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

2 10.84

3 12.98

4 14.11

5 16.31

6 17.21

7 18.37

8 18.45

9 18.40

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.

Year Quarter Revenue

1 1 20

2 100

3 175

4 13

2 1 37

2 136

3 245

4 26

3 1 75

2 155

3 326

4 48

4 1 92

2 202

3 384

4 82

5 1 176

2 282

3 445

4 181

a) Construct a time series plot. What type of pattern exists in the data?

b) Use the following dummy variables to develop an estimated regression

equation to account for seasonal effects in the data. Qtr1 = 1 if Quarter 1, 0

otherwise; Qtr2 = 1 if Quarter 2, 0 otherwise, Qtr3 = 1 if Quarter 3, 0

otherwise. Based only on the seasonal effects in the data, compute estimates

of quarterly sales for year 6.

c) Let Period t = 1 refer to the observation in quarter 1 of year 1; Period t = 2

refer to the observation in quarter 2 or year 1; … and Period t = 20 refer to

the observation in quarter 4 of year 5. Using the dummy variables defined in

part (b) and Period (t), develop an estimated regression equation to account

for seasonal effects and any linear trend in the time series. Based upon the

seasonal effects in the data and linear trend, compute the estimates of

quarterly sales for year 6.