dolution

Consider the following time series data.

Quarter	Year 1	Year 2	Year 3
1	3	5	6
2	1	2	5
3	2	4	5
4	6	8	9

(a)

Construct a time series plot. What type of pattern exists in the data?

(b)

Use a multiple regression model with dummy variables as follows to develop an equation to account for seasonal effects in the data. (Round your numerical values to three decimal places.)

x₁ = 1 if quarter 1, 0 otherwise; x₂ = 1 if quarter 2, 0 otherwise; x₃ = 1 if quarter 3, 0 otherwise

y_t =

(c)

Compute the quarterly forecasts for the next year based on the model you developed in part (b). (Round your answers to two 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. (Round your numerical values to three decimal places.)y_t =

(e)

Compute the quarterly forecasts for the next year based on the model you developed in part (d). (Round your answers to two 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? Justify your answer.