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.