---
class: transition

# Remember! Correlation does not equal causation

---
# What is `$R^2$`?

- (model variance)/(total variance), the amount of variance in response explained by the model. 
- Always ranges between 0 and 1, with 1 indicating a perfect fit. 
- Adding more variables to the model will always increase `$R^2$`, so what is important is how big an increase is gained. - Adjusted `$R^2$` reduces this for every additional variable added.

---
# unpacking lm and model objects

```r
(pp <- read_csv("data/paris-paintings.csv", na = c("n/a", "", "NA")))
```

```
## # A tibble: 3,393 x 61
## name sale lot position dealer year origin_author origin_cat school_pntg
## <chr> <chr> <chr> <dbl> <chr> <dbl> <chr> <chr> <chr> 
## 1 L176… L1764 2 0.0328 L 1764 F O F 
## 2 L176… L1764 3 0.0492 L 1764 I O I 
## 3 L176… L1764 4 0.0656 L 1764 X O D/FL 
## 4 L176… L1764 5 0.0820 L 1764 F O F 
## 5 L176… L1764 5 0.0820 L 1764 F O F 
## 6 L176… L1764 6 0.0984 L 1764 X O I 
## 7 L176… L1764 7 0.115 L 1764 F O F 
## 8 L176… L1764 7 0.115 L 1764 F O F 
## 9 L176… L1764 8 0.131 L 1764 X O I 
## 10 L176… L1764 9 0.148 L 1764 D/FL O D/FL 
## # … with 3,383 more rows, and 52 more variables: diff_origin <dbl>, logprice <dbl>,
## # price <dbl>, count <dbl>, subject <chr>, authorstandard <chr>, artistliving <dbl>,
## # authorstyle <chr>, author <chr>, winningbidder <chr>, winningbiddertype <chr>,
## # endbuyer <chr>, Interm <dbl>, type_intermed <chr>, Height_in <dbl>, Width_in <dbl>,
## # Surface_Rect <dbl>, Diam_in <dbl>, Surface_Rnd <dbl>, Shape <chr>, Surface <dbl>,
## # material <chr>, mat <chr>, materialCat <chr>, quantity <dbl>, nfigures <dbl>,
## # engraved <dbl>, original <dbl>, prevcoll <dbl>, othartist <dbl>, paired <dbl>,
## # figures <dbl>, finished <dbl>, lrgfont <dbl>, relig <dbl>, landsALL <dbl>,
## # lands_sc <dbl>, lands_elem <dbl>, lands_figs <dbl>, lands_ment <dbl>, arch <dbl>,
## # mytho <dbl>, peasant <dbl>, othgenre <dbl>, singlefig <dbl>, portrait <dbl>,
## # still_life <dbl>, discauth <dbl>, history <dbl>, allegory <dbl>, pastorale <dbl>,
## # other <dbl>
```

---
# unpacking linear models

```r
ggplot(data = pp, aes(x = Width_in, y = Height_in)) +
  geom_point() +
  geom_smooth(method = "lm") # lm for linear model
```

---
class: transition

# template for linear model

.large[
`lm(<FORMULA>, <DATA>)`

`<FORMULA>`

`RESPONSE ~ EXPLANATORY VARIABLES`
]

---
# Fitting a linear model

```r
m_ht_wt <- lm(Height_in ~ Width_in, data = pp)

m_ht_wt
```

```
## 
## Call:
## lm(formula = Height_in ~ Width_in, data = pp)
## 
## Coefficients:
## (Intercept)     Width_in  
##      3.6214       0.7808
```

---
class: transition
# using tidy, augment, glance

---
# tidy: return a tidy table of model information

.large[
`tidy(<MODEL OBJECT>)`
]

```r
tidy(m_ht_wt)
```

```
## # A tibble: 2 x 5
## term estimate std.error statistic p.value
## <chr> <dbl> <dbl> <dbl> <dbl>
## 1 (Intercept) 3.62 0.254 14.3 8.82e-45
## 2 Width_in 0.781 0.00950 82.1 0.
```

---
# Visualizing residuals

---
# Visualizing residuals (cont.)

---
# Visualizing residuals (cont.)

---
# glance: get a one-row summary out

.large[
`glance(<MODEL OBJECT>)`
]

```r
glance(m_ht_wt)
```

```
## # A tibble: 1 x 11
## r.squared adj.r.squared sigma statistic p.value df logLik AIC BIC deviance
## <dbl> <dbl> <dbl> <dbl> <dbl> <int> <dbl> <dbl> <dbl> <dbl>
## 1 0.683 0.683 8.30 6749. 0 2 -11083. 22173. 22191. 216055.
## # … with 1 more variable: df.residual <int>
```

---
# AIC, BIC, Deviance

- **AIC**, **BIC**, and **Deviance** are evidence to make a decision
- Deviance is the residual variation, how much variation in response that IS NOT explained by the model. The close to 0 the better, but it is not on a standard scale. In comparing two models if one has substantially lower deviance, then it is a better model.
- Similarly BIC (Bayes Information Criterion) indicates how well the model fits, best used to compare two models. Lower is better.

