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.