Below is some of the regression output from a regression of the amount various c

Question

Below is some of the regression output from a regression of the amount various customers paid for a new car (expressed in dollars) versus the age of the customer (expressed in years), the number of previous cars the customer had purchased from the dealership in the past, a dummy variable indicating the gender of the customer (=1 for a Man and = 0 for a woman), and an interactive term the multiplies the age of the customer with the gender dummy variable. Regression Statistics Multiple R 0.963 R Square Adjusted R Square Standard Error Observations 20 ANOVA df SS MS F Significance F Regression 24686354.49 6171589 47.8 2.3289E-08 Residual 129243 Total 26625000 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 6579.1 352.1 18.68 0.000 5828.5 7329.6 Age 63.3 36.8 0.089 -11.2 # of Prev. -791 295.3 -2.73 0.016 -1435.0 -176.2 Man -631 308.8 0.051 2.7 Age*Man 14.1 8.8 1.77 0.097 -3.2 34.4 Based on the regression output, what is predicted amount a customer who is a 45 year old male, has bought 0 previous car(s) from the dealership? (please express your answer using 1 decimal places) MUST SHOW ALL WORK AND CALCULATIONS

Explanation / Answer

The linear regression equation in this case is

Amount Paid for a new car = 6579.1 + 63.3* age - 792 * Number of prev. cars - 631 * X ( where X =1 for men and X=0 for women) + 14.1 Y [ where Y = Age when male and Y = 0 when femalle]

so here Age = 45 years

Number of prev. cars = 0

Male = 1

so Predicted amount paid for new car = 6579.1 + 63.3 * 45 - 791 * 0 - 631 * 1 + 14.1 * 45 = $ 9431.1

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