---
# augment: get the data

.large[
`augment<MODEL>`

`augment(<MODEL>, <DATA>)`
]

---
# augment

```r
augment(m_ht_wt)
```

```
## # A tibble: 3,135 x 10
## .rownames Height_in Width_in .fitted .se.fit .resid .hat .sigma .cooksd .std.resid
## <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 1 37 29.5 26.7 0.166 10.3 0.000399 8.30 3.10e-4 1.25 
## 2 2 18 14 14.6 0.165 3.45 0.000396 8.31 3.42e-5 0.415 
## 3 3 13 16 16.1 0.158 -3.11 0.000361 8.31 2.54e-5 -0.375 
## 4 4 14 18 17.7 0.152 -3.68 0.000337 8.31 3.30e-5 -0.443 
## 5 5 14 18 17.7 0.152 -3.68 0.000337 8.31 3.30e-5 -0.443 
## 6 6 7 10 11.4 0.185 -4.43 0.000498 8.31 7.09e-5 -0.534 
## 7 7 6 13 13.8 0.170 -7.77 0.000418 8.30 1.83e-4 -0.936 
## 8 8 6 13 13.8 0.170 -7.77 0.000418 8.30 1.83e-4 -0.936 
## 9 9 15 15 15.3 0.161 -0.333 0.000377 8.31 3.04e-7 -0.0401
## 10 10 9 7 9.09 0.204 -0.0870 0.000601 8.31 3.30e-8 -0.0105
## # … with 3,125 more rows
```

---
# understanding residuals

- variation explained by the model
- residual variation:  what's left over after fitting the model

---
class: transition
# Your turn: go to studio and start exercise 7B

---
# Going beyond a single model

Image source: https://balajiviswanathan.quora.com/Lessons-from-the-Blind-men-and-the-elephant

---
class: transition
# Going beyond a single model

- Beyond a single model
- Fitting many models

---
# Gapminder

- Hans Rosling was a Swedish doctor, academic and statistician, Professor of International Health at Karolinska Institute. Sadly he passed away in 2017. 
- He developed a keen interest in health and wealth across the globe, and the relationship with other factors like agriculture, education, energy. 
- You can play with the gapminder data using animations at https://www.gapminder.org/tools/.

---
<iframe width="1008" height="567" src="https://www.youtube.com/embed/jbkSRLYSojo" frameborder="0" allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe>

---
# R package: `gapminder`

Contains subset of the data on five year intervals from 1952 to 2007.

```r
library(gapminder)
glimpse(gapminder)
```

```
## Rows: 1,704
## Columns: 6
## $ country <fct> Afghanistan, Afghanistan, Afghanistan, Afghanistan, Afghanistan, Afgh…
## $ continent <fct> Asia, Asia, Asia, Asia, Asia, Asia, Asia, Asia, Asia, Asia, Asia, Asi…
## $ year <int> 1952, 1957, 1962, 1967, 1972, 1977, 1982, 1987, 1992, 1997, 2002, 200…
## $ lifeExp <dbl> 28.801, 30.332, 31.997, 34.020, 36.088, 38.438, 39.854, 40.822, 41.67…
## $ pop <int> 8425333, 9240934, 10267083, 11537966, 13079460, 14880372, 12881816, 1…
## $ gdpPercap <dbl> 779.4453, 820.8530, 853.1007, 836.1971, 739.9811, 786.1134, 978.0114,…
```

---
# "Change in life expectancy in countries over time?"

???

- Plot life expectancy by year, for each country.
- What do you learn?

---
# "Change in life expectancy in countries over time?"

- There generally appears to be an increase in life expectancy
- A number of countries have big dips from the 70s through 90s
- a cluster of countries starts off with low life expectancy but ends up close to the highest by the end of the period.

---
# Gapminder: Australia

Australia was already had one of the top life expectancies in the 1950s.

```r
oz <- gapminder %>% filter(country == "Australia")

oz
```

```
## # A tibble: 12 x 6
## country continent year lifeExp pop gdpPercap
## <fct> <fct> <int> <dbl> <int> <dbl>
## 1 Australia Oceania 1952 69.1 8691212 10040.
## 2 Australia Oceania 1957 70.3 9712569 10950.
## 3 Australia Oceania 1962 70.9 10794968 12217.
## 4 Australia Oceania 1967 71.1 11872264 14526.
## 5 Australia Oceania 1972 71.9 13177000 16789.
## 6 Australia Oceania 1977 73.5 14074100 18334.
## 7 Australia Oceania 1982 74.7 15184200 19477.
## 8 Australia Oceania 1987 76.3 16257249 21889.
## 9 Australia Oceania 1992 77.6 17481977 23425.
## 10 Australia Oceania 1997 78.8 18565243 26998.
## 11 Australia Oceania 2002 80.4 19546792 30688.
## 12 Australia Oceania 2007 81.2 20434176 34435.
```

---
# Gapminder: Australia

```r
ggplot(data = oz, 
       aes(x = year, 
           y = lifeExp)) + 
  geom_line() 
```

---
# Gapminder: Australia

```r
oz_lm <- lm(lifeExp ~ year, data = oz)

oz_lm
```

```
## 
## Call:
## lm(formula = lifeExp ~ year, data = oz)
## 
## Coefficients:
## (Intercept)         year  
##   -376.1163       0.2277
```

