B) size of the sample C) how many independent variables in this model D) calcula

Question

B) size of the sample C) how many independent variables in this model D) calculate the multiple coefficient of determination E) test the significance of the overall regresssion model using .05 F) calculate the adjusted multiple coefficient of determination 5.2.15-T Consider the following ANOVA table for a multiple regression model. Complete parts a through fbelow MS Source Regression Residual Total 8,000 11,200 52 a. Complete the remaining entries in the table. Source MS Regression2 Regression 2 Residual Total 8,000 11,200

Explanation / Answer

a)

regression SS=total SS - residual SS=11200-8000=3200

residual df=total df - regression df=52-2=50

MS=SS/df

F=MS(regression)/MS(residual)=1600/160=10

B) size of the sample=53

sample size=total df+1=52+1=53

C) how many independent variables in this model=2

since regression df=2 , total regression coefficient=2+1=3

one of the regression coefficient is intercept

so total number of independent varaibles=3-1=2

D) calculate the multiple coefficient of determination =regression SS/total SS=3200/11200=0.2857

E) test the significance of the overall regresssion model using 0.05

critical F(0.05,2,50)=3.18 is less than calculated F=10, so model is significant overall

F) calculate the adjusted multiple coefficient of determination = 1-(1-R2)(n-1)/(n-p-1)

=1-(1-0.2857)*(53-1)/(53-3-1)=0.2419

here n=53, p=3 and R2=0.2857

source df SS MS F regression 2 11200-8000=3200 3200/2=1600 1600/160=10 Residual 52-2=50 8000 8000/50=160 Total 52 11200 source df SS MS F regression 2 3200 1600 10 Residual 50 8000 160 Total 52 11200

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