{Exercise 17.29} Consider the following time series data. Use the following dumm

Question

{Exercise 17.29}

Consider the following time series data.

Use the following dummy variables to develop an estimated regression equation to account for any seasonal and linear trend 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 (to 3 decimals if necessary).

Value = + Qtr1 - Qtr2 - Qtr3 + t

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{Exercise 17.29}

Consider the following time series data.

Quarter Year 1 Year 2 Year 3 1 4 6 7 2 2 3 6 3 3 5 6 4 5 7 8

Which of the following is a time series plot?



Selecttime series plot #atime series plot #btime series plot #c

What type of pattern exists in the data?
Selectupward linear trendnonlinear trendlinear trend and a seasonal patternslight curvaturedownward linear trend

Use the following dummy variables to develop an estimated regression equation to account for any seasonal and linear trend 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 (to 3 decimals if necessary).

Value = + Qtr1 - Qtr2 - Qtr3 + t

Compute the quarterly forecasts for next year (to 2 decimals). Quarter 1 forecast Quarter 2 forecast Quarter 3 forecast Quarter 4 forecast

Explanation / Answer

Seasonal trend.

Regression with seasonal dummy variables:

Model Summary

S R-sq R-sq(adj) R-sq(pred)
0.469295 95.91% 93.57% 88.44%

Coefficients

Term Coef SE Coef T-Value P-Value VIF
Constant 3.417 0.428 7.98 0.000
Quarter 0.4063 0.0415 9.79 0.000 1.12
Q1 0.219 0.403 0.54 0.604 1.66
Q2 -2.188 0.392 -5.58 0.001 1.57
Q3 -1.594 0.385 -4.14 0.004 1.52

Regression Equation

Year = 3.417 + 0.4063 Quarter + 0.219 Q1 - 2.188 Q2 - 1.594 Q3

Forecast for next year:

Prediction for Year

Regression Equation

Year = 3.417 + 0.4063 Quarter + 0.219 Q1 - 2.188 Q2 - 1.594 Q3

Variable Setting
Quarter 13
Q1 1
Q2 0
Q3 0

Fit SE Fit 95% CI 95% PI
8.91667 0.428406 (7.90365, 9.92969) (7.41412, 10.4192)

Variable Setting
Quarter 14
Q1 0
Q2 1
Q3 0

Fit SE Fit 95% CI 95% PI
6.91667 0.428406 (5.90365, 7.92969) (5.41412, 8.41922)

Variable Setting
Quarter 15
Q1 0
Q2 0
Q3 1

Fit SE Fit 95% CI 95% PI
7.91667 0.428406 (6.90365, 8.92969) (6.41412, 9.41922)

Variable Setting
Quarter 16
Q1 0
Q2 0
Q3 0

Fit SE Fit 95% CI 95% PI
9.91667 0.428406 (8.90365, 10.9297) (8.41412, 11.4192)

Next year Year Q1 8.91667 Q2 6.91667 Q3 7.91667 Q4 9.91667

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