The following is a partial printout from a Regression routine run on quarterly s
ID: 3131065 • Letter: T
Question
The following is a partial printout from a Regression routine run on quarterly seasonal data with a trend in order to obtain a regression forecasting model. There were 20 consecutive quarters in the original time series. Time period 1 corresponds to a 1st quarter value. The trend variable is t, and the 3 dummy variables representing Quarters 1, 2 and 3 are Qtr1, Qtr2, and Qtr3 resp. Use the printout below to forecast the value of the time series for time period 23. Round your forecast to 1 decimal place.
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.988
R Square
0.976
Adjusted R Square
0.968
Standard Error
0.217
Observations
20
ANOVA
df
SS
MS
F
Significance F
Regression
4
21.248
5.312
156.235
0.000
Residual
15
0.516
0.034
Total
19
21.282
Variables
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
7.8
0.162
37.347
0.000
5.711
6.426
t
0.6
0.012
12.023
0.000
0.119
0.172
Qtr1
-0.9
0.157
-8.657
0.000
-1.710
-1.017
Qtr2
-2.9
0.155
-13.112
0.000
-2.375
-1.692
Qtr3
0.6
0.154
-1.981
0.073
-0.643
0.034
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.988
R Square
0.976
Adjusted R Square
0.968
Standard Error
0.217
Observations
20
ANOVA
df
SS
MS
F
Significance F
Regression
4
21.248
5.312
156.235
0.000
Residual
15
0.516
0.034
Total
19
21.282
Variables
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
7.8
0.162
37.347
0.000
5.711
6.426
t
0.6
0.012
12.023
0.000
0.119
0.172
Qtr1
-0.9
0.157
-8.657
0.000
-1.710
-1.017
Qtr2
-2.9
0.155
-13.112
0.000
-2.375
-1.692
Qtr3
0.6
0.154
-1.981
0.073
-0.643
0.034
Explanation / Answer
Answer to the question)
given time preriod = 23
this 23rd quarter , falls in Q3 , so we keep the dummy variable Q3 = 1, and Q1=Q2 =0
Thus the predicted value will be:
Predicted Value = 7.8 + 0.6*23 + 0+ 0 + 0.6*1
Predicted Value = 22.2
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