Question

The ANOVA summary table to the right is for a multiple regression model with five independent variables. Complete parts​ (a) through​ (e). Source Degrees of Freedom Sum of Squares Regression 5 270 Error 28 110 Total 33 380 a. Determine the regression mean square​ (MSR) and the mean square error​ (MSE). b. Compute the overall FSTAT test statistic. FSTAT=_______________________ ​(Round to four decimal places as​ needed.) c. Determine whether there is a significant relationship between Y and the two independent variables at the 0.05 level of significance. Choose the correct answer below. A.There is insufficient evidence of a linear relationship because the test statistic is greater than the critical value. B.There is sufficient evidence of a linear relationship because the test statistic is less than the critical value. C.There is sufficient evidence of a linear relationship because the test statistic is greater than the critical value. D.There is insufficient evidence of a linear relationship because the test statistic is lessthan the critical value. d. Compute the coefficient of multiple​ determination, r2, and interpret its meaning. r2=_____________________ ​(Round to four decimal places as​ needed.) Interpret the meaning of the coefficient of multiple determination. The coefficient of multiple determination indicates that_______________________ ​% of the variation in the (1) _________________ variable can be explained by the variation in the (2)___________________variables. e. Compute the adjusted r2. r2adj=_____________________ ​(Round to four decimal places as​ needed.)

Answer 1

From the table we have

a. Determine the regression mean square? (MSR) and the mean square error? (MSE).

b. Compute the overall FSTAT test statistic.

c. Determine whether there is a significant relationship between Y and the two independent

Critical value of F test using excel function "=FINV(0.05,5,28)" : 2.558

Since Fstat > 2.558 so we reject the null hypothesis.

Following option is correct:

B.There is sufficient evidence of a linear relationship because the test statistic is less than the critical value.

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d:

The coefficient of multiple determination indicates that 71.05?% of the variation in the (1) dependent variable can be explained by the variation in the (2) independent variables.

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(e)

Here we have k-1=5

n-k=28

So adjusted R square will be