Consider the Costello Music Company problem and its quarterly sales data follow.
ID: 3244567 • Letter: C
Question
Consider the Costello Music Company problem and its quarterly sales data follow. PianoSales.xls
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.
For four quarters, you need these 3 dummy variables (binary)
Compute the quarterly forecasts for the next year, using the regression that you estimated.
Year Quarter Sales 1 1 4 2 2 3 1 4 5 2 1 6 2 4 3 4 4 14 3 1 10 2 3 3 5 4 16 4 1 12 2 9 3 7 4 22 5 1 18 2 10 3 13 4 35Explanation / Answer
Answer:
Consider the Costello Music Company problem and its quarterly sales data follow. PianoSales.xls
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.
For four quarters, you need these 3 dummy variables (binary)
Compute the quarterly forecasts for the next year, using the regression that you estimated.
Regression Analysis
R²
0.856
Adjusted R²
0.817
n
20
R
0.925
k
4
Std. Error
3.501
Dep. Var.
Sales
ANOVA table
Source
SS
df
MS
F
p-value
Regression
1,092.1000
4
273.0250
22.27
3.64E-06
Residual
183.9000
15
12.2600
Total
1,276.0000
19
Regression output
confidence interval
variables
coefficients
std. error
t (df=15)
p-value
95% lower
95% upper
Intercept
7.1500
2.2827
3.132
.0068
2.2846
12.0154
Q1
-5.5875
2.2531
-2.480
.0255
-10.3898
-0.7852
Q2
-10.9250
2.2317
-4.895
.0002
-15.6818
-6.1682
Q3
-11.4625
2.2188
-5.166
.0001
-16.1918
-6.7332
t
0.9375
0.1384
6.774
6.27E-06
0.6425
1.2325
Predicted values for: Sales
95% Confidence Intervals
95% Prediction Intervals
Q1
Q2
Q3
t
Predicted
lower
upper
lower
upper
Leverage
1
0
0
21
21.250
16.385
26.115
12.341
30.159
0.425
0
1
0
22
16.850
11.985
21.715
7.941
25.759
0.425
0
0
1
23
17.250
12.385
22.115
8.341
26.159
0.425
0
0
0
24
29.650
24.785
34.515
20.741
38.559
0.425
The regression line is
Sales = 7.1500-5.5875*Q1-10.9250*Q2-11.4625*Q3+0.9375*t
Forecasts for next year,
For Q1=21.250
For Q2=16.850
For Q3=17.250
For Q4=29.650
Regression Analysis
R²
0.856
Adjusted R²
0.817
n
20
R
0.925
k
4
Std. Error
3.501
Dep. Var.
Sales
ANOVA table
Source
SS
df
MS
F
p-value
Regression
1,092.1000
4
273.0250
22.27
3.64E-06
Residual
183.9000
15
12.2600
Total
1,276.0000
19
Regression output
confidence interval
variables
coefficients
std. error
t (df=15)
p-value
95% lower
95% upper
Intercept
7.1500
2.2827
3.132
.0068
2.2846
12.0154
Q1
-5.5875
2.2531
-2.480
.0255
-10.3898
-0.7852
Q2
-10.9250
2.2317
-4.895
.0002
-15.6818
-6.1682
Q3
-11.4625
2.2188
-5.166
.0001
-16.1918
-6.7332
t
0.9375
0.1384
6.774
6.27E-06
0.6425
1.2325
Predicted values for: Sales
95% Confidence Intervals
95% Prediction Intervals
Q1
Q2
Q3
t
Predicted
lower
upper
lower
upper
Leverage
1
0
0
21
21.250
16.385
26.115
12.341
30.159
0.425
0
1
0
22
16.850
11.985
21.715
7.941
25.759
0.425
0
0
1
23
17.250
12.385
22.115
8.341
26.159
0.425
0
0
0
24
29.650
24.785
34.515
20.741
38.559
0.425
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.