Consider the following time series data.

Quarter Year 1 Year 2 Year 3

1 58 10

2 2 4 8

3 1 4 6

4 3 6 8

(a) Make a line chart using data above.

What type of pattern exists in the data?- Select your answer -

• Positive trend pattern, no seasonality
• Horizontal pattern, no seasonality
• Negative trend pattern, no seasonality
• Positive trend pattern, with seasonality
• Horizontal pattern, with seasonality

(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 make 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)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- _____________________ ______________________

- Select your answer -

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

Justify your answer.

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

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