Question

Jessica plots the data points relating the amount of money she needs to repay a loan and the number of months she has been making payments.
She calculates two regression models. Which is true?

A.) The linear model better represents the situation because the amount she owes is decreasing by about the same amount every 6 months.

B.) The linear model better represents the situation because according to the exponential model, the repayment amount will never be 0.

C.) The exponential model better represents the situation because the amount she owes decreases by about the same amount every 6 months.

D.) The exponential model better represents the situation because according to the linear model, the repayment amount will eventually be negative.

Answer 1

The difference between the linear model and the exponential model is the degree of difference of consecutive points. If their difference is constant, then it is more appropriate for the linear model. If their difference is increasing at a very fast rate, then that follows an exponential model. With that being said, let's look at the differences at every 6 month-intervals.

2700-2110 = 590
2110-1500 = 610
1500-870 = 630
870-220 = 650

Their differences are about the same having a mean of 620. Thus, this is a linear model. To check,you can see visually that the points are more fitted to the line than the curve. The answer is A.

Answer 2

A. The linear model better represents the situation because the amount she owes is decreasing by about the same amount every 6 months.