We give MINITAB and Excel outputs of simple linear regression analyses of the data sets related to six previously discussed case studies. Using the appropriate computer output.

a. Use the explained variation and the unexplained variation as given on the computer output to calculate (within rounding) the F(model) statistic.
b. Utilize the F(model) statistic and the appropriate critical value to test H0: β1 = 0 versus Ha: β1 ‰  0 by setting a equal to .05. What do you conclude about the regression relationship between y and x?
c. Utilize the F(model) statistic and the appropriate critical value to test H0: β1 = 0 versus Ha: β1 ‰  0 by setting a equal to .01. What do you conclude about the regression relationship between y and x?
d. Find the p-value related to F(model) on the computer output and report its value. Using the p value, test the significance of the regression model at the .10, .05, .01, and .001 levels of significance. What do you conclude?
e. Show that the /-"(model) statistic is (within rounding) the square of the t statistic for testing H0): β1 = 0 versus Ha: β1 ‰  0. Also, show that the F.05 critical value is the square of the t.025 critical value.
In the lower right hand corner of each output we give (in parentheses) the number of observations, n, used to perform the regression analysis and the t statistic for testing H0: β1 = 0 versus Ha: β1 ‰  0.

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ANOVA Regression Residual Total df MS F Significance F 5.04E-17 11024592.9043 1024592.904313720.4677 10 746.7624 11 1025339.6667 74.6762 (n-12; t-117.1344)