The Natural Gas Consumption Case

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 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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df ANOVA Regression Residual Total Significance F 0.0003 MS 2.5679 22.9808 25.5488 22.9808 53.6949 6 0.4280 (n-8 t-7.33)