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

mmHg. In the same way, you can say that the estimated slope is

mmHg/kg.

When reporting regression coefficients in professional publications, you may state the SE like this:

“The predicted increase in systolic blood pressure with weight (±1 SE) was

mmHg/kg.”

If you know the value of the SE, you can easily calculate a confidence interval (CI) around the

estimate (see Chapter 10 for more information on CIs). These expressions provide a very good

approximation of the 95 percent confidence limits (abbreviated CL), which mark the low and high

ends of the CI around a regression coefficient:

More informally, these are written as

.

So, the 95 percent CI around the slope in our example is calculated as

, which

works out to

, with the final confidence limits of 0.14 to 0.84 mmHg. If you submit a

manuscript for publication, you may express the precision of the results in terms of CIs instead of SEs,

like this: “The predicted increase in SBP as a function of body weight was 0.49 mmHg/kg

.”