---
# Tidy Gapminder Australia

```r
tidy(oz_lm)
```

```
## # A tibble: 2 x 5
## term estimate std.error statistic p.value
## <chr> <dbl> <dbl> <dbl> <dbl>
## 1 (Intercept) -376. 20.5 -18.3 5.09e- 9
## 2 year 0.228 0.0104 21.9 8.67e-10
```

.large[
`$$\widehat{lifeExp} = -376.1163 - 0.2277~year$$`
]

---
# Center year

- Let us treat 1950 is the first year
- so for model fitting we are going to shift year to begin in 1950
- This improved interpretability.

```r
gap <- gapminder %>% mutate(year1950 = year - 1950)
oz <- gap %>% filter(country == "Australia")
```

---
# Model for centred year

```r
oz_lm <- lm(lifeExp ~ year1950, data = oz)

oz_lm
```

```
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = oz)
## 
## Coefficients:
## (Intercept)     year1950  
##     67.9451       0.2277
```

---
# Tidy the model

```r
tidy(oz_lm)
```

```
## # A tibble: 2 x 5
## term estimate std.error statistic p.value
## <chr> <dbl> <dbl> <dbl> <dbl>
## 1 (Intercept) 67.9 0.355 192. 3.70e-19
## 2 year1950 0.228 0.0104 21.9 8.67e-10
```

.large[
`$$\widehat{lifeExp} = 67.9 +  0.2277~year$$`
]
---
# Augment

```r
oz_aug <- augment(oz_lm, oz)

oz_aug
```

```
## # A tibble: 12 x 14
## country continent year lifeExp pop gdpPercap year1950 .fitted .se.fit .resid
## <fct> <fct> <int> <dbl> <int> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 Austra… Oceania 1952 69.1 8.69e6 10040. 2 68.4 0.337 0.719 
## 2 Austra… Oceania 1957 70.3 9.71e6 10950. 7 69.5 0.294 0.791 
## 3 Austra… Oceania 1962 70.9 1.08e7 12217. 12 70.7 0.255 0.252 
## 4 Austra… Oceania 1967 71.1 1.19e7 14526. 17 71.8 0.221 -0.716 
## 5 Austra… Oceania 1972 71.9 1.32e7 16789. 22 73.0 0.195 -1.02 
## 6 Austra… Oceania 1977 73.5 1.41e7 18334. 27 74.1 0.181 -0.604 
## 7 Austra… Oceania 1982 74.7 1.52e7 19477. 32 75.2 0.181 -0.492 
## 8 Austra… Oceania 1987 76.3 1.63e7 21889. 37 76.4 0.195 -0.0508
## 9 Austra… Oceania 1992 77.6 1.75e7 23425. 42 77.5 0.221 0.0505
## 10 Austra… Oceania 1997 78.8 1.86e7 26998. 47 78.6 0.255 0.182 
## 11 Austra… Oceania 2002 80.4 1.95e7 30688. 52 79.8 0.294 0.583 
## 12 Austra… Oceania 2007 81.2 2.04e7 34435. 57 80.9 0.337 0.310 
## # … with 4 more variables: .hat <dbl>, .sigma <dbl>, .cooksd <dbl>, .std.resid <dbl>
```

---
# Plot fitted against values

```r
ggplot(data = oz_aug, 
       aes(x = year, 
           y = .fitted)) + 
  geom_line(colour = "blue") + 
  geom_point(aes(x = year,
                 y = lifeExp))
```

---
# Plot studentised residuals against year

```r
ggplot(data = oz_aug, 
             aes(x = year, 
                 y = .std.resid)) + 
  geom_hline(yintercept = 0,
             colour = "white", 
             size = 2) +
  geom_line() 
```

---
# Making inferences from this

- Life expectancy has increased 2.3 years every decade, on average. 
- There was a slow period from 1960 through to 1972, probably related to mortality during the Vietnam war.

---
# Can we fit for New Zealand?

```r
nz <- gap %>% filter(country == "New Zealand")
nz_lm <- lm(lifeExp ~ year1950, data = nz)
nz_lm
```

```
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = nz)
## 
## Coefficients:
## (Intercept)     year1950  
##     68.3013       0.1928
```

---
# Can we fit for Japan?

```r
japan <- gap %>% filter(country == "Japan")
japan_lm <- lm(lifeExp ~ year1950, data = japan)
japan_lm
```

```
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = japan)
## 
## Coefficients:
## (Intercept)     year1950  
##     64.4162       0.3529
```

---
# Can we fit for Italy?

```r
italy <- gap %>% filter(country == "Italy")
italy_lm <- lm(lifeExp ~ year1950, data = italy)
italy_lm
```

```
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = italy)
## 
## Coefficients:
## (Intercept)     year1950  
##     66.0574       0.2697
```

---
class: transition

# Is there a better way?

Like, what if we wanted to fit a model for ALL countries?

Let's tinker with the data.

