The following table is the output of simple linear regression analysis. Note tha
ID: 3154050 • 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?
ANOVA SS df MS F p-value Regression 19,918.8438 1 19,918.8438 935.15 .0000 Residual 191.7017 9 21.3002 Total 20,110.5454 10 (n = 11; t = 30.5802)Explanation / Answer
a) F=935.148 [F=MSR/MSE=19918.8438/21.3002]
b) At df=10 (n-1), alpha=0.05, the critical t is 2.228. The test statistic falls in critical region. Reject null hypothesis to conclude that x is useful for predicting y.
c) At df=10, and alph=0.01, the critical t is 3.169.The test statistic falls in critical region. Reject null hypothesis to conclude that x is useful for predicting y.
d) For each alpha level, null hypothesis is rejected. There is very strong eidence that there is significant relationship between x and y.
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