A P STATISTICS LESSON 3 – 3 (DAY 3) A P STATISTICS LESSON 3 – 3 (DAY 3) RISIDUALS

ESSENTIAL QUESTION: What is a residual and what can a residual graph tell us about linear regression lines? Objective: To define and use residuals in the analysis of linear regression lines.

Residuals A residual is the difference between an observed variable and the value predicted by the regression line. That is, residual = observed y – predicted y = y - ŷ

Residual Facts The mean of the least-square residuals is always zero. The sum is not exactly 0 because the software rounded the residuals to four decimal places. This is roundoff error. The horizontal line of the residual plot is at zero.

Residual Plots A residual plot is a scatterplot of the regression residuals against the explanatory variable. Residual plots help us assess the fit of a regression line. If the regression line captures the overall relationship between x and y, the residuals should should have no systematic pattern. The residual plot will look something like the simplfied pattern. That plot shows a uniform scatter of the points about the fitted line, with no unusual individual observations.