Question

Year	Quarter	Sales
1	Q1	7
	Q2	2
	Q3	4
	Q4	10
2	Q1	6
	Q2	3
	Q3	8
	Q4	14
3	Q1	10
	Q2	3
	Q3	5
	Q4	16
4	Q1	12
	Q2	4
	Q3	7
	Q4	22

1.Develop a model for trend and seasonality. Please clearly define your variables. How many independent variables do you have in your regression?

2.What is the intercept in your estimated regression model? Rounded to two decimal places.

3.Use the model to forecast for sales of last quarter in the 5th year. Rounded to two decimal places.

4.Calculate the MAE for this time series forecast.

Answer 1

1)

Year	Quarter	Sales	Q1	Q2	Q3	t
1	1	7	1	0	0	1
	2	2	0	1	0	2
	3	4	0	0	1	3
	4	10	0	0	0	4
2	1	6	1	0	0	5
	2	3	0	1	0	6
	3	8	0	0	1	7
	4	14	0	0	0	8
3	1	10	1	0	0	9
	2	3	0	1	0	10
	3	5	0	0	1	11
	4	16	0	0	0	12
4	1	12	1	0	0	13
	2	4	0	1	0	14
	3	7	0	0	1	15
	4	22	0	0	0	16

response variable is sales

independnet variables are, Q1,Q2,Q3,t = 4

2)

	coefficients	std error
intercept	11.1875	1.602799
Q1	-5.46	1.553052
Q2	-11.64	1.529905
Q3	-9.069	1.515848
t=	0.431	0.119466

intercept = 11.19

3) Y^=   11.1875+-5.45625Q1+-11.6375Q2+-9.06875Q3+0.43125*t              

Y^=   11.1875+-5.45625*0+-11.6375*0+-9.06875*0+0.43125*20 = 19.81