A finance manager employed by an automobile dealership believes that the number

Question

A finance manager employed by an automobile dealership believes that the number of cars sold in his local market can be predicted by the interest rate charged for a loan. Interest Rate (%) Number of Cars Sold (100s) 3 10 5 7 6 5 8 2 The finance manager performed a regression analysis of the number of cars sold and interest rates using the sample of data above. Shown below is a portion of the regression output. Regression Statistics Multiple R 0.998868 R2 0.997738 Coefficient Intercept 14.88462 Interest Rate -1.61538 Are there factors other than interest rate charged for a loan that the finance manager should consider in predicting future car sales? Is interest rate charged for a loan the most important factor to be considered in predicting future car sales? Explain your reasoning.The dealership’s vice-president of marketing has requested a sales forecast at the prevailing interest rate of 7%. As finance manager, what reasons would you convey to the vice-president in recommending this forecasting model? Is the prediction of car sales at 7% a reflection of the current downturn in the economy? How might this impact the dealership’s business?

Explanation / Answer

Since, the R2 is 0.997. It implies that the 99.7% of variation of Car sale is explained by the interest rate. Therefore, according to the model, the variable interest rate is enough.

Now, since interest rate is explaining 99.7% of the dependent variable car sale. Hence, it is the most important variable.

The model is given by

Car sale = 14.88462 - 1.61538 interest rate

therefore, for interest rate of 7%, the car sales(in 100s) will be 4.

Since, the interest rate has increased. The car sales has decreased. Therefore, the prediction of car sales at 7% a reflects the current downturn in the economy.

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