A study by the American Realtors Association investigated the relationship between the commissions earned by sales associates last year and the number of months since the associates earned their real estate licenses. Also of interest in the study is the gender of the sales associate. A portion of the regression output is shown on next page. The dependent variable is commissions, which is reported in $000, and the independent variables are months since the license was earned and gender (female = 1 and male = 0).

(a) Write out the regression equation. How much commission would you expect a female agent to make who earned her license 30 months ago?

(b) Do the female agents on the average make more or less than the male agents? How much more?

(c) Conduct a test of hypothesis to determine if the independent variable gender should be included in the analysis. Use the 0.05 significance level. What is your conclusion?

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Regression Analysis R2 0.642 Adjusted R2 0.600 R 0.801 Std. Error 3.219 n 20 k 2 Dep. Var. Commissions ANOVA table Source SS df MS Regression 315.9291 2 157.9645 15.25 F p-value .0002 Residual 176.1284 17 10.3605 Total 492.0575 19 Regression output Variables coefficients std. error t (df = 17) p-value Intercept Months Gender 15.7625 0.4415 3.0782 5.121 .0001 3.8598 0.0839 1.4724 5.263 .0001 2.621 .0179 95% lower 9.2680 0.2645 0.7533 958 upper 22.2570- 0.6186 6.9663