The following table is the output of simple linear regression analysis. Note tha
ID: 3357481 • Letter: T
Question
The following table is the output of simple linear regression analysis. Note that in the lower right hand corner of the output we give (in parentheses) the number of observations, n, used to perform the regression analysis and the t statistic for testing H0: 1 = 0 versus Ha: 1 0.
Use the explained variation and the unexplained variation as given on the computer output to calculate the F(model) statistic. (Round your answer to 3 decimal places.)
Utilize the F(model) statistic and the appropriate critical value to test H0: 1 = 0 versus Ha: 1 0 by setting equal to .05. What do you conclude about the regression relationship between y and x?
Utilize the F(model) statistic and the appropriate critical value to test H0: 1 = 0 versus Ha: 1 0 by setting equal to .01. What do you conclude about the regression relationship between y and x?
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?
The following table is the output of simple linear regression analysis. Note that in the lower right hand corner of the output we give (in parentheses) the number of observations, n, used to perform the regression analysis and the t statistic for testing H0: 1 = 0 versus Ha: 1 0.
Explanation / Answer
Solution:
From the computer output we have:
Total variation = 20764.5454, Explained variation = 20463.7692, Unexplained variation = 300.7762
(a) F = MSR/MSE = 20463.7692/33.4196= 612.3284
= 612.33 (within rounding)
Reported in the table is F = 612.33 (almost same as calculated value above)
(b) Critical F score for = 0.05, DfN = 1, DfD = 9 is 5.1173
Since F = 612.33 > 5.1173,
We conclude that at least one predictor variable is significant in the model
(c) Critical F score for = 0.01, DfN = 1, DfD = 9 is 10.5614
Since F = 612.33 > 10.5614,
We conclude that at least one predictor variable is significant in the model
(d) p- value = 0
Since 0 < all the given values 0.10, 0.05, 0.01 and 0.001, the model is significant at all values of .
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