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Residual Diagnostics

Source: vignettes/residual_diagnostics.Rmd
residual_diagnostics.Rmd

Introduction

olsrr offers tools for detecting violation of standard regression assumptions. Here we take a look at residual diagnostics. The standard regression assumptions include the following about residuals/errors:

  • The error has a normal distribution (normality assumption).
  • The errors have mean zero.
  • The errors have same but unknown variance (homoscedasticity assumption).
  • The error are independent of each other (independent errors assumption).

Residual QQ Plot

Graph for detecting violation of normality assumption.

model <- lm(mpg ~ disp + hp + wt + qsec, data = mtcars)
ols_plot_resid_qq(model)

Residual Normality Test

Test for detecting violation of normality assumption.

model <- lm(mpg ~ disp + hp + wt + qsec, data = mtcars)
ols_test_normality(model)
## -----------------------------------------------
##        Test             Statistic       pvalue  
## -----------------------------------------------
## Shapiro-Wilk              0.9366         0.0600 
## Kolmogorov-Smirnov        0.1152         0.7464 
## Cramer-von Mises          2.8122         0.0000 
## Anderson-Darling          0.5859         0.1188 
## -----------------------------------------------

Correlation between observed residuals and expected residuals under normality.

model <- lm(mpg ~ disp + hp + wt + qsec, data = mtcars)
ols_test_correlation(model)
## [1] 0.970066

Residual vs Fitted Values Plot

It is a scatter plot of residuals on the y axis and fitted values on the x axis to detect non-linearity, unequal error variances, and outliers.

Characteristics of a well behaved residual vs fitted plot:

  • The residuals spread randomly around the 0 line indicating that the relationship is linear.
  • The residuals form an approximate horizontal band around the 0 line indicating homogeneity of error variance.
  • No one residual is visibly away from the random pattern of the residuals indicating that there are no outliers.
model <- lm(mpg ~ disp + hp + wt + qsec, data = mtcars)
ols_plot_resid_fit(model)

Residual Histogram

Histogram of residuals for detecting violation of normality assumption.

model <- lm(mpg ~ disp + hp + wt + qsec, data = mtcars)
ols_plot_resid_hist(model)