Here are the characteristics of a well-behaved residual vs. fits plot and what they suggest about the appropriateness of the simple linear regression model:
* The residuals "bounce randomly" around the 0 line. This suggests that the assumption that the relationship is linear is reasonable.
* The residuals roughly form a "horizontal band" around the 0 line. This suggests that the variances of the error terms are equal.
* No one residual "stands out" from the basic random pattern of residuals. This suggests that there
Normal Probability Plot
Note that the relationship between the theoretical percentiles and the sample percentiles is approximately linear. Therefore, the normal ...view middle of the document...
10), we fail to reject the null hypothesis. There is insufficient evidence to conclude that the error terms are not normally distributed. We can proceed assuming that the error terms are normally distributed.
Let's take a look at examples of the different kinds of normal probability plots we can obtain and learn what each tells us.
Normally distributed residuals
The following histogram of residuals suggests that the residuals (and hence the error terms) are normally distributed:
The normal probability plot of the residuals is approximately linear supporting the condition that the error terms are normally distributed.
Normal residuals but with one outlier
The following histogram of residuals suggests that the residuals (and hence the error terms) are normally distributed. But, there is one extreme outlier (with a value of 10):
Here's the corresponding normal probability plot of the residuals:
This is a classic example of what a normal probability plot looks like when the residuals are normally distributed, but there is just one outlier. The relationship is approximately linear with the exception of the one data...