Introduction

Learning Objectives

By the end of this section, you should be able to:

• Explain when and why HCI researchers use regression analysis
• Fit and interpret a simple and multiple linear regression in R
• Check regression assumptions using residual plots and diagnostic tests
• Include and interpret interaction terms in a regression model
• Compare competing models using adjusted R-squared and AIC
• Fit a logistic regression for binary outcomes and interpret odds ratios
• Distinguish between prediction-oriented and explanation-oriented uses of regression
• Fit linear and generalized linear mixed-effects models in R using lme4
• Decide between random intercepts and random slopes, and report variance components, fixed effects, and p-values appropriately

1. Introduction

Regression analysis is one of the most versatile tools available to HCI researchers. At its core, regression models the relationship between an outcome variable (also called the dependent variable or response) and one or more predictor variables (independent variables or covariates). While t-tests and ANOVA ask "do group means differ?", regression asks a broader question: "how do one or more variables relate to the outcome, and by how much?"

When do HCI researchers use regression?

Regression appears throughout HCI research in several common scenarios:

• Modeling continuous outcomes. Predicting task completion time from participant characteristics (age, prior experience) and interface conditions.
• Controlling for covariates. You want to know whether a new interface design reduces errors, but participants differ in age and tech experience. Regression lets you estimate the effect of interface type while statistically adjusting for those individual differences.