ETC1010: Data Modelling and Computing

class: center, middle, inverse, title-slide

# ETC1010: Data Modelling and Computing
## Lecture 7B: Linear Models part II
### Dr. Nicholas Tierney & Professor Di Cook
### EBS, Monash U.
### 2019-09-13

---

---
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# Recap

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# Overview

- Feedback from the tests
- What is r2
  - (pull examples from exercise)
- short exercise in class to calculate correlation and r2 and answer questions
- augment?
- understanding residuals
- components of variation?
  
---
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# Feedback from assignment 1 (from Sherry)

.vlarge[
- Some students forgot to answer some of the questions: "Is there anything else in the excel spreadsheet we could look at?".
- Some groups need to follow Amelia's three-sentence interpretation to describe plots.
- For the last questions, I (Sherry) expect people to also talks about how the analysis would help with the business.
 
Presentation & grammar:
- Remember to do a spell check before submitting any of your files
- Don't need install.package in your Rmd library() is enough
]

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# Other Admin

## Mid-semester exam

.huge[
- Marks will be released at the end of class
]

## Project deadline (today)

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

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# What is correlation?

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

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## Strongest Positive correlation: As one variable increases, so does another variable

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## strong Positive correlation: As one variable increases, so does another variable

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## zero correlation: neither variables are related linearly

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## strong negative correlation: as one variable increases, another variable decreases

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## STRONG negative correlation: as one variable increases, another variable decreases

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# correlation: animated

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# definition of correlation

.huge[
For two variables `$X, Y$`, correlation is:
]

.vlarge[
`$$r=\frac{\sum_{i=1}^{n} (x_i-\bar{x})(y_i-\bar{y})}{\sqrt{\sum_{i=1}^{n}(x_i-\bar{x})^2}\sqrt{\sum_{i=1}^{n}(y_i-\bar{y})^2}} = \frac{cov(X,Y)}{s_xs_y}$$`
]
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# Dance of correlation

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# Remember! Correlation does not equal causation

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# What is `$R^2$`?

.huge[
- (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. 
]

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# plots of rsquared

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# unpacking lm and model objects

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

```
## # 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>
```

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# unpacking linear models

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

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# template for linear model

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

`<FORMULA>`

`RESPONSE ~ EXPLANATORY VARIABLES`
]

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# 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
```

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# using tidy, augment, glance

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# tidy: return a tidy table of model information

.huge[
`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.)

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# glance: get a one-row summary out

.huge[
`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>
```

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# AIC, BIC, Deviance

.huge[

- **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.

]

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# augment: get the data

.huge[
`augment<MODEL>>`

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

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# 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
```

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# understanding residuals

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

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# Your turn: go to rstudio cloud and get started on exercise 7B

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# Going beyond a single model

```r
include_graphics("images/blind-men-and-the-elephant.png")
```

.huge[
- Beyond a single model
- Fitting many models 
]

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

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# Gapminder

.huge[
- Hans Rosling was a Swedish doctor, academic and statistician, Professor of International Health at Karolinska Institute. Sadley 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/. 
]

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# R package: `gapminder`

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

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

```
## Observations: 1,704
## Variables: 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,…
```

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# "How has life expectancy changed over years, for each country?"

???

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

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# "How has life expectancy changed over years, for each country?"

.huge[
- 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.
]

---
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# Gapminder: Australia

.huge[
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.
```

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# Gapminder: Australia

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

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# 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
```

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```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
```

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

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# center year

.huge[
Let us treat 1950 is the first year, so for model fitting we are going to shift year to begin in 1950, makes interpretability easier.
]

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

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# model for centered 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
```

---
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```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
```

.huge[
`$$\widehat{lifeExp} = 67.9 +  0.2277~year$$`
]
---
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```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>
```

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

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

---
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# Making inferences from this

.huge[
- 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.
]

---
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# 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
```

---
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# 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
```

---
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# 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
```

---
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# Is there a better way?

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

# Let's tinker with the data.

---
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# 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
## 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
```

---
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# 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!

---
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# 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?

---
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# A case for map???

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

---
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# A case for map???

```r
mapped_lm <- 
map(by_country$data, 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
```

---
class: bg-main1

# Map inside the data?

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

country_model
```

```
## # A tibble: 142 x 4
## 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
```

---
class: bg-main1

# A case for map (shorthand function)

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

country_model
```

---
class: bg-main1

# where's the model?

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

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

---
class: bg-main1

# 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
```

---
class: bg-main1

# 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
```

---
class: bg-main1

# NO NICK, THERE's A BETTER WAY.

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

```
## # A tibble: 142 x 5
## 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
```

---
class: bg-main1

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

country_coefs
```

```
## # A tibble: 284 x 4
## 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
```

---
class: bg-main1

```r
tidy_country_coefs <- country_coefs %>%
 spread(key = term, 
 value = estimate) %>%
 rename(intercept = `(Intercept)`)

tidy_country_coefs
```

```
## # A tibble: 142 x 4
## 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
```

---
class: bg-main1

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

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

---
class: bg-main1

# Your turn: Five minute challenge

.huge[
- 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.
]

