CHAPTER 16 Getting Straight Talk on Straight-Line Regression 223

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 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.

© John Wiley & Sons, Inc.