The ANOVA summary table to the right is for a multiple regression model with eig

Question

The ANOVA summary table to the right is for a multiple regression model with eight independent variables. Complete parts (a) through (e). Degrees of Sum of urce Freedom Squares So Regression Error Total 180 100 280 20 28 The p-value is (Round to three decimal places as needed.) Draw a conclusion. Choose the correct answer below ( A. There is sufficient evidence of a significant linear relationship with at least one of the independent variables because the p-value is less than the level of significance. B. There is sufficient evidence of a significant linear relationship with at least one of the independent variables because the test statistic is greater than the level of signific C. There is insufficient evidence of a significant linear relationship with at least one of the independent variables because the test statistic is greater than the critical value D. There is insufficient evidence of a significant linear relationship with at least one of the independent variables because the test statistic is less than the critical value d. Compute the coefficient of multiple determination, r, and interpret its meaning (Round to four decimal places as needed.) Interpret the meaning of the coefficient of multiple determination.

Explanation / Answer

Ans:

c)F-statistic

F=MSbetween/MSwithin

F=(180/8)/(100/20)=4.5

p-value=FDIST(4.5,8,20)=0.003

d)

R-squared, often called the coefficient of determination, is defined as the ratio of the sum of squares explained by a regression model and the "total" sum of squares around the mean

R2 = 1 - SSE / SST

Given that

SSE=100

SST=280

R2 = 1 - 100 / 280

=1-0.3571=0.6429

R2 = 0.6429

The cofficient of determination indicates that 64.29% of the variation in the dependent variable can be explained by the variation in the independent variables.

e)

R2adj = 1 - MSE / MST

R2adj = 1 - (100/20)/(280/28)

=1-5/10

=1-0.5=0.5

R2adj =0.5

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