---
class: bg-main1

# Plot all the models

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

country_aug
```

```
## # A tibble: 1,704 x 11
## country continent lifeExp year1950 .fitted .se.fit .resid .hat .sigma .cooksd
## <fct> <fct> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 Afghan… Asia 28.8 2 29.9 0.664 -1.11 0.295 1.21 2.43e-1
## 2 Afghan… Asia 30.3 7 31.3 0.580 -0.952 0.225 1.24 1.13e-1
## 3 Afghan… Asia 32.0 12 32.7 0.503 -0.664 0.169 1.27 3.60e-2
## 4 Afghan… Asia 34.0 17 34.0 0.436 -0.0172 0.127 1.29 1.65e-5
## 5 Afghan… Asia 36.1 22 35.4 0.385 0.674 0.0991 1.27 1.85e-2
## 6 Afghan… Asia 38.4 27 36.8 0.357 1.65 0.0851 1.15 9.23e-2
## 7 Afghan… Asia 39.9 32 38.2 0.357 1.69 0.0851 1.15 9.67e-2
## 8 Afghan… Asia 40.8 37 39.5 0.385 1.28 0.0991 1.21 6.67e-2
## 9 Afghan… Asia 41.7 42 40.9 0.436 0.754 0.127 1.26 3.17e-2
## 10 Afghan… Asia 41.8 47 42.3 0.503 -0.534 0.169 1.27 2.33e-2
## # … with 1,694 more rows, and 1 more variable: .std.resid <dbl>
```

---
class: bg-main1

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

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

---
class: bg-main1

```r
grid.arrange(p1, p2, ncol=2)
```

---
class: bg-main1

# 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")
```

