A multiple regression analysis between yearly income Y in 10

A multiple regression analysis between yearly income (Y in $1,000s), college grade point average (X₁), age of the individuals (X₂), and the gender of the individual (X₃; zero representing female and one representing male) was performed on a sample of 10 people, and the following results were obtained.

                                    Coefficient            Standard Error

            Constant              4.0928                      1.4400

               X₁                   10.0230                      1.6512

               X₂                     0.1020                      0.1225

               X₃                    -4.4811                      1.4400

Analysis of Variance

            Source of             Degrees               Sum of                Mean

            Variation          of Freedom             Squares              Square                 F

           

            Regression                                        360.59

            Error                                                  23.91

            a.   Write the regression equation for the above.

            b.   Interpret the meaning of the coefficient of X₃.

            c.   Compute the coefficient of determination.

            d.   Is the coefficient of X₁ significant? Use a = 0.05.

            e.   Is the coefficient of X₂ significant? Use a = 0.05.

            f.    Is the coefficient of X₃ significant? Use a = 0.05.

            g.   Perform an F test and determine whether or not the model is significant.

Solution

A multiple regression analysis between yearly income (Y in $1,000s), college grade point average (X₁), age of the individuals (X₂), and the gender of the individual (X₃; zero representing female and one representing male) was performed on a sample of 10 people, and the following results were obtained.

Coefficient           

Standard Error

t= coeff/SE

Constant             

4.0928

1.44

2.842222

X1                  

10.023

1.6512

6.070131

X2                    

0.102

0.1225

0.832653

X3                   

-4.4811

1.44

-3.11188

           

completed ANOVA table

Variation

DF

SS

MSS

F

Regression

3

360.59

120.1967

30.16228

Error

6

23.91

3.985

Total

9

384.5

y =4.0928+10.023*X1+0.102*X2-4.4811*X3

When the person is male and other variables are same, the income decreased by 4.4811 ( in thousands) ie $4481.10

R² =360.59/384.5 = 0.93782

Table value of t with 6DF at 0.05 level =2.45

Calculated t=6.070131 > table value 2.45 , coefficient of X₁ significant

Calculated t= 0.832653 < table value 2.45 , coefficient of X₂ not significant

Calculated t= 3.11188 > table value 2.45 , coefficient of X₃ significant

Table value of F(3,6) at 0.05 level =4.76

Calculated F= 30.162 > table value 4.76 , model is significant

	Coefficient	Standard Error	t= coeff/SE
Constant	4.0928	1.44	2.842222
X1	10.023	1.6512	6.070131
X2	0.102	0.1225	0.832653
X3	-4.4811	1.44	-3.11188