Question

In: Statistics and Probability

South Shore Construction builds permanent docks and seawalls along the southern shore of Long Island, New...

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

Solutions

Expert Solution

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

orchestra answered 1 year ago
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