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FIGURE 16-6: The residuals versus fitted (a) and normal (b) Q-Q graphs help you determine whether your data meets the

requirements for straight-line regression.

As stated at the beginning of this section, you calculate the residual for each point by subtracting the

predicted Y from the observed Y. As shown in Figure 16-6, a residuals versus fitted graph displays the

values of the residuals plotted along the Y axis and the predicted Y values from the fitted straight line

plotted along the X axis. A normal Q-Q graph shows the standardized residuals, which are the

residuals divided by the RMS value, along the Y axis, and theoretical quantiles along the X axis.

Theoretical quantiles are what you’d expect the standardized residuals to be if they were exactly

normally distributed.

Together, the two graphs shown in Figure 16-6 provide insight into whether your data

conforms to the requirements for straight-line regression:

Your data must lie above and below the line randomly across the whole range of data.

The average amount of scatter must be fairly constant across the whole range of data.

The residuals should be approximately normally distributed.

You need years of experience examining residual plots before you can interpret them confidently, so

don’t feel discouraged if you can’t tell whether your data complies with the requirements for straight-

line regression from these graphs. Here’s how we interpret them, allowing for other biostatisticians to

disagree:

We read the residuals versus fitted chart in Figure 16-6 to show the points lying equally above and

below the fitted line, because this appears true whether you’re looking at the left, middle, or right

part of the graph.

Figure 18-6 shows most of the residuals lie within

mmHg of the line, but several larger

residuals appear to be where the SBP is around 115 mmHg. We think this is a little suspicious. If

you see a pattern like this, you should examine your raw data to see whether there are unusual

values associated with these particular participants.