# Multiple regression analysis on Income using GPA, Age, & Gender

31.) 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.

Coefficients Standard Error

Intercept 4.0928 1.4400

X1 10.0230 1.6512

X2 0.1020 0.1225

X3 -4.4811 1.4400

ANOVA

DF SS MS F

Regression 360.59

Residual (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 ± = 0.05.

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

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

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

Use ± = 0.05.

https://brainmass.com/statistics/regression-analysis/multiple-regression-analysis-income-using-gpa-age-gender-334275

#### Solution Preview

(a) Y = 10.0230X1 + 0.1020X2 - 4.4811X3 + 4.0928

(b) If the gender is male, the income reduces by approximately $4481.10

(c) r^2 = SSR/SST = 360.59/(360.59 + 23.91) ...

#### Solution Summary

The Correct Answers are provided.