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least-squares regression for Hertz Rental Cars

24. Hertz Rental Car offers rental cars in an off-airport location near a major tourist destination in Florida. Management would like to better understand the behavior of the company's costs. One of those costs is the cost of washing cars. The company operates its own car wash facility in which each rental car that is returned is thoroughly cleaned before being released for rental to another customer. Management believes that the costs of operating the car wash should be related to the number of rental returns. Accordingly, the following data has been compiled:

Month Rental
Returns Car Wash
Costs
January 2,310 $10,113
February 2,453 $12,691
March 2,641 $10,905
April 2,874 $12,949
May 3,540 $15,334
June 4,861 $21,455
July 5,432 $21,270
August 5,268 $19,930
September 4,628 $21,860
October 3,720 $18,383
November 2,106 $9,830
December 2,495 $11,081

Using least-squares regression, estimate the fixed cost and variable cost elements of monthly car wash costs and calculate R2. The fixed cost element should be estimated to the nearest dollar and the variable cost element to the nearest cent. Express your cost formula in the form Y = a + bX.

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Excel file contains estimation of the fixed cost and variable cost elements of monthly car wash costs using least-squares regression.

$2.19