Consider the following time series data.

Quarter	Year 1	Year 2	Year 3
1	3	6	8
2	2	4	8
3	4	7	9
4	6	9	11

(a)

Choose the correct time series plot.

(i)
(ii)
(iii)
(iv)

- Select your answer -Plot (i)Plot (ii)Plot (iii)Plot (iv)Item 1

What type of pattern exists in the data?

- Select your answer -Positive trend pattern, no seasonalityHorizontal pattern, no seasonalityNegative trend pattern, no seasonalityPositive trend pattern, with seasonalityHorizontal pattern, with seasonalityItem 2

(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.

= + Qtr1 + Qtr2 + Qtr3

(c)

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 variabletsuch thatt= 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).

= + 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)

Calculate the MSE for the regression models developed in parts (b) and (d).

If required, round your intermediate calculations and final answer to three decimal places.

	Model developed in part (b)	Model developed in part (d)
MSE

Is the model you developed in part (b) or the model you developed in part (d) more effective?