Gapminder

GDP and life expectancy

What is the association?

library(gapminder)
library(tidyverse)

## ── Attaching packages ─────────────────────────────────────── tidyverse 1.3.0 ──

## ✓ ggplot2 3.3.3     ✓ purrr   0.3.4
## ✓ tibble  3.0.5     ✓ dplyr   1.0.3
## ✓ tidyr   1.1.2     ✓ stringr 1.4.0
## ✓ readr   1.4.0     ✓ forcats 0.5.0

## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## x dplyr::filter() masks stats::filter()
## x dplyr::lag()    masks stats::lag()

ggplot(gapminder, aes(x = gdpPercap, y = lifeExp)) + 
  geom_point()

gapminder %>% 
  filter(year == 2007) %>%
  ggplot(aes(x = gdpPercap, y = lifeExp)) + 
  geom_point() +
  geom_smooth()

## `geom_smooth()` using method = 'loess' and formula 'y ~ x'

gm2007 <- gapminder %>% 
  filter(year == 2007)

model_lm <- lm(lifeExp ~ gdpPercap, data = gm2007)
summary(model_lm)

## 
## Call:
## lm(formula = lifeExp ~ gdpPercap, data = gm2007)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -22.828  -6.316   1.922   6.898  13.128 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 5.957e+01  1.010e+00   58.95   <2e-16 ***
## gdpPercap   6.371e-04  5.827e-05   10.93   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 8.899 on 140 degrees of freedom
## Multiple R-squared:  0.4606, Adjusted R-squared:  0.4567 
## F-statistic: 119.5 on 1 and 140 DF,  p-value: < 2.2e-16

library(broom)
tidy(model_lm)

## # A tibble: 2 x 5
##   term         estimate std.error statistic   p.value
##   <chr>           <dbl>     <dbl>     <dbl>     <dbl>
## 1 (Intercept) 59.6      1.01           59.0 9.89e-101
## 2 gdpPercap    0.000637 0.0000583      10.9 1.69e- 20

glance(model_lm)

## # A tibble: 1 x 12
##   r.squared adj.r.squared sigma statistic  p.value    df logLik   AIC   BIC
##       <dbl>         <dbl> <dbl>     <dbl>    <dbl> <dbl>  <dbl> <dbl> <dbl>
## 1     0.461         0.457  8.90      120. 1.69e-20     1  -511. 1028. 1037.
## # … with 3 more variables: deviance <dbl>, df.residual <int>, nobs <int>

augment(model_lm) %>%
  ggplot(aes(gdpPercap, lifeExp)) +
  geom_point() +
  geom_line(aes(gdpPercap, .fitted))

model_loess <- loess(lifeExp ~ gdpPercap,
                     span = .5,
                     degree = 2,
                     data = gm2007)

augment(model_loess) %>%
  ggplot(aes(gdpPercap, lifeExp)) +
  geom_point() +
  geom_line(aes(gdpPercap, .fitted))

model_lm2 <- lm(lifeExp ~ gdpPercap + poly(gdpPercap, 2), data = gm2007)
augment(model_lm2) %>%
  ggplot(aes(gdpPercap, lifeExp)) +
  geom_point() +
  geom_line(aes(gdpPercap, .fitted))

c(.2, .7) %>% map_dfr(~ loess(lifeExp ~ gdpPercap, span = .x, data = gapminder) %>% augment() %>% mutate(span = .x))