Notes from the lecture on simple linear regression

LinearRegression.R

library(tibble)
library(ggplot2)
library(moderndive)

# 1. Implement linear regression-----------------
# Make a shortcut to the data:
beer_data <- as_tibble(DataScienceExercises::beer)
head(beer_data)

# Conduct the linear regression:
beer_lm <- lm(
  formula = consumption ~ income, 
  data = beer_data)
beer_lm

# To get more information about the regression:
summary(beer_lm)
moderndive::get_regression_table(beer_lm)

# Digression: the results might change drastically if you do a multiple linear
#  regression
summary(lm(
  formula = consumption ~ income + price, 
  data = beer_data))
# More info on this: "omitted variable bias"

# 2. Compute R2-----------------

# Illustrating what we mean by total variation:
mean_consumption <- mean(beer_data$consumption)

ggplot(data = beer_data, aes(x=1:30, y=consumption)) +
  geom_hline(yintercept = mean_consumption) +
  geom_point() + theme_linedraw()

# Compute TSS, RSS and ESS manually:
tss <- sum((beer_data$consumption - mean_consumption)**2)
rss <- sum(beer_lm$residuals**2)
ess <- sum((beer_lm$fitted.values - mean_consumption)**2)

# From this we can compute R2 manually:
ess/tss

# Compare to what you get from, e.g., summary():
summary(beer_lm)[["r.squared"]]