Question

Consider the following time series:

Quarter	Year 1	Year 2	Year 3
1	69	66	60
2	44	36	46
3	60	62	55
4	79	82	73

(a)	Choose a time series plot.
	- Select your answer -Graph (i)Graph (ii)Graph (iii)Graph (iv)Item 1
	What type of pattern exists in the data? Is there an indication of a seasonal pattern?
	- 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 linear 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. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300)
	ŷ = ___ + ___Qtr1 + ___Qtr2 + ___ Qtr3
(c)	Compute the quarterly forecasts for next year.
	YearQuarterFt41__42__43__44__

Answer 1

1) graph(iv)

Horizontal pattern, with seasonality

b)

Quarter	Period	Qtr1	Qtr2	Qtr3	Series
1	1	1	0	0	69
2	2	0	1	0	44
3	3	0	0	1	60
4	4	0	0	0	79
1	5	1	0	0	66
2	6	0	1	0	36
3	7	0	0	1	62
4	8	0	0	0	82
1	9	1	0	0	60
2	10	0	1	0	46
3	11	0	0	1	55
4	12	0	0	0	73

Applying multiple regression on above data:

y^ =78+(-13)*Qtr1+(-36)*Qtr2+(-19)*Qtr3

c)

forecast for 1st qtr of next year =			65
forecast for 2nd qtr of next year =			42
forecast for 3rd qtr of next year =			59
forecast for 4th qtr of next year =			78