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

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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) ...