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

(a)

Choose the correct time series plot.

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

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

What type of pattern exists in the data?

Trend Pattern- Select your answer -Horizontal PatternTrend PatternItem 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)

Value = + Qtr1t + Qtr2t + Qtr3t

(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.

Quarter 1 forecast
Quarter 2 forecast
Quarter 3 forecast
Quarter 4 forecast

(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 = + Qtr1t + Qtr2t + Qtr3t + t

(e)

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

Round your interim computations and final answers to three decimal places.

Quarter 1 forecast
Quarter 2 forecast
Quarter 3 forecast
Quarter 4 forecast

(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

Model developed in part (d)- Select your answer -Model developed in part (b)Model developed in part (d)Item 22

Justify your answer.

The input in the box below will not be graded, but may be reviewed and considered by your instructor.

Transcribed Image Text:

Year 1. Quarter 1 Quarter 2 Quarter 3 Quarter a Quarter 1 Quarter 2 Quarter 3 Quarter 4 Quarter 1 Quarter 2 Quarter3 Quarter 4 Year 1, Year 1. Year 1, Year 2. Year 2, Year 2. Year 2, Year 3, Year 3, Year 3. Year 3, Time Period Time Series Values Year 1. Quarter 1 Quarter 2 Quarter 3 Quarter a Quarter 1 Quarter 2 Quarter 3 Quarter 4 Quarter 1 Quarter 2 Quarter3 Quarter 4 Year 1, Year 1. Year 1, Year 2. Year 2, Year 2. Year 2, Year 3, Year 3, Year 3. Year 3, Time Period Time Series Values