Regression Analysis, Project Template, Residual Plots
Intuition: Residual Plots
(The attached PDF file has better formatting.)
Updated: February 13, 2006
Jacob: Can you show how to use residual plots to see if the slope parameter β is constant?
Rachel: Suppose we have 20 pairs of values for X and Y:
X | Y | X | Y | X | Y | X | Y |
10 | 18 | 17 | 28 | 22 | 33 | 25 | 33 |
10 | 19 | 18 | 29 | 22 | 32 | 25 | 31 |
11 | 22 | 20 | 29 | 24 | 31 | 28 | 33 |
14 | 23 | 20 | 31 | 25 | 32 | 29 | 33 |
15 | 25 | 21 | 31 | 25 | 32 | 30 | 34 |
Ordinary least squares estimation gives
= 13.671, with a standard error of 1.427 and a t statistic of 9.58
= 0.74351, with a standard error of 0.06666 and a t statistic of 11.15
Both coefficients have p-values of zero. The R2 is 87.4% and the adjusted R2 is 86.7%. The regression equation seems fine.
But the residual plots shows the relation is not linear. We use residual plots of the residual vs X and the residual vs the fitted value of Y. In both plots, the residuals look like a carot: v.
Jacob: What does that indicate?
Rachel: The slope of the residual line is first positive and then negative. This means that the estimated β is too low for low values of X and too high for high values of X.