CHAPTER 16 Getting Straight Talk on Straight-Line Regression 225

Looking at the rows in Figure 16-4, the intercept (labeled (Intercept)) is the pre-

dicted value of Y when X is equal to 0, and is expressed in the same units of mea-

surement as the Y variable. The slope (labeled Wgt) is the amount the predicted

value of Y changes when X increases by exactly one unit of measurement, and is

expressed in units equal to the units of Y divided by the units of X.

In the example shown in Figure  16-4, the estimated value of the intercept is

76.8602 mmHg, and the estimated value of the slope is 0.4871 mmHg/kg.»

» ^{The intercept value of 76.9 mmHg means that a person who weighs 0 kg is}

predicted to have a SBP of about 77 mmHg. But nobody weighs 0 kg! The

intercept in this example (and in many straight-line relationships in biology)

has no physiological meaning at all, because 0 kg is completely outside the

range of possible human weights.»

» ^{The slope value of 0.4871 mmHg/kg does have a real-world meaning. It means}

that every additional 1 kg of weight is associated with a 0.4871 mmHg increase

in SBP. If we multiply both estimates by 10, we could say that every additional

10 kg of body weight is associated with almost a 5 mmHg SBP increase.

The standard errors of the coefficients

The second column in the regression table often contains the standard errors of

the estimated parameters. In Figure 16-4, it is labeled Std. Error, but it could be

stated as SE or use a similar term. We use SE to mean standard error for the rest

of this chapter.

Because data from your sample always have random fluctuations, any estimate

you calculate from your data will be subject to random fluctuations, whether it is

a simple summary statistic or a regression coefficient. The SE of your estimate

tells you how precisely you were able to estimate the parameter from your data,

which is very important if you plan to use the value of the slope (or the intercept)

in a subsequent calculation.

Keep these facts in mind about SE:»

» ^{SEs always have the same units as the coefficients themselves. In the}

example shown in Figure 16-4, the SE of the intercept has units of mmHg,

and the SE of the slope has units of mmHg/kg.»

» ^{Round off the estimated values. It is not helpful to report unnecessary}

digits. In this example, the SE of the intercept is about 14.7, so you can say that

the estimate of the intercept in this regression is about 77

15

mmHg. In the

same way, you can say that the estimated slope is 0 49

0 18

.

.

mmHg/kg.