Math 104 Homework 6

Problem 1 Forecasting Revenues

Giovanni Food Products produces and sells frozen pizzas to public schools throughout the eastern United States. Using a very aggressive marketing strategy they have been able to increase their annual revenue by approximately $10 million over the past 10 years. But increased competition has slowed their growth rate in the past few years. The annual review, in millions of dollars, for the previous 10 years is shown.

Year Revenue

1 8.53

210.84

312.98

414.11

516.31

617.21

718.37

818.45

918.40

10 18.43

a)Construct a time series plot. Comment on the appropriateness of a linear model.

b)Develop a quadratic trend equation that can be used to forecast revenue.

c)Report the measures of accuracy: MAE, RMSE, MAPE

d)Using the trend equation developed in part b, forecast revenue in year 11.

e)Does autocorrelation appear to be a problem? Plot the forecast error against the time variable. Compute the DW test statistic. Is the value close to 2? (You don't have to use the critical values here)

Problem 2 Seasonal Sales

South Shore Construction builds permanent docks and seawalls along the southern shore of Long Island, New York. Although the firm has been in business only 5 years, revenue has increased from $308,000 in the first year of operation to $1,084,000 in the most recent year. The following data show the quarterly sales revenue in thousand of dollars.

YearQuarterRevenue

1120

2100

3175

413

2137

2136

3245

426

3175

2155

3326

448

4192

2202

3384

482

51176

2282

3445

4181

AutoSave . OH Problem 1 Forecasting Revenue - Excel File Home Insert Draw Page Layout Formulas Data Review View E11 A B C D E 1 Year Revenue 2 8.53 2 10.84 4 3 12.98 4 14.11 16.31 6 17.21 8 18.37 9 8 18.45 10 9 18.40 11 10 18.43 12 13 14 15 16 17 18 19 Shoot1 ReadyAuto Save OOH Problem 2 Seasonal Sales - Excel File Home Insert Draw Page Layout Formulas Data Review View M8 X V G A B C D E F G H Year Quarter Revenue 1 20 100 175 4 13 37 2 136 245 26 3 75 2 155 326 48 92 2 202 3 384 4 82 5 1 176 282 145 181 24 26 27 28 29 30 Data Sheet2 Sheets + Ready