Visualize the 4 Assuptions of Linear Regression
Jack Ruso asked - Is there a R function that can quickly check if these assumptions are met? Or is the best way to simply graph the residuals for each model and check the assumptions visually?
Jack I would argue the best way to go would be to setup some ggplots in an Rmarkdown document or find a package that has done it for you. To my way of thinking using plots will not only answer your questions about the four assumptions, but will likely provide you with some additional insights about your data and/or model. Given the four key assumptions below here is one plotting solution for you consideration.
The Four Key Assumptions For Linear Regression are:
- Linearity of the data. The relationship between the predictor (x) and the outcome (y) is assumed to be linear.
- Normality of residuals. The residual errors are assumed to be normally distributed.
- Homogeneity of residuals variance. The residuals are assumed to have a constant variance (homoscedasticity)
- Independence of residuals error terms.
Let’s use the Cars package to create a linear model that we can use to validate our four assmptions. First we utilize base R’s plot() function to perform our regression diagnostic. This function creates four plots:
- Residual vs. Fitted. Used to check the linear relationship assumptions.
- Normal Q-Q. Used to examine whether the residuals are normally distributed. It’s good if residuals points follow the straight dashed line.
- Scale-Location. Used to check the homogeneity of variance of the residuals (homoscedasticity).
- Residuals vs Leverage. Used to identify influential cases, that is extreme values that might influence the regression results when included or excluded from the analysis.
Another alternative is the ggfortify’s autoplot function. This creates as similar set of plots to help validate the assumptiosn.
