Question

(Regression Analysis)

Consider the simple linear regression model (I) and the corresponding scatter plot with the covariates XX (x-axis) vs residuals (y-axis). What model assumption violations can be diagnosed by this scatter plot?

Answer 1

we can check for independence of residuals,Checking the error variance (hetero-skedasticity )

1) Independence

The pattern structures of residual plots not only help to check the validity of a regression model, but they can also provide hints on how to improve it. For example, a curved pattern in the Residual vs. Independent plot suggests that a higher order term should be introduced to the fitting model.

2)

Checking the error variance

A residuals plot (see the picture below) which has an increasing trend suggests that the error variance increases with the independent variable; while a distribution that reveals a decreasing trend indicates that the error variance decreases with the independent variable. Neither of these distributions are constant variance patterns. Therefore they indicate that the assumption of constant variance is not likely to be true and the regression is not a good one. On the other hand, a horizontal-band pattern suggests that the variance of the residuals is constant.