Year	Quarter	Revenue	Q1	Q2	Q3
1	1	25	1	0	0
1	2	98	0	1	0
1	3	156	0	0	1
1	4	43	0	0	0
2	1	35	1	0	0
2	2	143	0	1	0
2	3	254	0	0	1
2	4	23	0	0	0
3	1	67	1	0	0
3	2	149	0	1	0
3	3	311	0	0	1
3	4	50	0	0	0
4	1	99	1	0	0
4	2	220	0	1	0
4	3	396	0	0	1
4	4	76	0	0	0
5	1	167	1	0	0
5	2	321	0	1	0
5	3	433	0	0	1
5	4	154	0	0	0

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 five 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 thousands of dollars.

Download ts2.xlsxhere

(a)

Use a multiple regression model with dummy variables as follows to develop an 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. If required, round your answers to one decimal place. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank (Example: -300).

Revenue= + Qtr1 + Qtr2 + Qtr3

(b)

Based on the model you developed in part (b), compute estimates of quarterly sales for year 6. If required, round your answers to one decimal place.

Quarter		Revenue ($1,000s)
Qtr1
Qtr2
Qtr3
Qtr4

(c)

Let Period = 1 refer to the observation in quarter 1 of year 1; Period = 2 refer to the observation in quarter 2 of year 1; ... and Period = 20 refer to the observation in quarter 4 of year 5. Using the dummy variables defined in part (b) and the variable Period, develop an equation to account for seasonal effects and any linear trend in the time series. If required, round your answers to three decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank (Example: -300).

Revenue = + Qtr1 + Qtr2 + Qtr3 + t

(d)

Based on the seasonal effects in the data and linear trend estimated in part (c), compute estimates of quarterly sales for year 6. If required, round your answers to one decimal place.

Quarter		Period (t)		Revenue ($1,000s)
Qtr1		21
Qtr2		22
Qtr3		23
Qtr4		24

(e)

Is the model you developed in part (b) or the model you developed in part (d) more effective? Justify your answer.

The model developed in (Select your answer: 1. part (b); 2. part (d)) is more effective, because it has a (Select your answer: 1. greater; 2. lower) MSE.