Statistical software output, continued. The computer outputs in Figure 10.4 (pages 562–564) for the physical activity study contain the information needed for inference about the regression slope and intercept. Let’s look at the JMP output. The column labeled “Std Error’’ gives the standard errors of the estimates. The value of appears on the line labeled with the variable name for the explanatory variable, PA. Rounding to three decimal places, it is given as 0.158. In a summary, we would report that the regression coefficient for the average number of steps per day is −0.655 with a standard error of 0.158.
The t statistic and P-value for the test of H0: β1 = 0 against the two-sided alternative Ha: β1 ≠ 0 appear in the columns labeled “t Ratio’’ and “Prob>|t|.’’ We can verify the t calculation from the formula for the standardized estimate:
The P-value is given as <0.0001. The other outputs in Figure 10.4 also indicate that the P-value is very small. Less than one chance in 10,000 is sufficiently small for us to decisively reject the null hypothesis.