Question

Consider the following time series data. Quarter Year 1 Year 2 Year 3 1 5 8 10 2 2 4 8 3 1 4 6 4 3 6 8

(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) If the constant is "1" it must be entered in the box. Do not round intermediate calculation.

ŷ =_ + _Qtr1 + _Qtr2 + _Qtr3

Compute the quarterly forecasts for next year based on the model you developed in part (b).

If required, round your answers to three decimal places. Do not round intermediate calculation.

Year	Quarter	Ft
4	1
4	2
4	3
4	4

(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)
	ŷ = _ + _Qtr1 + _Qtr2 + _Qtr3 + _ t

(e)

Compute the quarterly forecasts for next year based on the model you developed in part (d).

Do not round your interim computations and round your final answer to three decimal places.

Year	Quarter	Period	Ft
4	1	13
4	2	14
4	3	15
4	4	16

(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

Answer 1

(b) ŷ = 5.667 + (2)Qtr1 + (-1)Qtr2 + (-2)Qtr3

(c) Quarter 1 forecast: x1 = 1, x2 = 0, x3 = 0  

ŷ = 5.667 + (2)*1 + (-1)*0 + (-2)*0 =    7.667

Quarter 2 forecast: x1 = 0, x2 = 1, x3 = 0  

ŷ = 5.667 + (2)*0 + (-1)*1 + (-2)*0 =    4.667

Quarter 3 forecast: x1 = 0, x2 = 0, x3 = 1  

ŷ = 5.667 + (2)*0 + (-1)*0 + (-2)*1 =    3.667

Quarter 4 forecast: x1 = 0, x2 = 0, x3 = 0  

ŷ = 5.667 + (2)*0 + (-1)*0 + (-2)*0 =    5.667

(d) ŷ = 0.417 + (3.969)Qtr1 + (0.313)Qtr2 + (-1.344)Qtr3 + (0.656)t

(e) MSE for b) = 7.083

MSE for d) = 0.220