The quarterly sales data (number of copies sold) for a college textbook over the
ID: 3362664 • Letter: T
Question
The quarterly sales data (number of copies sold) for a college textbook over the past three years are as follows:
Dummy Variables
Year
Quarter
Qtr1
Qtr2
Qtr3
yt
1
1
1
0
0
1690
1
2
0
1
0
940
1
3
0
0
1
2625
1
4
0
0
0
2500
2
1
1
0
0
1800
2
2
0
1
0
900
2
3
0
0
1
2900
2
4
0
0
0
2360
3
1
1
0
0
1850
3
2
0
1
0
1100
3
3
0
0
1
2930
3
4
0
0
0
2615
a. Use Excel to find the regression model that to accounts for seasonal effects in the data.
b. Based on the model in part (a), compute the quarterly forecasts for next year.
Dummy Variables
Year
Quarter
Qtr1
Qtr2
Qtr3
t
yt
1
1
1
0
0
1
1690
1
2
0
1
0
2
940
1
3
0
0
1
3
2625
1
4
0
0
0
4
2500
2
1
1
0
0
5
1800
2
2
0
1
0
6
900
2
3
0
0
1
7
2900
2
4
0
0
0
8
2360
3
1
1
0
0
9
1850
3
2
0
1
0
10
1100
3
3
0
0
1
11
2930
3
4
0
0
0
12
2615
c. Use Excel to find the regression model that to accounts for seasonal effects and any linear trend in the time series.
d. Based on the model in part (c), compute the quarterly forecasts for next year.
DO FOR ME PART d
Dummy Variables
Year
Quarter
Qtr1
Qtr2
Qtr3
yt
1
1
1
0
0
1690
1
2
0
1
0
940
1
3
0
0
1
2625
1
4
0
0
0
2500
2
1
1
0
0
1800
2
2
0
1
0
900
2
3
0
0
1
2900
2
4
0
0
0
2360
3
1
1
0
0
1850
3
2
0
1
0
1100
3
3
0
0
1
2930
3
4
0
0
0
2615
Explanation / Answer
Result:
c. Use Excel to find the regression model that to accounts for seasonal effects and any linear trend in the time series.
Regression Analysis
R²
0.991
Adjusted R²
0.986
n
12
R
0.995
k
4
Std. Error
89.828
Dep. Var.
yt
ANOVA table
Source
SS
df
MS
F
p-value
Regression
6,065,391.6667
4
1,516,347.9167
187.92
3.37E-07
Residual
56,483.3333
7
8,069.0476
Total
6,121,875.0000
11
Regression output
confidence interval
variables
coefficients
std. error
t (df=7)
p-value
95% lower
95% upper
Intercept
2,306.6667
82.0013
28.130
1.84E-08
2,112.7645
2,500.5688
Qtr1
-642.2917
77.1150
-8.329
.0001
-824.6396
-459.9437
Qtr2
-1,465.4167
75.0435
-19.528
2.30E-07
-1,642.8663
-1,287.9671
Qtr3
349.7917
73.7727
4.741
.0021
175.3471
524.2363
t
23.1250
7.9397
2.913
.0226
4.3505
41.8995
The regression trend line is
y = 2,306.6667-642.2917*Qtr1-1,465.4167*Qtr2+349.7917* Qtr3+23.1250*t
d. Based on the model in part (c), compute the quarterly forecasts for next year.
Predicted values for: yt
95% Confidence Intervals
95% Prediction Intervals
Qtr1
Qtr2
Qtr3
t
Predicted
lower
upper
lower
upper
1
0
0
13
1,965.000
1,771.098
2,158.902
1,677.397
2,252.603
0
1
0
14
1,165.000
971.098
1,358.902
877.397
1,452.603
0
0
1
15
3,003.333
2,809.431
3,197.235
2,715.730
3,290.937
0
0
0
16
2,676.667
2,482.765
2,870.569
2,389.063
2,964.270
Regression Analysis
R²
0.991
Adjusted R²
0.986
n
12
R
0.995
k
4
Std. Error
89.828
Dep. Var.
yt
ANOVA table
Source
SS
df
MS
F
p-value
Regression
6,065,391.6667
4
1,516,347.9167
187.92
3.37E-07
Residual
56,483.3333
7
8,069.0476
Total
6,121,875.0000
11
Regression output
confidence interval
variables
coefficients
std. error
t (df=7)
p-value
95% lower
95% upper
Intercept
2,306.6667
82.0013
28.130
1.84E-08
2,112.7645
2,500.5688
Qtr1
-642.2917
77.1150
-8.329
.0001
-824.6396
-459.9437
Qtr2
-1,465.4167
75.0435
-19.528
2.30E-07
-1,642.8663
-1,287.9671
Qtr3
349.7917
73.7727
4.741
.0021
175.3471
524.2363
t
23.1250
7.9397
2.913
.0226
4.3505
41.8995
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