226 PART 5 Looking for Relationships with Correlation and Regression

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 0 49

0 18

.

.

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 expres-

sions 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:

Lower

CL

Coefficient

SE

%

95

2

Upper

CL

Coefficient

SE

95

2

%

More informally, these are written as 95%

coefficient 2

CI

SE.

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

0 49

2

0 176

.

.

, which works out to 0 49

0 35

.

.

, 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

95% CI : 0.14 0.84 .”

The Student t value

In most output, there is a column in the regression table that shows the ratio of

the coefficient divided by its SE. This column is labeled t value in Figure 16-4, but

it can be labeled t or other names. This column is not very useful. You can think of

this column as an intermediate quantity in the calculation of what you’re really

interested in, which is the p value for the coefficient.

The p value

A column in the regression tables (usually the last one) contains the p value,

which indicates whether the regression coefficient is statistically significantly

different from 0. In Figure 16-4, it is labeled Pr

t|

|

, but it can be called a variety

of other names, including p value, p, and Signif.

In Figure 16-4, the p value for the intercept is shown as 5 49

05

.

e

, which is equal

to 0.0000549 (see the description of scientific notation in Chapter 2). Assuming

we set α at 0.05, the p value is much less than 0.05, so the intercept is statistically

significantly different from zero. But recall that in this example (and usually in

straight-line regression), the intercept doesn’t have any real-world importance.

It’s equals the estimated SBP for a person who weighs 0 kg, which is nonsensical,

so you probably don’t care whether it’s statistically significantly different from

zero or not.