EXAMPLE 10.15

Interpreting SAS output for BMI and physical activity. The output generated by SAS for the physical activity study in Example 10.3 is given in Figure 10.15. Note that SAS uses the labels Model and Error but replaces Total with Corrected Total. Other statistical software packages may use slightly different labels. The F statistic is 17.10; the P-value is given as < 0.0001. There is strong evidence against the null hypothesis that there is no relationship between BMI and average number of steps per day (PA).

Now look at the output for the regression coefficients. The t statistic for PA is given as −4.13. If we square this number, we obtain the F statistic (accurate up to roundoff error). The value of r² is also given in the output. Average number of steps per day explains only 14.9% of the variability in BMI. Strong evidence against the null hypothesis that there is no relationship does not imply that a large percentage of the total variability is explained by the model.