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data(mtcars) # Simple linear regression: mpg ~ wt model1 <- lm(mpg ~ wt, data = mtcars) summary(model1) # Coefficients: # Estimate Std. Error t value Pr(>|t|) # (Intercept) 37.285 1.878 19.858 < 2e-16 *** # wt -5.344 0.559 -9.559 1.29e-10 *** coef(model1) # intercept and slope confint(model1) # 95% CI for each coefficient residuals(model1)[1:5] fitted(model1)[1:5] # Multiple linear regression model2 <- lm(mpg ~ wt + hp + cyl, data = mtcars) summary(model2) # Model with interaction model3 <- lm(mpg ~ wt * cyl, data = mtcars) # equivalent to: mpg ~ wt + cyl + wt:cyl summary(model3) # Polynomial term model4 <- lm(mpg ~ wt + I(wt^2), data = mtcars) summary(model4) # Predict for new data new_cars <- data.frame(wt = c(2.5, 3.0, 3.5), hp = c(110, 130, 150), cyl = c(4, 6, 8)) predict(model2, newdata = new_cars) predict(model2, newdata = new_cars, interval = "confidence") # ANOVA table for the model anova(model2) # Compare nested models anova(model1, model2) # F-test for added predictors # Diagnostic plots (opens 4 plots) # par(mfrow = c(2, 2)) # plot(model1) # R-squared and F-statistic s <- summary(model1) s$r.squared # 0.7528 s$adj.r.squared # 0.7446 s$fstatistic # F-value and df
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