Cars Sold A finance manager employed by an automobile dealership believes that t
ID: 3020478 • Letter: C
Question
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.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?
Explanation / Answer
Answer to the question)
Question#1)
There may be other factors as well, like the credit limit of the customers, the savings of the customers, their income level , cost of living and so on
.
Question# 2)
Yes interest rate is one of the dominant factors because the correlation coefficient value is 0.998868. This value is close to -1. This implies there is a strong relation between interest rate and number of cars sold. As the interest rate increases, the number of cars sold decreases.
.
Question# 3)
The reason we recommend this model is because of the R square value of this model
R square is the coefficient of determination which means it tells us the percent of variation in sales as explained by the model
we got R square = 0.99, this implies 99% of the variation in the number of cars sold is explained by this model. Thus this model is valid to be used to predict the number of cars sold on the basis of the interest rate.
.
Question# 4)
The model is:
Number of cars sold = 14.88462 - 1.61538* Interest rate
For interest rate = 7
Predicted sales = 14.88462 - 1.61538 * 7
Predicted sales = 3.57696 ~ 4 cars
yes this definitely shows the downward trend