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Residual Diagnostics

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)

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They may not be fully stable and should be used with caution. We make no claims about them.
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