Residuals and Residual Plots

Statistics · Axiom Academy

LESSON Residuals and Residual Plots Understanding how residuals help us evaluate regression models and check assumptions A residual is the vertical distance between an observed data point and the regression line. It represents the error in our prediction for that particular observation. where y is the actual observed value and ŷ (y-hat) is the predicted value from the regression line Positive residuals occur when the actual value is above the regression line (we underpredicted). Negative residuals occur when the actual value is below the line (we overpredicted). A residual plot is a scatter plot with predicted values (ŷ) on the x-axis and residuals (e) on the y-axis. This plot helps us check whether the regression model fits the data appropriately. The horizontal line at y = 0 represents perfect predictions (zero error). Points above this line are positive residuals, points below are negative residuals. 3. What Good Residual Plots Look Like An ideal residual plot shows random scatter around the horizontal zero line with no obvious patterns. This indicates that our linear model is appropriate for the data. Random scatter with no clear pattern or structure Points roughly evenly distributed above and below zero Consistent spread (variance) across all predicted values No extreme outliers or influential points

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