CHAPTER 16 Getting Straight Talk on Straight-Line Regression 221

The actual equation of the straight line is not SBP = weight, but more accurately

SBP = a + b × weight, with the a (intercept) and b (slope) parameters having been

left out of the model. This is a reminder that although the goal is to evaluate the

SBP = weight model conceptually, in reality, this relationship will be numerically

different with each data set we use.

Evaluating residuals

The residual for a point is the vertical distance of that point from the fitted line.

It’s calculated as Residual

Y

a

b

X

(

), where a and b are the intercept and

slope of the fitted straight line, respectively.

Most regression software outputs several measures of how the data points scatter

above and below the fitted line, which provides an idea of the size of the residuals

(see “Summary statistics for the residuals” for how to interpret these measures).

The residuals for the sample data are shown in Figure 16-5.

FIGURE 16-4:

Sample straight-

line regression

output from R.

FIGURE 16-5:

Scattergram of

SBP versus

weight, with the

fitted straight line

and the residuals

of each point

from the line.

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