16. () The following table lists the number of home im- provement loans approved
ID: 349551 • Letter: 1
Question
16. () The following table lists the number of home im- provement loans approved by a finance company, along with the loan interest rate: INTEREST RATE 7% 5% 4% 8% 10% 5% 11% 9% 5% 12% NUMBER OF LOANS 20 30 35 18 15 MONTH 4 6 15 20 27 10 10 a. Develop a regression forecast model using the inter- est rate as the predictor (i.e., independent) variable. Is this a time series or a causal forecasting model? Explain b. How many loans should the bank expect to make if the interest rate is 10%76.5%? Do these results make sense?Explanation / Answer
a. Regression model with y = no. of loans and x = interest rate
The regression equation is in the form of y = a+bx
a = (sum of y)*(sum of x^2) - (sum of x)*(sum of x*y)/(n*sum of x^2) - (sum of x)^2
b = (n(sum of x*y) - (sum of x*sum of y)/(n*sum of x^2 - (sum of x)^2
n = 10
Thus a = (212*661)-(77*1456)/(10*661)-(77^2)
= 41.15
b = (10*1456) - (77*212)/(10*661) - (77^2)
= -2.59
Thus the regression equation is: y = 41.15-2.59x
where y = no. of loans and x = interest rate
This is a casual forecasting model as the forecast for the number of loans rides piggyback on the interest rate. In this model our knowledge of the interest rate enables us to forecast the value of no. of loans.
b. When interest rate (x) = 10% then y = 41.15 - (2.59*10) = 15.25 loans or 15 loans (rounded off)
When interest rate (x) = 6.5% then y = 41.15 - (2.59*6.5) = 24.32 loans or 24 loans (rounded off)
Yes, this result does make sense as when interest rate falls (from 10% to 6.5%) the number of loans increases (15.25 to 24.32). This makes economic sense as when the cost of borrowing falls the number of loans that will be taken will rise.
x y x^2 x*y 7.00 20.00 49.00 140.00 5.00 30.00 25.00 150.00 4.00 35.00 16.00 140.00 8.00 18.00 64.00 144.00 10.00 15.00 100.00 150.00 6.00 22.00 36.00 132.00 11.00 15.00 121.00 165.00 9.00 20.00 81.00 180.00 5.00 27.00 25.00 135.00 12.00 10.00 144.00 120.00 Total 77.00 212.00 661.00 1,456.00Related Questions
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