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.
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
Consider the following time series data: Quarter Year 1 Year 2 Year 3 1 71 68...
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