In joepowers16/rethinking: Statistical Rethinking book package

06.01 R^2^ Review

Overview:

Adding parameters will always improve a model's fit as measured by R^2^.

knitr::opts_chunk$set(
  fig.align='center', dpi = 150, 
  include=FALSE, echo=FALSE, message=FALSE, warning=FALSE
)

library(magrittr)
library(modelr)
library(tidyverse)

file_r2 <- paste(dir_images, "r2_explained.png", sep = "/")
file_r2v2 <- paste(dir_images, "r_squared_formula.png", sep = "/")

knitr::include_graphics(file_r2)

Note that the classic formula for R^2^ seen below is derived from the formula seen above.

knitr::include_graphics(file_r2v2)
# image from http://www.simages.org/r-squared-formula/

Explore what large and small R^2^ look like in models of data.

m1 <- lm(mpg ~ drat, data = mtcars)
rsquare(m1, mtcars)

m3 <- lm(mpg ~ drat + wt + hp, data = mtcars)
rsquare(m3, mtcars)

Residuals

mtcars %<>% 
  add_residuals(m1, var = "resid1") %>% 
  add_residuals(m3, var = "resid3") %>% 
  gather(resid1, resid3, key = resid_type, value = resid_value)  

ggplot(mtcars) + 
  geom_hline(yintercept = 0) + 
  geom_point(aes(x = wt, y = resid_value), color = "red") +
  facet_grid(~resid_type)