A finance manager employed by an automobile dealership belie

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. 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?

3. 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?

4. How might this impact the dealership’s business?

Solution

we wil get the regression model for this problem as x=a+bt

here , t is Interest rate

x is number of cars sold

we are given that

Intercept =a=14.88462

Interest Rate =b=-1.61538

so, we get

x= 14.88 - 1.61 53*t

(1)

now, we are given that R sqare is 0.997.

so, this model will be best model because R square is close to 1.

that\'s why we can say that finance manager need not to consider other factors because we know that we have 99.7% variation is because of interest rate

(2)

we know that it has a good coefficient of determination(R sqaure)

and we are getting forcasting the Number of cars when interest rate is 7%

as

y= 14.88 - 1.61 53*t

y= 14.88 -1.6153 *7

so, we get

y= 3.57

Hence , Yes, interest rate charged for a loan the most important factor to be considered in predicting future car sales............Answer

(3)

we can see that correlation and coefficient of determination are large

Hence , Yes finance manager, what reasons would you convey to the vice-president in recommending this forecasting model ............Answer

(4)

we are given that the dealership’s vice-president of marketing has requested a sales forecast at the prevailing interest rate of 7%

that\'s why it is true that the prediction of car sales at 7% a reflection of the current downturn in the economy.........Answer