Question

6. The following estimated regression model was developed relating yearly income (Y in $1,000s) of 30 individuals with their age (X1) and their gender (X2) (0 if male and 1 if female).

ˆ Y =20+0.7X1 +2X2 SST = 1,000 and SSE = 256

b) Is there a significant relationship between the yearly income and the set of predictors (i.e., age and gender)? Use α=0.05 and make sure to show all your steps.

Answer 1

null hypothesis: Ho:               β1 =β2		=	0
Alternate Hypothesis: Ha: β1 =β2		≠	0

df(regression) =number of independent variable =2

df(error)=n-p-1 =30-2-1=27

for 0.05 level and (2,27) df , critical value =3.35

SS(regression) =SST-SSE =1000-256 =744

test statistic F =MS(regression)/MS(error) =(744/2)/(256/27)= 39.23

since test statistic falls in rejection region we reject null hypothesis

we have sufficient evidence to conclude that  there is a significant relationship between the yearly income and the set of predictors