Question

The ANOVA summary table to the right is for a multiple regression model with six independent variables. Complete parts​ (a) through​ (e).

Source: Degrees of Freedom / Sum of Squares Regression 6 90 Error 14 170 Total 20 260

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

MSR= ​ (Round to four decimal places as​ needed.)

MSE=   (Round to four decimal places as​ needed.)

b. Compute the overall F STAT test statistic. (Round to two 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.

d. Compute the coefficient of multiple​ determination, r squared , and interpret its meaning.

e. Compute the adjusted r squared.

Answer 1

a)

MSR =SSR/df(regression)=90/6=15

MSE=SSE/df(error)=170/14=12.1429

b)

F  STAT test statistic =MSR/MSE=15/12.1429=1.24

c)

here for 0.05 level and (6,14)df crtiical value F=2.85

as test statistic is not higher then critical value we can not reject null hypothesis

there is not a  a significant relationship between Y and the two independent variables

d)

coefficient of multiple​ determination =R2=SSR/SST =90/260=0.3462

this means that 34.62% of variation in Y can be explained by variation in 6 independent variables

e)

R2adj=

=1-(1-R2)*(n-1)/(n-k-1)=

0.0659