---
# `nest()` country level data (one row = one country)

```r
by_country <- gap %>% 
 select(country, year1950, lifeExp, continent) %>%
 group_by(country, continent) %>% 
 nest()

by_country
```

```
## # A tibble: 142 x 3
## # Groups: country, continent [710]
## country continent data 
## <fct> <fct> <list> 
## 1 Afghanistan Asia <tibble [12 × 2]>
## 2 Albania Europe <tibble [12 × 2]>
## 3 Algeria Africa <tibble [12 × 2]>
## 4 Angola Africa <tibble [12 × 2]>
## 5 Argentina Americas <tibble [12 × 2]>
## 6 Australia Oceania <tibble [12 × 2]>
## 7 Austria Europe <tibble [12 × 2]>
## 8 Bahrain Asia <tibble [12 × 2]>
## 9 Bangladesh Asia <tibble [12 × 2]>
## 10 Belgium Europe <tibble [12 × 2]>
## # … with 132 more rows
```

---
# What is in `data`?

```r
by_country$data[[1]]
```

```
## # A tibble: 12 x 2
## year1950 lifeExp
## <dbl> <dbl>
## 1 2 28.8
## 2 7 30.3
## 3 12 32.0
## 4 17 34.0
## 5 22 36.1
## 6 27 38.4
## 7 32 39.9
## 8 37 40.8
## 9 42 41.7
## 10 47 41.8
## 11 52 42.1
## 12 57 43.8
```

# It's a list!

---
# fit a linear model to each one?

```r
lm_afganistan <- lm(lifeExp ~ year1950, data = by_country$data[[1]])
lm_albania <- lm(lifeExp ~ year1950, data = by_country$data[[2]])
lm_algeria <- lm(lifeExp ~ year1950, data = by_country$data[[3]])
```

But we are copying and pasting this code **more than twice**...is there a better way?

---
# A case for our friend, `map` ... ???

.large[
`map(<data object>, <function>)`
]

