Quarterly billing for water usage is shown below. Year Quarter 1 2 3 4 Winter 64
ID: 3428164 • Letter: Q
Question
Quarterly billing for water usage is shown below.
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
The data was used to estimate a regression equation to explain the variation in demand. Given the following minitab output:
Coefficients
Term Coef SE Coef T-Value P-Value VIF
Constant 58.74 2.59 22.68 0.00
Period 1.28 0.228 5.65 0.00 1.06
Qtr2 38.46 2.89 13.29 0.00 1.51
Qtr3 92.18 2.92 31.56 0.00 1.54
Qtr4 6.14 2.96 2.07 0.063 1.58
Note: qtr2 is Spring, qtr3 is Summer, and qtr4 is Fall and are binary.
Equation=
Usage= Winter? Spring? Summer? Fall?
Explanation / Answer
Term Coef SE Coef T-Value P-Value VIF
Constant 58.74 2.59 22.68 0.00
Period 1.28 0.228 5.65 0.00 1.06
Qtr2 38.46 2.89 13.29 0.00 1.51
Qtr3 92.18 2.92 31.56 0.00 1.54
Qtr4 6.14 2.96 2.07 0.063 1.58
Note: qtr2 is Spring, qtr3 is Summer, and qtr4 is Fall and are binary.
The trend component is significant, t=5.65, P=0.00 which is less than 0.10
The Spring seasonal trend component is significant, t=13.29, P=0.00 which is less than 0.10
The Summer seasonal trend component is significant, t=31.56, P=0.00 which is less than 0.10
The Fall seasonal trend component is significant, t=2.07, P=0.063 which is less than 0.10
Equation= 58.74+1.28t+38.46*spring +92.18*summer+6.14*fall
Time t=5
Prediction for winter
Equation= 58.74+1.28*5+38.46*0 +92.18*0+6.14*0 =65.14
Prediction for spring
Equation= 58.74+1.28*5+38.46*1 +92.18*0+6.14*0 =103.6
Prediction for summer
Equation= 58.74+1.28*5+38.46*0 +92.18*1+6.14*0 =157.32
Prediction for winter
Equation= 58.74+1.28*5+38.46*0 +92.18*0+6.14*1 =71.28
Term Coef SE Coef T-Value P-Value VIF
Constant 58.74 2.59 22.68 0.00
Period 1.28 0.228 5.65 0.00 1.06
Qtr2 38.46 2.89 13.29 0.00 1.51
Qtr3 92.18 2.92 31.56 0.00 1.54
Qtr4 6.14 2.96 2.07 0.063 1.58