“The average college senior graduated this year with more than $19,000 in debt” was the beginning sentence of a recent article in USA Today. The majority of students have loans that are not due until the student leaves school. This can result in the student ignoring the size of debt that piles up. Federal loans obtained to finance college education are steadily mounting. The data given here show the amount of loans ($million) for the last 20 academic years, with year 20 being the most recent.

Year Amount Year Amount Year Amount 1 9,914 8 16,221 15 37,228 2 10,182 9 22,557 16 39,101 3 12,493 10 26,011 17 42,761 4 13,195 11 28,737 18 49,360 5 13,414 12 31,906 19 57,463 6 13,890 13 33,930 20 62,614 7 15,232 14 34,376

a. Produce a time-series plot for these data. Specify the exponential forecasting model that should be used to obtain next year’s forecast.

b. Assuming a double exponential smoothing model, fit the least squares trend to the historical data to determine the smoothed constant-process value and the smoothed trend value for period 0.

c. Using data for periods 1 through 20 and using a  0.20 and   0.30, forecast the total student loan volume for the year 21.

d. Calculate the MAD for this model.