2. Track Stats! To investigate the effect of a training program on the time to complete the 100-yard dash, nine students were placed in the program. The reduction y in time to complete the race was measured for three students at the end of 2 weeks, for three at the end of 4 weeks, and for three at the end of 6 weeks of training. The data are given in the table.

a. Plot the data. Do the data appear to have a linear relationship?

b. Find the least-squares line. Graph the line along with the data points as a check on your calculations.

c. Construct the ANOVA table and use two different test statistics (t and F) to test whether x and y are linearly related. Use the p-value approach.

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1.6, .8, 1.0 2.1, 1.6, 2.5 3.8, 2.7, 3.1 Reduction in Time, y (sec) Length of Training, x (wk) 2 4 6