Chapter 5 Multiple Linear Regression

In this chapter, you will learn how to:

• Write and interpret a multiple linear regression equation;
• Examine variables prior to including them in a regression model;
• Fit a multiple linear regression model;
• Interpret the estimated regression coefficients;
• Distinguish between confounders, mediators, and moderators;
• Test and visualize interactions between predictors;
• Obtain predictions from the model;
• Compute three types of confidence or prediction intervals;
• Diagnose the fit of the model;
• Adjust the model to improve the fit, if needed;
• Examine collinearity of predictors and remove redundancies;
• Look for outliers and influential observations;
• Distinguish between confirmatory and exploratory analyses;
• Prevent an increase in Type I error when carrying out multiple tests;
• Carry out a sensitivity analysis to assess the robustness of results;
• Avoid overgeneralizing the implications of a regression model; and
• Appropriately summarize the methods and results of a multiple linear regression analysis.

Load tidyverse before proceeding. In addition, we will use a few custom functions found in the file Functions_rmph.R (downloadable from RMPH Resources). To access these functions, source() the file containing their code.

library(tidyverse)
# Put Functions_rmph.R in same folder as your R project
source("Functions_rmph.R")