Cars Sold A finance manager employed by an automobile dealer

Cars Sold 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 1.

1. Are there factors other than interest rate charged for a loan that the finance manager should consider in predicting future car sales?

2. 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%.

3. As finance manager, what reasons would you convey to the vice-president in recommending this forecasting model?

4. 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?

Solution

Since correlation coefficient is 0.998868,

nearly 99.88% of the change in sales depend on interest rate

There may be other factors such as social status of having a car, introduction of new brand of car, increase of income due to some other reasons, etc.

But there are negligible compared to interest rates

The regression analysis cannot be totally accurate as sample size is very small. Sample size should be increased to atleast 30 or more and randomness should be strictly followed to ascertain the true relation.

Regression equation is

y = -1.61538 x+14.88462

Hence for 7% interest y = 3.57696

4) Since slope is negative as interest rate increases y comes down.

Thus interest rate decrease increases demand and sales for the dealer.