为什么质量差的钻石更贵

低质量的钻石（切工差、颜色差、净度差）价格较高。

ggplot(diamonds, aes(cut, price)) + geom_boxplot()

ggplot(diamonds, aes(color, price)) + geom_boxplot()

ggplot(diamonds, aes(clarity, price)) + geom_boxplot()

最差的钻石颜色为 J（略带黄色），最差的净度为 I1（肉眼可见的内含物）

价格与重量

看起来质量较差的钻石价格较高，是因为有一个重要的混淆变量：carat（钻石的重量）。钻石的重量是决定钻石价格的最重要因素，质量越差的钻石往往越重。

ggplot(diamonds, aes(carat, price)) + 
  geom_hex(bins = 50)

diamonds2 <- diamonds %>% 
  filter(carat <= 2.5) %>% 
  mutate(lprice = log2(price), lcarat = log2(carat))
ggplot(diamonds2, aes(lcarat, lprice)) + 
  geom_hex(bins = 50)

mod_diamond <- lm(lprice ~ lcarat, data = diamonds2)
grid <- diamonds2 %>% 
  data_grid(carat = seq_range(carat, 20)) %>% 
  mutate(lcarat = log2(carat)) %>% 
  add_predictions(mod_diamond, "lprice") %>% 
  mutate(price = 2 ^ lprice)

ggplot(diamonds2, aes(carat, price)) + 
  geom_hex(bins = 50) + 
  geom_line(data = grid, colour = "red", size = 1)

diamonds2 <- diamonds2 %>% 
  add_residuals(mod_diamond, "lresid")

ggplot(diamonds2, aes(lcarat, lresid)) + 
  geom_hex(bins = 50)

ggplot(diamonds2, aes(cut, lresid)) + geom_boxplot()

ggplot(diamonds2, aes(color, lresid)) + geom_boxplot()

ggplot(diamonds2, aes(clarity, lresid)) + geom_boxplot()

##一个更复杂的模型

mod_diamond2 <- lm(lprice ~ lcarat + color + cut + clarity, data = diamonds2)
grid <- diamonds2 %>% 
  data_grid(cut, .model = mod_diamond2) %>% 
  add_predictions(mod_diamond2)
grid
## # A tibble: 5 × 5
##   cut       lcarat color clarity  pred
##   <ord>      <dbl> <chr> <chr>   <dbl>
## 1 Fair      -0.515 G     VS2      11.2
## 2 Good      -0.515 G     VS2      11.3
## 3 Very Good -0.515 G     VS2      11.4
## 4 Premium   -0.515 G     VS2      11.4
## 5 Ideal     -0.515 G     VS2      11.4
#> # A tibble: 5 x 5
#>   cut       lcarat color clarity  pred
#>   <ord>      <dbl> <chr> <chr>   <dbl>
#> 1 Fair      -0.515 G     VS2      11.2
#> 2 Good      -0.515 G     VS2      11.3
#> 3 Very Good -0.515 G     VS2      11.4
#> 4 Premium   -0.515 G     VS2      11.4
#> 5 Ideal     -0.515 G     VS2      11.4

ggplot(grid, aes(cut, pred)) + 
  geom_point()

diamonds2 <- diamonds2 %>% 
  add_residuals(mod_diamond2, "lresid2")

ggplot(diamonds2, aes(lcarat, lresid2)) + 
  geom_hex(bins = 50)