# load the data

d = read.csv("galton_students_110.csv")
head(d)
plot(x = d$child_height_cm, y = d$mid_parent_height_cm)

library(tinyplot)
plt(d$mid_parent_height_cm, d$child_height_cm, grid = TRUE)
plt_add(type = "lm")

# 2. run the model and save as m
m = lm( formula = child_height_cm ~ mid_parent_height_cm, 
        data = d )

# where is this R2 thing?
summary(m) # R2 = 0.26

# predict 160 and 180 cm tall parents
predictions = data.frame(mid_parent_height_cm = c(160, 180))
predictions$pred_child = predict(m , newdata = predictions)

# get residual standard error
summary(m) # 4.5

# how to compute b1 from correlation?
r = cor(d$mid_parent_height_cm, d$child_height_cm) # 0.51
sy = sd(d$child_height_cm)
sx = sd(d$mid_parent_height_cm)

# standard way: cov(x,y) / var(x)
b1 = r * sy / sx
# compare to coef(m)[2]
coef(m)[2]


# load STAR data
star_df = read.csv("star_data.csv")
star_df = star_df[complete.cases(star_df) , ]

library(dplyr)
# create 3 indicator variables TRUE/FALSE for each level of the `star` variable

star_dummies = star_df %>%
    mutate(
        is_regular = (star == "regular"),
        is_regular_plus = (star == "regular+aide"),
        is_small = (star == "small")
    )

# quick check: all of those need to have an average
# in (0,1)
star_dummies %>%
    summarise(across(starts_with("is_"), mean))

# create sum of those 3 
star_dummies = star_dummies %>%
    mutate(
        is_sum_of_all = is_regular + is_regular_plus + is_small
    )

star_dummies %>%
    summarise(across(starts_with("is_"), mean))

# regress math on is_regular_plus
lm(math  ~ is_regular_plus, data = star_dummies)

# predicted score in regular plus class
555.4726 + (-0.5487 ) * 1


# regress math on is_regular_plus
lm(math ~ is_regular + is_regular_plus + is_small,
   data = star_dummies)

# wrong
# small is the reference category
lm(math ~ is_regular + is_regular_plus,
   data = star_dummies)

# regular is the reference category
lm(math ~ is_small + is_regular_plus,
   data = star_dummies)

# full setup
# regress math on star
lm(math ~ star, star_dummies)
# regressing number on a character variable!
# R is smart to convert that into a as many dummies
# as there are different levels in `star`