---
# A case for `map` ???

```r
mapped_lm <- map(.x = by_country$data, 
 .f = function(x){
 lm(lifeExp ~ year1950, data = x) 
 })

mapped_lm
```

```
## [[1]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     29.3566       0.2753  
## 
## 
## [[2]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     58.5598       0.3347  
## 
## 
## [[3]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     42.2364       0.5693  
## 
## 
## [[4]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     31.7080       0.2093  
## 
## 
## [[5]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     62.2250       0.2317  
## 
## 
## [[6]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     67.9451       0.2277  
## 
## 
## [[7]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##      65.964        0.242  
## 
## 
## [[8]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     51.8142       0.4675  
## 
## 
## [[9]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     35.1392       0.4981  
## 
## 
## [[10]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     67.4738       0.2091  
## 
## 
## [[11]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     38.9200       0.3342  
## 
## 
## [[12]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     37.7566       0.4999  
## 
## 
## [[13]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     57.3901       0.3498  
## 
## 
## [[14]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##    52.80778      0.06067  
## 
## 
## [[15]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     50.7319       0.3901  
## 
## 
## [[16]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     65.4459       0.1457  
## 
## 
## [[17]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##      33.957        0.364  
## 
## 
## [[18]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     40.2704       0.1541  
## 
## 
## [[19]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     36.2236       0.3959  
## 
## 
## [[20]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     40.7492       0.2501  
## 
## 
## [[21]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     68.4461       0.2189  
## 
## 
## [[22]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     38.4417       0.1839  
## 
## 
## [[23]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     39.3029       0.2532  
## 
## 
## [[24]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     53.3640       0.4768  
## 
## 
## [[25]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     46.1291       0.5307  
## 
## 
## [[26]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     52.6656       0.3808  
## 
## 
## [[27]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     39.0952       0.4504  
## 
## 
## [[28]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##    41.77325      0.09392  
## 
## 
## [[29]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     46.7466       0.1951  
## 
## 
## [[30]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     58.2991       0.4028  
## 
## 
## [[31]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     44.5847       0.1306  
## 
## 
## [[32]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     63.4049       0.2255  
## 
## 
## [[33]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     61.5711       0.3212  
## 
## 
## [[34]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     67.2384       0.1448  
## 
## 
## [[35]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     70.7909       0.1213  
## 
## 
## [[36]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     35.5423       0.3674  
## 
## 
## [[37]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     47.6555       0.4712  
## 
## 
## [[38]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     48.0653       0.5001  
## 
## 
## [[39]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     39.8571       0.5555  
## 
## 
## [[40]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     45.5577       0.4771  
## 
## 
## [[41]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     33.8100       0.3102  
## 
## 
## [[42]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     34.9459       0.3747  
## 
## 
## [[43]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     35.4138       0.3072  
## 
## 
## [[44]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     65.9731       0.2379  
## 
## 
## [[45]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     67.3131       0.2385  
## 
## 
## [[46]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     38.0419       0.4467  
## 
## 
## [[47]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     27.2367       0.5818  
## 
## 
## [[48]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     67.1408       0.2137  
## 
## 
## [[49]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     42.8493       0.3217  
## 
## 
## [[50]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     66.5824       0.2424  
## 
## 
## [[51]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     41.0569       0.5313  
## 
## 
## [[52]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     30.7073       0.4248  
## 
## 
## [[53]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     31.1935       0.2718  
## 
## 
## [[54]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     38.4520       0.3971  
## 
## 
## [[55]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     41.9067       0.5429  
## 
## 
## [[56]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##      62.697        0.366  
## 
## 
## [[57]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     65.7455       0.1236  
## 
## 
## [[58]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     71.6328       0.1654  
## 
## 
## [[59]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     38.2591       0.5053  
## 
## 
## [[60]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     35.6138       0.6346  
## 
## 
## [[61]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     43.9857       0.4966  
## 
## 
## [[62]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     49.6430       0.2352  
## 
## 
## [[63]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     67.1432       0.1991  
## 
## 
## [[64]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     65.7662       0.2671  
## 
## 
## [[65]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     66.0574       0.2697  
## 
## 
## [[66]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     62.2182       0.2214  
## 
## 
## [[67]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     64.4162       0.3529  
## 
## 
## [[68]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     42.9204       0.5717  
## 
## 
## [[69]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     46.5890       0.2065  
## 
## 
## [[70]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     54.2727       0.3164  
## 
## 
## [[71]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     48.6167       0.5554  
## 
## 
## [[72]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     56.6257       0.4168  
## 
## 
## [[73]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##      58.165        0.261  
## 
## 
## [[74]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##    47.18789      0.09557  
## 
## 
## [[75]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##    39.64444      0.09599  
## 
## 
## [[76]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     40.8509       0.6255  
## 
## 
## [[77]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     35.8606       0.4037  
## 
## 
## [[78]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     36.4419       0.2342  
## 
## 
## [[79]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     50.5762       0.4645  
## 
## 
## [[80]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     32.2976       0.3768  
## 
## 
## [[81]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     39.1328       0.4464  
## 
## 
## [[82]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     54.6739       0.3485  
## 
## 
## [[83]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##      52.103        0.451  
## 
## 
## [[84]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     42.9490       0.4387  
## 
## 
## [[85]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##      61.656        0.293  
## 
## 
## [[86]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     41.6059       0.5425  
## 
## 
## [[87]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     33.7572       0.2245  
## 
## 
## [[88]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     40.5454       0.4331  
## 
## 
## [[89]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     46.6720       0.2312  
## 
## 
## [[90]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     33.3731       0.5293  
## 
## 
## [[91]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     71.6162       0.1367  
## 
## 
## [[92]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     68.3013       0.1928  
## 
## 
## [[93]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     41.9321       0.5565  
## 
## 
## [[94]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     34.4664       0.3421  
## 
## 
## [[95]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     37.4434       0.2081  
## 
## 
## [[96]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     71.9507       0.1319  
## 
## 
## [[97]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     35.6634       0.7722  
## 
## 
## [[98]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     42.9114       0.4058  
## 
## 
## [[99]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     57.3526       0.3542  
## 
## 
## [[100]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     62.1671       0.1574  
## 
## 
## [[101]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     43.2922       0.5277  
## 
## 
## [[102]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     48.5634       0.4205  
## 
## 
## [[103]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     64.3885       0.1962  
## 
## 
## [[104]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     60.4724       0.3372  
## 
## 
## [[105]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     66.5274       0.2106  
## 
## 
## [[106]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     53.0778       0.4599  
## 
## 
## [[107]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     63.6473       0.1574  
## 
## 
## [[108]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##    42.83361     -0.04583  
## 
## 
## [[109]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     47.8462       0.3407  
## 
## 
## [[110]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     39.5149       0.6496  
## 
## 
## [[111]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     35.7373       0.5047  
## 
## 
## [[112]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     61.0240       0.2552  
## 
## 
## [[113]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##      30.455        0.214  
## 
## 
## [[114]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     61.1641       0.3409  
## 
## 
## [[115]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##      66.742        0.134  
## 
## 
## [[116]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     65.6853       0.2005  
## 
## 
## [[117]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     34.2163       0.2296  
## 
## 
## [[118]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     49.0030       0.1692  
## 
## 
## [[119]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     65.9160       0.2809  
## 
## 
## [[120]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     59.3017       0.2449  
## 
## 
## [[121]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     37.1086       0.3828  
## 
## 
## [[122]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##    46.19771      0.09507  
## 
## 
## [[123]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     71.2725       0.1663  
## 
## 
## [[124]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     69.0093       0.2222  
## 
## 
## [[125]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     44.9926       0.5544  
## 
## 
## [[126]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     60.6829       0.3272  
## 
## 
## [[127]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     42.7590       0.1747  
## 
## 
## [[128]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##      51.962        0.347  
## 
## 
## [[129]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     40.2123       0.3826  
## 
## 
## [[130]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     61.7050       0.1737  
## 
## 
## [[131]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     43.3796       0.5878  
## 
## 
## [[132]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     45.0278       0.4972  
## 
## 
## [[133]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     44.0320       0.1216  
## 
## 
## [[134]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##      68.437        0.186  
## 
## 
## [[135]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     68.0455       0.1842  
## 
## 
## [[136]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     65.3751       0.1833  
## 
## 
## [[137]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     56.8539       0.3297  
## 
## 
## [[138]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     37.6668       0.6716  
## 
## 
## [[139]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     42.5962       0.6011  
## 
## 
## [[140]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##     28.9194       0.6055  
## 
## 
## [[141]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##    47.77888     -0.06043  
## 
## 
## [[142]]
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = x)
## 
## Coefficients:
## (Intercept)     year1950  
##    55.40729     -0.09302
```