---
class: bg-main1

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

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0.20650769 continent: Africa country: Kenya","intercept: 47.18789 year1950: 0.09556573 continent: Africa country: Lesotho","intercept: 39.64444 year1950: 0.09599371 continent: Africa country: Liberia","intercept: 40.85086 year1950: 0.62553566 continent: Africa country: Libya","intercept: 35.86061 year1950: 0.40372797 continent: Africa country: Madagascar","intercept: 36.44192 year1950: 0.23422587 continent: Africa country: Malawi","intercept: 32.29761 year1950: 0.37680979 continent: Africa country: Mali","intercept: 39.13277 year1950: 0.44641748 continent: Africa country: Mauritania","intercept: 54.67386 year1950: 0.34845385 continent: Africa country: Mauritius","intercept: 41.60589 year1950: 0.54247273 continent: Africa country: Morocco","intercept: 33.75718 year1950: 0.22448531 continent: Africa country: Mozambique","intercept: 46.67201 year1950: 0.23116364 continent: Africa country: Namibia","intercept: 34.46645 year1950: 0.34210909 continent: Africa country: Niger","intercept: 37.44339 year1950: 0.20806573 continent: Africa country: Nigeria","intercept: 53.07778 year1950: 0.45988042 continent: Africa country: Reunion","intercept: 42.83361 year1950: -0.04583147 continent: Africa country: Rwanda","intercept: 47.84620 year1950: 0.34068252 continent: Africa country: Sao Tome and Principe","intercept: 35.73727 year1950: 0.50470000 continent: Africa country: Senegal","intercept: 30.45514 year1950: 0.21403497 continent: Africa country: Sierra Leone","intercept: 34.21625 year1950: 0.22957343 continent: Africa country: Somalia","intercept: 49.00296 year1950: 0.16915944 continent: Africa country: South Africa","intercept: 37.10864 year1950: 0.38277483 continent: Africa country: Sudan","intercept: 46.19771 year1950: 0.09507483 continent: Africa country: Swaziland","intercept: 42.75903 year1950: 0.17468811 continent: Africa country: Tanzania","intercept: 40.21228 year1950: 0.38259231 continent: Africa country: Togo","intercept: 43.37962 year1950: 0.58784336 continent: 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29.35664 year1950: 0.27532867 continent: Asia country: Afghanistan","intercept: 51.81419 year1950: 0.46750769 continent: Asia country: Bahrain","intercept: 35.13923 year1950: 0.49813077 continent: Asia country: Bangladesh","intercept: 36.22362 year1950: 0.39590280 continent: Asia country: Cambodia","intercept: 46.12905 year1950: 0.53071485 continent: Asia country: China","intercept: 62.69670 year1950: 0.36597063 continent: Asia country: Hong Kong, China","intercept: 38.25911 year1950: 0.50532098 continent: Asia country: India","intercept: 35.61383 year1950: 0.63464126 continent: Asia country: Indonesia","intercept: 43.98571 year1950: 0.49663986 continent: Asia country: Iran","intercept: 49.64304 year1950: 0.23521049 continent: Asia country: Iraq","intercept: 65.76620 year1950: 0.26710629 continent: Asia country: Israel","intercept: 64.41624 year1950: 0.35290420 continent: Asia country: Japan","intercept: 42.92040 year1950: 0.57172937 continent: Asia country: Jordan","intercept: 54.27275 year1950: 0.31642657 continent: Asia country: Korea, Dem. Rep.","intercept: 48.61670 year1950: 0.55540000 continent: Asia country: Korea, Rep.","intercept: 56.62566 year1950: 0.41683636 continent: Asia country: Kuwait","intercept: 58.16530 year1950: 0.26102937 continent: Asia country: Lebanon","intercept: 50.57617 year1950: 0.46452238 continent: Asia country: Malaysia","intercept: 42.94903 year1950: 0.43868811 continent: Asia country: Mongolia","intercept: 40.54536 year1950: 0.43309510 continent: Asia country: Myanmar","intercept: 33.37312 year1950: 0.52926154 continent: Asia country: Nepal","intercept: 35.66339 year1950: 0.77217902 continent: Asia country: Oman","intercept: 42.91138 year1950: 0.40579231 continent: Asia country: Pakistan","intercept: 48.56341 year1950: 0.42046923 continent: Asia country: Philippines","intercept: 39.51487 year1950: 0.64962308 continent: Asia country: Saudi Arabia","intercept: 61.16411 year1950: 0.34088601 continent: Asia country: Singapore","intercept: 59.30170 year1950: 0.24489441 continent: Asia country: Sri 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, Rep."],"type":"scatter","mode":"markers","marker":{"autocolorscale":false,"color":"rgba(117,112,179,1)","opacity":0.5,"size":7.55905511811024,"symbol":"circle","line":{"width":1.88976377952756,"color":"rgba(117,112,179,1)"}},"hoveron":"points","name":"Asia","legendgroup":"Asia","showlegend":true,"xaxis":"x","yaxis":"y","hoverinfo":"text","frame":null},{"x":[58.5597617715618,65.964476923077,67.4737538461539,57.3900536130536,65.4459300699301,63.4048631701632,67.2384461538462,70.7909296037296,65.9731240093241,67.3131254079254,67.1407617715618,66.5824079254079,65.7455226107226,71.6328386946387,67.1432223776224,66.0573738927739,61.6556254079254,71.616241958042,71.9507328671329,64.3884596736597,60.4723920745921,63.6473254079254,61.0240440559441,66.7417836829837,65.6852986013986,65.915958974359,71.2724909090909,69.009255011655,45.0278407925408,68.4365941724942],"y":[0.334683216783216,0.241992307692307,0.209084615384615,0.349755244755244,0.14568881118881,0.22545944055944,0.144815384615384,0.121330069930069,0.237925174825174,0.238501398601399,0.213683216783216,0.242398601398601,0.123648951048951,0.165375524475524,0.19911958041958,0.269710489510489,0.293001398601398,0.136686713286713,0.131941258741258,0.196218881118881,0.337201398601398,0.157401398601398,0.255151048951048,0.134044055944055,0.200523776223776,0.280930769230768,0.166254545454545,0.222231468531468,0.49723986013986,0.185965734265734],"text":["intercept: 58.55976 year1950: 0.33468322 continent: Europe country: Albania","intercept: 65.96448 year1950: 0.24199231 continent: Europe country: Austria","intercept: 67.47375 year1950: 0.20908462 continent: Europe country: Belgium","intercept: 57.39005 year1950: 0.34975524 continent: Europe country: Bosnia and Herzegovina","intercept: 65.44593 year1950: 0.14568881 continent: Europe country: Bulgaria","intercept: 63.40486 year1950: 0.22545944 continent: Europe country: Croatia","intercept: 67.23845 year1950: 0.14481538 continent: Europe country: Czech Republic","intercept: 70.79093 year1950: 0.12133007 continent: Europe country: Denmark","intercept: 65.97312 year1950: 0.23792517 continent: Europe country: Finland","intercept: 67.31313 year1950: 0.23850140 continent: Europe country: France","intercept: 67.14076 year1950: 0.21368322 continent: Europe country: Germany","intercept: 66.58241 year1950: 0.24239860 continent: Europe country: Greece","intercept: 65.74552 year1950: 0.12364895 continent: 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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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---
class: bg-main1

# Let's summarise the information learned from the model coefficients.

.vlarge[
- 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: Rwand, Zimbabwe, Zambia
]

---
class: bg-main1

# Model diagnostics by country

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

country_glance
```

```
## # A tibble: 142 x 15
## 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>
```

---
class: bg-main1

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

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

---
class: bg-main1

# Countries with worst fit

.huge[
Examine the countries with the worst fit, countries with `$R^2<0.45$`, by making scatterplots 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)
```

---
class: bg-main1

.vlarge[
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: bg-main1

# Your Turn:

.huge[
- Use google to explain these dips using world history and current affairs information. 
- finish the lab exercise (with new data)
- once you are done, you can collect mid semester exam
- remember the project deadline: **Find team members, and potential topics to study (List of groups will be posted here)**
]

---
class: bg-main1

## Share and share alike

<a rel="license" href="http://creativecommons.org/licenses/by/4.0/"><img alt="Creative Commons License" style="border-width:0" src="https://i.creativecommons.org/l/by/4.0/88x31.png" /></a> This work is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by/4.0/">Creative Commons Attribution 4.0 International License</a>.

???

# 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?