Consider the following time series data. 8 b.) Use the following dummy variables
ID: 2908528 • Letter: C
Question
Consider the following time series data.
8
b.) Use the following dummy variables to develop an estimated regression equation to account for any seasonal and linear trend effects in the data: Qtr1 = 1 if Quarter 1, 0 otherwise; Qtr2 = 1 if Quarter 2, 0 otherwise; Qtr3 = 1 if Quarter 3, 0 otherwise (to 3 decimals if necessary).
Value = ____ +____ Qtr1____ - Qtr2____ - Qtr3____ + t
Compute the quarterly forecasts for next year (to 2 decimals).
Quarter Year 1Year2 Year 3 1 4 6 7 2 2 3 6 3 3 5 6 4 5 78
b.) Use the following dummy variables to develop an estimated regression equation to account for any seasonal and linear trend effects in the data: Qtr1 = 1 if Quarter 1, 0 otherwise; Qtr2 = 1 if Quarter 2, 0 otherwise; Qtr3 = 1 if Quarter 3, 0 otherwise (to 3 decimals if necessary).
Value = ____ +____ Qtr1____ - Qtr2____ - Qtr3____ + t
Compute the quarterly forecasts for next year (to 2 decimals).
Quarter 1 forecast Quarter 2 forecast Quarter 3 forecast Quarter 4 forecastExplanation / Answer
Result:
b.) Use the following dummy variables to develop an estimated regression equation to account for any seasonal and linear trend effects in the data: Qtr1 = 1 if Quarter 1, 0 otherwise; Qtr2 = 1 if Quarter 2, 0 otherwise; Qtr3 = 1 if Quarter 3, 0 otherwise (to 3 decimals if necessary).
Value = 3.147 +(-1)*Qtr1+(-3) *Qtr2+(-2)* Qtr3 + 1.625* t
Compute the quarterly forecasts for next year (to 2 decimals).
Quarter 1 forecast
8.92
Quarter 2 forecast
6.92
Quarter 3 forecast
7.92
Quarter 4 forecast
9.92
Recoded data
value
t
Qtr1
Qtr2
Qtr3
4
1
1
0
0
2
1
0
1
0
3
1
0
0
1
5
1
0
0
0
6
2
1
0
0
3
2
0
1
0
5
2
0
0
1
7
2
0
0
0
7
3
1
0
0
6
3
0
1
0
6
3
0
0
1
8
3
0
0
0
Regression Analysis
R²
0.959
Adjusted R²
0.936
n
12
R
0.979
k
4
Std. Error
0.469
Dep. Var.
value
ANOVA table
Source
SS
df
MS
F
p-value
Regression
36.1250
4
9.0313
41.01
.0001
Residual
1.5417
7
0.2202
Total
37.6667
11
Regression output
confidence interval
variables
coefficients
std. error
t (df=7)
p-value
95% lower
95% upper
Intercept
3.4167
0.4284
7.975
.0001
2.4036
4.4297
t
1.6250
0.1659
9.794
2.45E-05
1.2327
2.0173
Qtr1
-1.0000
0.3832
-2.610
.0349
-1.9061
-0.0939
Qtr2
-3.0000
0.3832
-7.829
.0001
-3.9061
-2.0939
Qtr3
-2.0000
0.3832
-5.220
.0012
-2.9061
-1.0939
Predicted values for: value
95% Confidence Intervals
95% Prediction Intervals
t
Qtr1
Qtr2
Qtr3
Predicted
lower
upper
lower
upper
Leverage
4
1
0
0
8.917
7.904
9.930
7.414
10.419
0.833
4
0
1
0
6.917
5.904
7.930
5.414
8.419
0.833
4
0
0
1
7.917
6.904
8.930
6.414
9.419
0.833
4
0
0
0
9.917
8.904
10.930
8.414
11.419
0.833
Quarter 1 forecast
8.92
Quarter 2 forecast
6.92
Quarter 3 forecast
7.92
Quarter 4 forecast
9.92