---
# Map inside the data?

```r
*country_model <- by_country %>%
* mutate(model = map(.x = data,
 .f = function(x){
 lm(lifeExp ~ year1950, data = x)
 }))

country_model
```

```
## # A tibble: 142 x 4
## # Groups: country, continent [710]
## country continent data model 
## <fct> <fct> <list> <list>
## 1 Afghanistan Asia <tibble [12 × 2]> <lm> 
## 2 Albania Europe <tibble [12 × 2]> <lm> 
## 3 Algeria Africa <tibble [12 × 2]> <lm> 
## 4 Angola Africa <tibble [12 × 2]> <lm> 
## 5 Argentina Americas <tibble [12 × 2]> <lm> 
## 6 Australia Oceania <tibble [12 × 2]> <lm> 
## 7 Austria Europe <tibble [12 × 2]> <lm> 
## 8 Bahrain Asia <tibble [12 × 2]> <lm> 
## 9 Bangladesh Asia <tibble [12 × 2]> <lm> 
## 10 Belgium Europe <tibble [12 × 2]> <lm> 
## # … with 132 more rows
```

---
# A case for map (shorthand function)

```r
country_model <- by_country %>% 
 mutate(model = map(.x = data, 
* .f = ~lm(lifeExp ~ year1950, data = .)))

country_model
```

---
# Where's the model?

```r
country_model$model[[1]]
```

```
## 
## Call:
## lm(formula = lifeExp ~ year1950, data = .)
## 
## Coefficients:
## (Intercept)     year1950  
##     29.3566       0.2753
```

---
# We need to summarise this content

```r
tidy(country_model$model[[1]])
```

```
## # A tibble: 2 x 5
## term estimate std.error statistic p.value
## <chr> <dbl> <dbl> <dbl> <dbl>
## 1 (Intercept) 29.4 0.699 42.0 1.40e-12
## 2 year1950 0.275 0.0205 13.5 9.84e- 8
```

---
# So should we repeat it for each one?

```r
tidy(country_model$model[[1]])
```

```r
tidy(country_model$model[[2]])
```

```
## # A tibble: 2 x 5
## term estimate std.error statistic p.value
## <chr> <dbl> <dbl> <dbl> <dbl>
## 1 (Intercept) 58.6 1.13 51.7 1.79e-13
## 2 year1950 0.335 0.0332 10.1 1.46e- 6
```

```r
tidy(country_model$model[[3]])
```

```
## # A tibble: 2 x 5
## term estimate std.error statistic p.value
## <chr> <dbl> <dbl> <dbl> <dbl>
## 1 (Intercept) 42.2 0.756 55.8 8.22e-14
## 2 year1950 0.569 0.0221 25.7 1.81e-10
```

---
# Use `map`

```r
country_model %>%
  mutate(tidy = map(model, tidy))
```

```
## # A tibble: 142 x 5
## # Groups: country, continent [710]
## country continent data model tidy 
## <fct> <fct> <list> <list> <list> 
## 1 Afghanistan Asia <tibble [12 × 2]> <lm> <tibble [2 × 5]>
## 2 Albania Europe <tibble [12 × 2]> <lm> <tibble [2 × 5]>
## 3 Algeria Africa <tibble [12 × 2]> <lm> <tibble [2 × 5]>
## 4 Angola Africa <tibble [12 × 2]> <lm> <tibble [2 × 5]>
## 5 Argentina Americas <tibble [12 × 2]> <lm> <tibble [2 × 5]>
## 6 Australia Oceania <tibble [12 × 2]> <lm> <tibble [2 × 5]>
## 7 Austria Europe <tibble [12 × 2]> <lm> <tibble [2 × 5]>
## 8 Bahrain Asia <tibble [12 × 2]> <lm> <tibble [2 × 5]>
## 9 Bangladesh Asia <tibble [12 × 2]> <lm> <tibble [2 × 5]>
## 10 Belgium Europe <tibble [12 × 2]> <lm> <tibble [2 × 5]>
## # … with 132 more rows
```

---
# `unnest`

```r
country_coefs <- country_model %>%
 mutate(tidy = map(model, tidy)) %>%
* unnest(tidy) %>%
 select(country, continent, term, estimate)

country_coefs
```

```
## # A tibble: 284 x 4
## # Groups: country, continent [710]
## country continent term estimate
## <fct> <fct> <chr> <dbl>
## 1 Afghanistan Asia (Intercept) 29.4 
## 2 Afghanistan Asia year1950 0.275
## 3 Albania Europe (Intercept) 58.6 
## 4 Albania Europe year1950 0.335
## 5 Algeria Africa (Intercept) 42.2 
## 6 Algeria Africa year1950 0.569
## 7 Angola Africa (Intercept) 31.7 
## 8 Angola Africa year1950 0.209
## 9 Argentina Americas (Intercept) 62.2 
## 10 Argentina Americas year1950 0.232
## # … with 274 more rows
```

