Quarterly billing for water usage is shown below Year Quarte

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?

Solution

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