# Refresher on multiple regression for the applied researcher

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## Overview of our refresher on multiple regression workshop

Many researchers have taken a course that covers multiple regression, the statistical workhorse of the social sciences, but have forgotten much of what they learned. The goal of this workshop is to review many of the main concepts of regression, from the perspective of the applied researcher (in other words, we won’t be reviewing any proofs!). The workshop focuses on 1) the underlying statistical assumptions, what happens when they are violated, and simple ways to address violations, 2) interpreting a variety of regression coefficients correctly, and 3) model fit.

## Expected outcomes

By the end of the workshop, participants should understand the basic assumptions underlying multiple regression and what they mean for the applied researcher, how to interpret regression coefficients, and how to discuss model fit. This is a great workshop to take prior to enrolling in our logistic regression workshop.

## Who should attend?

The target audience is researchers who have taken a statistics course that covered multiple regression at some point, but who have forgotten some of the basics. Researchers who know univariate statistics and would like to learn more about multiple regression are welcome, but should realize that this is not a complete course on multiple regression. Software demonstrations will use Stata, but syntax and output from SAS and SPSS will be included for participants who use those software packages in their work.

## Agenda

1. Review the assumptions of regression
1. Independence of errors and clustered standard errors
2. Homoskedasticity and robust standard errors
3. No omitted relevant variables and causal inference
4. Collinearity
5. Error term
1. What the random error term really is (it’s not random)
2. Normality assumption: it’s the errors, not the dependent variable
2. Interpretation of regression coefficients
1. Understanding the null hypothesis and p values for coefficients
2. What the intercept tells you
3. Unstandardized regression coefficients
4. Standardized regression coefficients and when to use them
5. Dummy variables for two and more groups
6. Interpreting nonlinear relationships
1. Logged dependent and independent variables
2. Squared terms
7. Interaction terms
1. Why you can’t use standard software output to understand the interaction
2. Correctly estimating the standard errors
3. How to interpret the interactions by plotting
3. Model fit
1. Interpreting R-squared and standard error of the estimate
2. When measures of model fit matter