Consider the following time series data. a. Which of the following time series p
ID: 3229475 • Letter: C
Question
Consider the following time series data.
a. Which of the following time series plots is correct for this data?
(Select your answer: time series plot a, time series plot b, time series plot c)
i) What type of pattern exists in the data?
(Select your answer: upward linear trend, nonlinear trend, linear trend and a seasonal pattern, slight curvature, downward linear trend)
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).
______ + ______ Qtr1 - ______ Qtr2 - ______ Qtr3 + _____ t
c. Compute the quarterly forecasts for next year (to 2 decimals).
Quarter 1 forecast ______ Quarter 2 forecast ______ Quarter 3 forecast ______ Quarter 4 forecast ______Quartel Year 1 Year 2 Year 3 a 7668 a 6357 a 4235 a 1234
Explanation / Answer
Answer:
a). Which of the following time series plots is correct for this data?
time series plot c
i) What type of pattern exists in the data?
linear trend and a seasonal pattern
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).
3.417 + 0.219 Qtr1 - 2.188 Qtr2 – 1.594 Qtr3 + 0.406 t
c. 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
Regression Analysis
R²
0.959
Adjusted R²
0.936
n
12
R
0.979
k
4
Std. Error
0.469
Dep. Var.
data
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
3.417
0.4284
7.975
.0001
2.4036
4.4297
Q1
0.219
0.4029
0.543
.6040
-0.7339
1.1714
Q2
-2.188
0.3921
-5.580
.0008
-3.1146
-1.2604
Q3
-1.594
0.3854
-4.135
.0044
-2.5051
-0.6824
t
0.406
0.0415
9.794
2.45E-05
0.3082
0.5043
Predicted values for: data
95% Confidence Intervals
95% Prediction Intervals
Q1
Q2
Q3
t
Predicted
lower
upper
lower
upper
Leverage
1
0
0
13
8.92
7.904
9.930
7.414
10.419
0.833
0
1
0
14
6.92
5.904
7.930
5.414
8.419
0.833
0
0
1
15
7.92
6.904
8.930
6.414
9.419
0.833
0
0
0
16
9.92
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
Regression Analysis
R²
0.959
Adjusted R²
0.936
n
12
R
0.979
k
4
Std. Error
0.469
Dep. Var.
data
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
3.417
0.4284
7.975
.0001
2.4036
4.4297
Q1
0.219
0.4029
0.543
.6040
-0.7339
1.1714
Q2
-2.188
0.3921
-5.580
.0008
-3.1146
-1.2604
Q3
-1.594
0.3854
-4.135
.0044
-2.5051
-0.6824
t
0.406
0.0415
9.794
2.45E-05
0.3082
0.5043
Predicted values for: data
95% Confidence Intervals
95% Prediction Intervals
Q1
Q2
Q3
t
Predicted
lower
upper
lower
upper
Leverage
1
0
0
13
8.92
7.904
9.930
7.414
10.419
0.833
0
1
0
14
6.92
5.904
7.930
5.414
8.419
0.833
0
0
1
15
7.92
6.904
8.930
6.414
9.419
0.833
0
0
0
16
9.92
8.904
10.930
8.414
11.419
0.833