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 H_a: β₁ ≠ 0 by setting α 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 F(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.

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Analysis of Variance Source Regression Residual Error Total DF SS MS P 1 59.942 59.942 208.39 0.000 5 1.438 0.288 6 61.380 F (n=7; t=14.44)