Residual

In: Computers and Technology

Submitted By gagsing
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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 probability plot of the residuals suggests that the error terms are indeed normally distributed.
We did what seems like an awful lot of work to create our normal probability plot of residuals. That's because we effectively created it "by hand." The good news is that most statistical software, including Minitab, will create the normal probability plot of the residuals for us. In fact, Minitab offers three different versions of the plots. The first one looks just like the above plot.
The second version of the plot:

draws a line (with a confidence band) through the points to help you decide if the relationship is linear. And, the third version of the plot — the one we will probably use the most often — looks like:

The advantage of this version of the plot is that it includes (in the lower right hand corner) the P-value for the Ryan-Joiner test: * for testing the null hypothesis H0: The error terms are normally distributed * against the alternative hypothesis HA: The error terms are not normally distributed.
The Ryan-Joiner test basically assesses the correlation (r = 0.9811) between the sample percentiles and the theoretical normal percentiles. Since the P-value is…...

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