Search⌘ K
AI Features
Home
Courses
Data-Centric Statistical Inference Using R and Tidyverse

Conditions for Inference for Regression-II

Explore the critical conditions necessary for valid regression inference, such as normality and equal variance of residuals. Understand how to assess these with graphical methods, the importance of each condition, and the implications when they are not fully met. This lesson guides you through interpreting residual analysis and recognizing potential model shortcomings to improve regression analysis outcomes.

We'll cover the following...

Normality of residuals

The third condition is that the residuals should follow a normal distribution. Furthermore, the center of this distribution should be 0. In other words, sometimes the regression model will make positive errors — y−y^>0y−\hat{y} >0. Other times, the regression model will make equally negative errors — y−y^<0y−\hat{y} <0. However, on average, the errors should equal 0 and their shape should be similar to that of a bell.

The simplest way to check the normality of the residuals is to look at a histogram, which we visualize in the figure below.

R
ggplot(regression_points, aes(x = residual)) +
  geom_histogram(binwidth = 0.25, color = "white") +
  labs(x = "Residual")

This histogram shows that we have more positive residuals than negative. The residual ...