3. Below is a regression based on census data for people age 20 and above with a

Question

3. Below is a regression based on census data for people age 20 and above with at least $1,000 in annual income and at least a ninth-grade education. Annual income in dollars is regressed on age in years, education (9 to 17 years of school), and gender (1-female, 0-male). Use the regression table to answer the following questions Regression Statistics Multiple R R Square Adjusted R Square 0.16 Standard Error 53062.018 Observations 0.40 0.16 Example of Data Education (12-HS, (1-Female, 0-Male 16-Coll Income $28,000 $29,000 $30,000 $30,000 $30,000 $32,000 $35,000 21 14 12 12 12 16 16 12 63,742 23 ANOVA MS F Significance F 0 0 23 23 23 24 Regression Residual 3 3.39E+13 1.13E+13 4016.19 63738 1.79E+14 2.82E+09 63741 2.13E+14 0 Standard Coefficients Error 88,9861,577 12 102 421 t Stat -56 16 97 52 P-value Lower 95% Upper 95% Intercept -92,078 -85,894 8.4E-61 Education Female 197 9,918 -22,029 173 9,719 -22,855 220 10,118 21,204 0 A. What is the expected (predicted) income of a male age 30 with a 12th grade education? $ B. Does the average person earn $88,986? C. Based on this regression, could an extra year of education be worth $12,000? D. What is the correlation between the actual and the predicted values? E. What fraction of the variation in income is explained by age, education and gender?

Explanation / Answer

a) expected income =-88986+197*30+9918*12+0*(-22029)=35940

b) No

c) No an extra year of education is worth of $9918

d) correlation =0.40

e) fraction of variation in income is explained by age ; education ' gender =R2 =0.16

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