A multiple regression analysis between yearly income (y in $1,000s),

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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.

Predictor

Coefficient

Std Error

Constant

4.0928

1.44

X1

10.023

1.6512

X2

0.102

0.1225

X3

-4.4811

1.44

 

Analysis of Variance

Source of Variation

Degrees of Freedom

Sum of  Squares

Mean Square

F

Regression

360.59

Error

23.91

 

Total

   

 

a. Write the regression equation for the above information.

b. Interpret the meaning of the coefficients of X1, X2 and X3.

c. Compute the coefficient of determination and interpret its meaning.

d. Is the variable X1 statistically significant? Use α = 0.05.

e. Is the variable X2 statistically significant? Use α = 0.05.

f. Is the variable X3 statistically significant? Use α = 0.05.

g. Perform an F test to determine whether or not the overall model is statistically significant.