A construction company builds permanent docks and seawalls along the southern shore of Long Island, New York. Although the firm has been in business only five years, revenue has increased from $318,000 in the first year of operation to $1,094,000 in the most recent year. The following data show the quarterly sales revenue in thousands of dollars.
Quarter / Year 1 / Year 2 / Year 3 / Year 4 / Year 5
1 / 25 / 42 / 80 / 97 / 181
2 / 105 / 141 / 160 / 207 / 287
3 / 170 / 240 / 321 / 379 / 440
4 / 18 / 31 / 53 / 87 / 186
PART B
Use the following dummy variables to develop an estimated regression equation for the time series data (in $1,000s) to account for seasonal effects in the data. x1 = 1 if quarter 1, 0 otherwise; x2 = 1 if quarter 2, 0 otherwise; x3 = 1 if quarter 3, 0 otherwise.
PART C
Based on the model you developed in part (b), compute estimates of quarterly sales (in $1,000s) for year 6.
quarter 1 forecast - $ thousand
quarter 2 forecast - $ thousand
quarter 3 forecast - $ thousand
quarter 4 forecast - $ thousand
PART D
Let t = 1 refer to the observation in quarter 1 of year 1; t = 2 refer to the observation in quarter 2 of year 1; and t = 20 refer to the observation in quarter 4 of year 5. Using the dummy variables defined in part (b) and t, develop an estimated regression equation for the time series data (in $1,000s) to account for seasonal effects and any linear trend in the time series. (Round your numerical values to one decimal place.)
PART E
Based on the seasonal effects in the data and linear trend estimated in part (c), compute estimates of quarterly sales (in $1,000s) for year 6. (Round your answers to the nearest thousand dollars.)
quarter 1 forecast - $ thousand
quarter 2 forecast - $ thousand
quarter 3 forecast - $ thousand
quarter 4 forecast - $ thousand