Data-Centric Statistical Inference Using R and Tidyverse/

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Conditions for Inference for Regression-II

Conditions for Inference for Regression-II

Learn about the normality of residuals and equality of variance in regression inference conditions.

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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.

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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 ...