---
# Pivot the term

```r
tidy_country_coefs <- country_coefs %>%
 pivot_wider(id_cols = c(term, country, continent), 
 names_from = term,
 values_from = estimate) %>%
 rename(intercept = `(Intercept)`)

tidy_country_coefs
```

```
## # A tibble: 142 x 4
## # Groups: country, continent [710]
## country continent intercept year1950
## <fct> <fct> <dbl> <dbl>
## 1 Afghanistan Asia 29.4 0.275
## 2 Albania Europe 58.6 0.335
## 3 Algeria Africa 42.2 0.569
## 4 Angola Africa 31.7 0.209
## 5 Argentina Americas 62.2 0.232
## 6 Australia Oceania 67.9 0.228
## 7 Austria Europe 66.0 0.242
## 8 Bahrain Asia 51.8 0.468
## 9 Bangladesh Asia 35.1 0.498
## 10 Belgium Europe 67.5 0.209
## # … with 132 more rows
```

---
# Filter to only Australia

```r
tidy_country_coefs %>%
  filter(country == "Australia")
```

```
## # A tibble: 1 x 4
## # Groups: country, continent [710]
## country continent intercept year1950
## <fct> <fct> <dbl> <dbl>
## 1 Australia Oceania 67.9 0.228
```

---
class: transition
# Your turn: Five minute challenge

.vlarge[
- Fit the models to all countries
- Pick your favourite country (not Australia), print the coefficients, and make a hand sketch of the the model fit.
]

---
# Plot all the models

```r
country_aug <- country_model %>% 
 mutate(augmented = map(model, augment)) %>%
 unnest(augmented)

country_aug
```

```
## # A tibble: 1,704 x 13
## # Groups: country, continent [710]
## country continent data model lifeExp year1950 .fitted .se.fit .resid .hat .sigma
## <fct> <fct> <lis> <lis> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 Afghan… Asia <tib… <lm> 28.8 2 29.9 0.664 -1.11 0.295 1.21
## 2 Afghan… Asia <tib… <lm> 30.3 7 31.3 0.580 -0.952 0.225 1.24
## 3 Afghan… Asia <tib… <lm> 32.0 12 32.7 0.503 -0.664 0.169 1.27
## 4 Afghan… Asia <tib… <lm> 34.0 17 34.0 0.436 -0.0172 0.127 1.29
## 5 Afghan… Asia <tib… <lm> 36.1 22 35.4 0.385 0.674 0.0991 1.27
## 6 Afghan… Asia <tib… <lm> 38.4 27 36.8 0.357 1.65 0.0851 1.15
## 7 Afghan… Asia <tib… <lm> 39.9 32 38.2 0.357 1.69 0.0851 1.15
## 8 Afghan… Asia <tib… <lm> 40.8 37 39.5 0.385 1.28 0.0991 1.21
## 9 Afghan… Asia <tib… <lm> 41.7 42 40.9 0.436 0.754 0.127 1.26
## 10 Afghan… Asia <tib… <lm> 41.8 47 42.3 0.503 -0.534 0.169 1.27
## # … with 1,694 more rows, and 2 more variables: .cooksd <dbl>, .std.resid <dbl>
```

---
# Plot all the models

```r
p1 <- gapminder %>% 
 ggplot(aes(year, lifeExp, group = country)) +
 geom_line(alpha = 1/3) + labs(title = "Data")

p2 <- ggplot(country_aug) + 
 geom_line(aes(x = year1950 + 1950, 
 y = .fitted, 
 group = country), 
 alpha = 1/3) +
 labs(title = "Fitted models",
 x = "year")
```

---
# Plot all the models

---
# Plot all the model coefficients

```r
p <- ggplot(tidy_country_coefs, 
 aes(x = intercept, 
 y = year1950, 
 colour = continent, 
 label = country)) +
 geom_point(alpha = 0.5, 
 size = 2) +
 scale_color_brewer(palette = "Dark2")
```

---
# Plot all the model coefficients

```r
p
```

---
# Make it interactive!

```r
library(plotly)
ggplotly(p)
```

<div id="htmlwidget-e918b16a264914b1a0bc" style="width:90%;height:324px;" class="plotly html-widget"></div>
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Lanka","intercept: 44.99256 year1950: 0.55435944 continent: Asia country: Syria","intercept: 60.68295 year1950: 0.32724476 continent: Asia country: Taiwan","intercept: 51.96233 year1950: 0.34704825 continent: Asia country: Thailand","intercept: 37.66685 year1950: 0.67161538 continent: Asia country: Vietnam","intercept: 42.59620 year1950: 0.60110070 continent: Asia country: West Bank and Gaza","intercept: 28.91936 year1950: 0.60545944 continent: Asia country: Yemen, 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year1950: 0.28093077 continent: Europe country: Spain","intercept: 71.27249 year1950: 0.16625455 continent: Europe country: Sweden","intercept: 69.00926 year1950: 0.22223147 continent: Europe country: Switzerland","intercept: 45.02784 year1950: 0.49723986 continent: Europe country: Turkey","intercept: 68.43659 year1950: 0.18596573 continent: Europe country: United Kingdom"],"type":"scatter","mode":"markers","marker":{"autocolorscale":false,"color":"rgba(231,41,138,1)","opacity":0.5,"size":7.55905511811024,"symbol":"circle","line":{"width":1.88976377952756,"color":"rgba(231,41,138,1)"}},"hoveron":"points","name":"Europe","legendgroup":"Europe","showlegend":true,"xaxis":"x","yaxis":"y","hoverinfo":"text","frame":null},{"x":[67.9450652680653,68.3012811188811],"y":[0.227723776223776,0.192820979020979],"text":["intercept: 67.94507 year1950: 0.22772378 continent: Oceania country: Australia","intercept: 68.30128 year1950: 0.19282098 continent: Oceania country: New 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---
# Let's summarise the information learned from the model coefficients.

