Question

QUESTION 13

1. 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	60.3	33.8		0.089	-11.2
   # of Prev.	-844	295.3	-2.73	0.016	-1435.0	-176.2
   Man	-636	304.2		0.051		2.7
   Age*Man	14.7	8.8	1.77	0.097	-3.2	34.4

     
   
     
   Based on the regression output, how much more or less on average does a customer who has bought 1 previous car pay versus a customer who has not bought a previous car? (please express your answer using 1 decimal places)

Answer 1

By using the outputs you have given, Regression Equation is:

Let Amount a customer would pay for a new car be y. So,

y = 6579.1 + 60.3*Age - 844* (# of Prev.) - 636* Man + 14.7(Age*Man)

For,

(# of Prev.) = 1

y₁ = 6579.1 + 60.3*Age - 636* Man + 14.7(Age*Man) - 844

For,

(# of Prev.) = 0

y₀ = 6579.1 + 60.3*Age - 636* Man + 14.7(Age*Man)

If everything else is unchanged:

y₁ - y₀ = -844

Thus we can say that, if a person already has purchased a car he would pay $844 less than a person who has not bought a car previously.

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