Question

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 $315,000 in the first year of operation to $1,075,000 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	24		40		80		92		163
2	97		144		154		197		292
3	172		245		329		389		439
4	22		23		48		83		181

a. Which of the following is the correct time series plot?

What type of pattern exists in the data?

There appears to be a seasonal pattern in the data and perhaps a

b. Use the following dummy variables to develop an estimated regression equation to account for any 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. Round your answers to whole number.

Revenue= _ + _ Qtr1 + _ Qtr2 + _ Qtr3

Compute the quarterly forecasts for next year.

Quarter 1 forecast
Quarter 2 forecast
Quarter 3 forecast
Quarter 4 forecast

c. Let Period =1 to refer to the observation in quarter 1 of year 1; Period=2 to refer to the observation in quarter 2 of year 1; . . . and Period=20 to refer to the observation in quarter 4 of year . Using the dummy variables defined in part (b) and Period, 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 quarterly forecasts for next year. Round your answers to whole number. Enter negative value as negative number.

The regression equation is:

Revenue = _ + _ Qtr1 + _ Qtr2 + _ Qtr3 + _ Period

The quarterly forecasts for next year are as follows:

Quarter 1 forecast
Quarter 2 forecast
Quarter 3 forecast
Quarter 4 forecast

Answer 1

a)

Seasonal pattern with trend

b)

Year	Sales	Q1	Q2	Q3
1	24	1	0	0
1	97	0	1	0
1	172	0	0	1
1	22	0	0	0
2	40	1	0	0
2	144	0	1	0
2	245	0	0	1
2	23	0	0	0
3	80	1	0	0
3	154	0	1	0
3	329	0	0	1
3	48	0	0	0
4	92	1	0	0
4	197	0	1	0
4	389	0	0	1
4	83	0	0	0
5	163	1	0	0
5	292	0	1	0
5	439	0	0	1
5	181	0	0	0

Excel > Data > Data Analysis > Regression

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.815126259
R Square	0.664430817
Adjusted R Square	0.601511596
Standard Error	77.97659905
Observations	20
ANOVA
	df	SS	MS	F	Significance F
Regression	3	192626.6	64208.86667	10.56006096	0.000449538
Residual	16	97285.6	6080.35
Total	19	289912.2
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	71.4	34.87219523	2.047476493	0.057396533	-2.525751459	145.3257515	-2.525751459	145.3257515
Q1	8.4	49.31673144	0.17032759	0.866887688	-96.14680032	112.9468003	-96.14680032	112.9468003
Q2	105.4	49.31673144	2.137205709	0.048367668	0.853199678	209.9468003	0.853199678	209.9468003
Q3	243.4	49.31673144	4.935444684	0.000149101	138.8531997	347.9468003	138.8531997	347.9468003

Ft = 71+8*Q1+105*Q2+243*Q3

Year 6	Ft= 71.4+8.4*Q1+105.4*Q2+243.4*Q3	Q1	Q2	Q3
Q1	79	1	0	0
Q2	176	0	1	0
Q3	314	0	0	1
Q4	71	0	0	0

c)

Year	Sales	Q1	Q2	Q3	t
1	24	1	0	0	1
1	97	0	1	0	2
1	172	0	0	1	3
1	22	0	0	0	4
2	40	1	0	0	5
2	144	0	1	0	6
2	245	0	0	1	7
2	23	0	0	0	8
3	80	1	0	0	9
3	154	0	1	0	10
3	329	0	0	1	11
3	48	0	0	0	12
4	92	1	0	0	13
4	197	0	1	0	14
4	389	0	0	1	15
4	83	0	0	0	16
5	163	1	0	0	17
5	292	0	1	0	18
5	439	0	0	1	19
5	181	0	0	0	20

Ft = -66+43*Q1+128*Q2+255*Q3+11*t

Year 6	Ft= -66+43*Q1+128*Q2+255*Q3+11*t	Q1	Q2	Q3	t
Q1	208	1	0	0	21
Q2	304	0	1	0	22
Q3	442	0	0	1	23
Q4	198	0	0	0	24