- Generally the relationship is negative: this means that if a country started with a high intercept tends to have lower rate of increase.
- There is a difference across the continents: Countries in Europe and Oceania tended to start with higher life expectancy and increased; countries in Asia and America tended to start lower but have high rates of improvement; Africa tends to start lower and have a huge range in rate of change.
- Three countries had negative growth in life expectancy: Rwanda, Zimbabwe, Zambia

---
# Model diagnostics by country

```r
country_glance <- country_model %>% 
 mutate(glance = map(model, glance)) %>%
 unnest(glance)

country_glance
```

```
## # A tibble: 142 x 15
## # Groups: country, continent [710]
## country continent data model r.squared adj.r.squared sigma statistic p.value df
## <fct> <fct> <lis> <lis> <dbl> <dbl> <dbl> <dbl> <dbl> <int>
## 1 Afghan… Asia <tib… <lm> 0.948 0.942 1.22 181. 9.84e- 8 2
## 2 Albania Europe <tib… <lm> 0.911 0.902 1.98 102. 1.46e- 6 2
## 3 Algeria Africa <tib… <lm> 0.985 0.984 1.32 662. 1.81e-10 2
## 4 Angola Africa <tib… <lm> 0.888 0.877 1.41 79.1 4.59e- 6 2
## 5 Argent… Americas <tib… <lm> 0.996 0.995 0.292 2246. 4.22e-13 2
## 6 Austra… Oceania <tib… <lm> 0.980 0.978 0.621 481. 8.67e-10 2
## 7 Austria Europe <tib… <lm> 0.992 0.991 0.407 1261. 7.44e-12 2
## 8 Bahrain Asia <tib… <lm> 0.967 0.963 1.64 291. 1.02e- 8 2
## 9 Bangla… Asia <tib… <lm> 0.989 0.988 0.977 930. 3.37e-11 2
## 10 Belgium Europe <tib… <lm> 0.995 0.994 0.293 1822. 1.20e-12 2
## # … with 132 more rows, and 5 more variables: logLik <dbl>, AIC <dbl>, BIC <dbl>,
## # deviance <dbl>, df.residual <int>
```

---
# Plot the `$R^2$` values as a histogram.

```r
ggplot(country_glance, 
       aes(x = r.squared)) + 
  geom_histogram()
```

---
# Countries with worst fit

Examine the countries with the worst fit, countries with `$R^2<0.45$`, by making scatter plots of the data, with the linear model overlaid.

```r
badfit <- country_glance %>% filter(r.squared <= 0.45)

gap_bad <- gap %>% filter(country %in% badfit$country)

gg_bad_fit <-
ggplot(data = gap_bad, 
 aes(x = year, 
 y = lifeExp)) + 
 geom_point() +
 facet_wrap(~country) +
 scale_x_continuous(breaks = seq(1950,2000,10), 
 labels = c("1950", "60","70", "80","90","2000")) +
 geom_smooth(method = "lm", 
 se = FALSE)
```

---
# Countries with worst fit

Each of these countries had been moving on a nice trajectory of increasing life expectancy, and then suffered a big dip during the time period.

---
class: transition

# Your Turn:

.large[
- Use Google to explain these dips using world history and current affairs information. 
- finish the lab exercise (with new data)
- remember the project deadline: **Find team members, and potential topics to study (List of groups will be posted here)**
]

???

# many models
  - gapminder
  - fit with year
    - recenter year to be from 1950
    - fit again (ask a quiz question about this)
  - What is the average life expectancy?
  - What if we want to fit a separate model for each country? Can we fit a linear model for each country?
- why are making day0
- why are we standardization

Open the app available at [https://ebsmonash.shinyapps.io/SSregression/](https://ebsmonash.shinyapps.io/SSregression/). (The original version was obtained from [https://github.com/paternogbc/SSregression](https://github.com/paternogbc/SSregression), developed by Gustavo Brant Paterno, a PhD student from Brazil.)

The app simulates some data using different slopes and error variance. It allows you to see how characteristics of the data affect model summaries. Time to play!

1. Vary the slope from high positive to zero. What happens to the error variance? The total variance and the regression variance (due to model)? Does the proportion of variation of each component change? How? Is this the same if you vary from large negative slope to zero?
2. Holding the slope fixed at 1, increase the standard deviation of the error model. What happens to components of variation?
3. As the slope changes, what happens to the intercept?
4. Why isn't the estimated slope the same as what is set by the slider?

plots of `$R^2$`