# Consider the following time series data.

Problem 5-23

Consider the following time series data.

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Consider the following time series data.
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 Quarter Year 1 Year 2 Year 3 1 4 6 7 2 2 3 6 3 3 5 6 4 5 7 8
(a) Choose the correct time series plot.
 (i) (ii) (iii) (iv)
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What type of pattern exists in the data?
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(b) Use a multiple regression model with dummy variables as follows to develop an equation to account for 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.
If required, round your answers to three decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300)
Value = __________6.667_______ + ___-1______________ Qtr1t + _____-3____________ Qtr2t + __________-2_______ Qtr3t
(c) Compute the quarterly forecasts for next year based on the model you developed in part (b).
 Quarter 1 forecast _____5.667____________ Quarter 2 forecast _____3.667____________ Quarter 3 forecast _______4.667__________ Quarter 4 forecast ______6.667___________
(d) Use a multiple regression model to develop an equation to account for trend and seasonal effects in the data. Use the dummy variables you developed in part (b) to capture seasonal effects and create a variable t such that t = 1 for Quarter 1 in Year 1, t = 2 for Quarter 2 in Year 1,… t = 12 for Quarter 4 in Year 3.
If required, round your answers to three decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300)
Value =   3.4167______________ + __0.2188______________ Qtr1t + _____-2.1875___________ Qtr2t + __-1.5938_______________ Qtr3t + ___0.4063______________ t
(e) Compute the quarterly forecasts for next year based on the model you developed in part (d).
 Quarter 1 forecast _8.9167________________ Quarter 2 forecast ___6.9167______________ Quarter 3 forecast 7.9167_________________ Quarter 4 forecast _9.9167________________
(f) Is the model you developed in part (b) or the model you developed in part (d) more effective?
If required, round your intermediate calculations and final answer to three decimal places.
 Model developed in part (b) Model developed in part (d) MSE _________________ _________________