Residuals

Earlier, we defined the residuals as the vertical distance between the fitted regression line and the data points. Another way to look at this is, the residual is the difference between the predicted value and the observed value,

Note that the sum of residuals, , always equals zero. However, the quantity we minimized to obtain our least squares equation was the residual sum of squares, SSRes,

An alternative formula for SSRes is

Notice that the residual sum of squares is never negative. The larger SSRes is, the further away from the line data points fall.

• A data point which does not follow the patterns of the majority of the data..
• Point A point whose removal makes a large difference in the equation of the regression line.
• Variable A variable which affects the response but is not one of the explanatory variables.
• Plot A plot of the residuals versus x (or the fitted value). We do not want any pattern in this plot.