Question

In: Statistics and Probability

  Quarterly billing for water usage is shown below. Assume the time series has seasonality with a...

  Quarterly billing for water usage is shown below. Assume the time series has seasonality with a long term trend.

Year

Quarter

1

2

3

4

Winter

  64

  66

  68

  73

Spring

103

103

104

120

Summer

152

160

162

176

Fall

  73

  72

  78

  88

Forecast the next four quarters:

FWinter = 81.625, FSpring = 126.375, FSummer= 175.375, FFall= 92.625
FWinter = 80.625, FSpring = 120.375, FSummer= 175.375, FFall= 90.625

FWinter = 82.625, FSpring = 120.375, FSummer= 174.375, FFall= 90.625
FWinter = 80.625, FSpring = 120.375, FSummer= 174.375, FFall= 95.625

Solutions

Expert Solution

data

Quarter 1 winter spring summer t
Winter 64 1 0 0 1
Spring 103 0 1 0 2
Summer 152 0 0 1 3
Fall 73 0 0 0 4
66 1 0 0 5
103 0 1 0 6
160 0 0 1 7
72 0 0 0 8
68 1 0 0 9
104 0 1 0 10
162 0 0 1 11
78 0 0 0 12
73 1 0 0 13
120 0 1 0 14
176 0 0 1 15
88 0 0 0 16

here winter, spring and summer are three dummy variable

t = 1 to 16

result

SUMMARY OUTPUT
Regression Statistics
Multiple R 0.995917324
R Square 0.991851316
Adjusted R Square 0.988888158
Standard Error 4.079327039
Observations 16
ANOVA
df SS MS F Significance F
Regression 4 22280.7 5570.175 334.7278066 2.09358E-11
Residual 11 183.05 16.64090909
Total 15 22463.75
Coefficients Standard Error t Stat P-value Lower 95%
Intercept 64.875 3.059495279 21.20447789 2.85131E-10 58.14109629
winter -6.1375 2.964537083 -2.070306368 0.062739758 -12.66240213
spring 32.325 2.92035373 11.06886459 2.65619E-07 25.89734478
summer 86.0375 2.893519896 29.73454585 7.34358E-12 79.66890565
t 1.2875 0.228041314 5.645906775 0.000149723 0.785584452

using regression result

17 80.625
18 120.375
19 175.375
20 90.625

formula

17 =B17+B18+B21*17
18 =B17+B19+B21*18
19 =B17+B20+B21*19
20 =B17+B21*20

B17 is

64.875

B18 slope of winter , B19 - spring , B20 for summer , B21 for t

option B) is correct

orchestra answered 3 years ago
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