Question

OC Music Company has been in business for 4 years. Data about the sales of each quarter were collected below. The manager wants use these data to forecast sales of the 5^th year. Please copy and paste it to Excel and run regression analysis. Answer the following 4 questions. Please also upload your EXCEL file on Titanium, otherwise you will NOT receive any point for this problem.

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

Question 16

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

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Question 17

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

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Question 18

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

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Question 19

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Calculate the MAE for this time series forecast. Rounded to two decimal places.

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Answer 1

Using Excel, input data in the following manner:

Year	Q1	Q2	Q3	Q4	Sales
1	1	0	0	0	7
1	0	1	0	0	2
1	0	0	1	0	4
1	0	0	0	0	10
2	1	0	0	0	6
2	0	1	0	0	3
2	0	0	1	0	8
2	0	0	0	0	14
3	1	0	0	0	10
3	0	1	0	0	3
3	0	0	1	0	5
3	0	0	0	0	16
4	1	0	0	0	12
4	0	1	0	0	4
4	0	0	1	0	7
4	0	0	0	0	22

Go to Data, select Data Analysis, choose Regression. Put Year, Q1,Q2, Q3 and Q4 in X input range. Put Sales in Y input range. Tick Residuals.

	Coefficients	Standard Error	t Stat	P-value
Intercept	11.1875	1.673458103	6.685258	5.46E-05
Year	1.725	0.49892881	3.457407	0.006149
Q1	-6.75	1.57775143	-4.27824	0.001616
Q2	-12.5	1.57775143	-7.92267	1.28E-05
Q3	-9.5	1.57775143	-6.02123	0.000128
Q4	0	0	65535	--

16. Sales = 11.19 + 1.73*Year - 6.75*Q1 - 12.5*Q2 - 9.5*Q3

Independent variables: Q1, Q2, Q3, Year (4)

Dependent variable: Sales

17. Intercept = 11.19

18. Forecast for last quarter of 5th year:

Sales = 11.19 + 1.73*5 - 6.75*0 - 12.5*0 - 9.5*0 = 19..84

19.

Sales	Predicted	Residuals	Absolute Error
7	6.163	0.837	0.837
2	0.413	1.588	1.588
4	3.413	0.587	0.587
10	12.913	-2.913	2.913
6	7.888	-1.888	1.888
3	2.138	0.863	0.863
8	5.138	2.863	2.863
14	14.638	-0.638	0.638
10	9.613	0.387	0.387
3	3.863	-0.862	0.862
5	6.863	-1.863	1.863
16	16.363	-0.363	0.363
12	11.338	0.663	0.663
4	5.588	-1.588	1.588
7	8.588	-1.588	1.588
22	18.088	3.913	3.913
		Total	23.4

MAE = 23.4/16 = 1.463