How do you run a linear regression in R?

Fit the model with model |t|) tests whether it differs from zero, and Multiple R-squared is the variance explained. Add more predictors with the + operator for multiple regression, then check the assumptions with plot(model).

How do you check regression assumptions in R?

Run plot(model) to get four diagnostic plots: Residuals vs Fitted for linearity and equal variance, Normal Q-Q for residual normality, Scale-Location for homoscedasticity, and Residuals vs Leverage for influential points. For multicollinearity in a multiple model, use vif() from the car package.

What does a high VIF mean in R regression?

A high variance inflation factor, generally above 5 or 10, means a predictor is strongly explained by the other predictors, so its coefficient is unstable and hard to interpret. The usual fix is to drop or combine the redundant variables rather than keep them all in the model.

How to run a linear regression in R

Q: How do you do multiple regression in R?

Add predictors to the formula with the + operator, for example lm(score ~ hours + prior_gpa + motivation, data = df). Each coefficient is the effect of that predictor holding the others constant. Use the * operator for an interaction, and make categorical predictors factors so R creates the dummy variables automatically.

To run a linear regression in R, you fit the model with lm(outcome ~ predictor, data = df), read the coefficients, R-squared, and F test with summary(), and then check the four regression assumptions through the diagnostic plots before trusting a single number. Moving from one predictor to multiple regression is just adding terms to the formula, but it brings multicollinearity and model-comparison questions that the simple model never raised. This guide covers both with the code to keep.

Simple linear regression with lm()

Linear regression models a continuous outcome as a straight-line function of one or more predictors. Fit and read it with two lines:

model <- lm(score ~ hours, data = df)
summary(model)

The Estimate for hours is the slope: the predicted change in score for each additional hour. The Pr(>|t|) column tests whether that slope differs from zero, Multiple R-squared is the proportion of variance explained, and the F statistic at the foot tests the model as a whole. Understanding what those p-values mean is covered in our p-value guide.

The assumptions and how to check them

Ordinary least squares assumes linearity, independent errors, constant error variance (homoscedasticity), and roughly normal residuals. R gives all four checks in one place:

par(mfrow = c(2, 2))
plot(model)
# Residuals vs Fitted: linearity and equal variance
# Normal Q-Q: residual normality
# Scale-Location: homoscedasticity
# Residuals vs Leverage: influential points (Cook's distance)

The full reasoning behind each plot, and what a violation looks like, is set out in linear regression assumptions. Checking residuals rather than the raw variables is the same habit used in ANOVA in R.

Multiple regression: adding predictors

Add predictors with +, and an interaction with *:

model2 <- lm(score ~ hours + prior_gpa + motivation, data = df)
summary(model2)

# an interaction between two predictors
model3 <- lm(score ~ hours * motivation, data = df)

In a multiple model each coefficient is the effect of that predictor holding the others constant, which is why a predictor can be significant alone yet drop out once related variables enter. Categorical predictors should be factors; R then creates the dummy variables automatically and reports each level against the reference.

Checking multicollinearity

When predictors are strongly correlated, their coefficients become unstable and hard to interpret. Quantify it with the variance inflation factor from the car package:

library(car)
vif(model2)   # values above 5 (some say 10) signal a problem

A high VIF means a predictor is largely explained by the others; the usual remedy is to drop or combine the redundant variables, not to keep them all and report unstable estimates.

Comparing and choosing models

To decide whether an added predictor earns its place, compare nested models with an F test, and compare non-nested models with AIC:

anova(model, model2)   # is the larger model a real improvement?
AIC(model, model2)     # lower AIC is better

Resist adding predictors just to lift R-squared; the Adjusted R-squared in the summary penalizes that, and a model justified by theory beats one fitted by trial and error.

Reporting linear regression in APA style

Report the model fit as F(df1, df2) = value with its p and the R-squared, then each predictor as its unstandardized coefficient (b), standard error, and p-value, with a confidence interval from confint(model). A clean sentence reads: hours of study significantly predicted exam score, b = 2.13, 95% CI [1.40, 2.86], p < .001, with the model explaining 38% of the variance, R-squared = .38, F(3, 146) = 29.7, p < .001. The conventions sit in writing the result up in APA style, and the prose belongs in your results section of a research paper. When the outcome is binary rather than continuous, switch to logistic regression in R.