Residual Analysis Examples

Statistics · Axiom Academy

EXAMPLE Residual Analysis Examples Learn how to compute residuals and interpret residual plots to assess model fit Dataset: Study Hours vs. Test Score Excellent work! You've completed these residual analysis examples. Here's what we learned: Computing Residuals: A residual is the difference between the observed value and the predicted value from the regression line: e = y - ŷ . Positive residuals mean the model underestimated, negative residuals mean it overestimated. Creating Residual Plots: Plot residuals on the y-axis versus predictor values (or predicted values) on the x-axis. This visualization helps identify whether the linear model is appropriate for the data. Interpreting Patterns: A good residual plot shows random scatter around zero with no clear patterns. Curved patterns suggest non-linearity, funnel shapes indicate non-constant variance, and outliers may need investigation. Model Assessment: Residual analysis is essential for checking regression assumptions. Even if R² is high, residual plots can reveal serious problems with model fit that need to be addressed. Always create and examine residual plots when performing regression analysis. They provide critical insights that summary statistics alone cannot reveal!

This is the written version of the interactive lesson above. See the full Statistics course.