Question

Consider the following time series data:

Quarter	Year 1	Year 2	Year 3
1	71	68	62
2	49	41	51
3	58	60	53
4	78	81	72

Question: Use a multiple regression linear model with dummy variables as follows to develop an equation to account for seasonal effects in the data:

Q1=1 if quarter 1, 0 otherwise

Q2=1 if quarter 2, 0 otherwise

Q3=1 if quarter 3, 0 otherwise

What is the R^2 (coefficient of determination)? Round to 4 decimal places.

Answer 1

Let's input the following data into Excel of any other statistical software:

Value	Qtr1	Qtr2	Qtr3
71	1	0	0
49	0	1	0
58	0	0	1
78	0	0	0
68	1	0	0
41	0	1	0
60	0	0	1
81	0	0	0
62	1	0	0
51	0	1	0
53	0	0	1
72	0	0	0

Q1=1 if quarter 1, 0 otherwise

Q2=1 if quarter 2, 0 otherwise

Q3=1 if quarter 3, 0 otherwise

We will use these three dummy variables to form the regression equation. The dependent variable is the value and quarter variables are the independent variables.

Let's go to Data -> Data analysis -> Regression -> Select the data -> OK

THe results are:

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.948873
R Square	0.90036
Adjusted R Square	0.862995
Standard Error	4.555217
Observations	12
ANOVA
	df	SS	MS	F	Significance F
Regression	3	1500	500	24.09639	0.000233
Residual	8	166	20.75
Total	11	1666
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	77	2.629956	29.27806	2.01E-09	70.93531	83.06469	70.93531	83.06469
Qtr1	-10	3.719319	-2.68866	0.027554	-18.5768	-1.42324	-18.5768	-1.42324
Qtr2	-30	3.719319	-8.06599	4.12E-05	-38.5768	-21.4232	-38.5768	-21.4232
Qtr3	-20	3.719319	-5.37733	0.000664	-28.5768	-11.4232	-28.5768	-11.4232

The R-square value = 0.9004