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

, 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

, 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.

But the p value for the slope is very important. Assuming α = 0.05, if it’s less than 0.05, it means that

the slope of the fitted straight line is statistically significantly different from zero. This means that the X

and Y variables are statistically significantly associated with each other. A p value greater than 0.05

would indicate that the true slope could equal zero, and there would be no conclusive evidence for a

statistically significant association between X and Y. In Figure 18-4, the p value for the slope is

0.0127, which means that the slope is statistically significantly different from zero. This tells you that

in your model, body weight is statistically significantly associated with SBP.

If you want to test for a significant correlation between two variables at α = 05, you can look

at the p value for the slope of the least-squares straight line. If it’s less than 0.05, then the X and Y

variables are also statistically significantly correlated. The p value for the significance of the

slope in a straight-line regression is always exactly the same as the p value for the correlation test

of whether r is statistically significantly different from zero, as described in Chapter 15.

Wrapping up with measures of goodness-of-fit

The last few lines of output in Figure 16-4 contain several indicators of how well the straight line

represents the data. The following sections describe this part of the output.

The correlation coefficient

Most straight-line regression programs provide the classic Pearson r correlation coefficient between X

and Y (see Chapter 15 for details). But the program may provide you the correlation coefficient in a

roundabout way by outputting

rather than r itself. In Figure 16-4, at the bottom under Multiple R-

squared, the

is listed as 0.2984. If you want Pearson r, just use Microsoft Excel or a calculator to

take square root of 0.2984 to get 0.546.