Quarterly sales totals are shown below. quarter year 1 year 2 year 3 year 4 1 57
ID: 3217676 • Letter: Q
Question
Quarterly sales totals are shown below.
quarter
year 1
year 2
year 3
year 4
1
57
73
89
105
2
79
95
111
127
3
52
68
84
100
4
61
77
93
109
Use multiple regression with dummy variables to develop an additive decomposition forecasting model for these data.
Model the trend component using the time periods, numbered 1-16. Model the seasonality using dummy variables for quarters 1-3 (use quarter 4 as the baseline).
Hints: Copy-and-paste data into Excel. Re-format the data into columns. Create a period variable and dummy variables for quarter 1, quarter 2, and quarter 3.
Fill in the blanks below with the coefficients that you estimate from the data.
Predicted sales =
+
x period +
x Q1 +
x Q2 +
quarter
year 1
year 2
year 3
year 4
1
57
73
89
105
2
79
95
111
127
3
52
68
84
100
4
61
77
93
109
Explanation / Answer
Answer:
MINITAB used
Regression Equation
sales = 45.00 + 4.000 period + 8.000 Q1 + 26.00 Q2 - 5.000 Q3
period
Q1
Q2
Q3
sales
1
1
0
0
57
2
0
1
0
79
3
0
0
1
52
4
0
0
0
61
5
1
0
0
73
6
0
1
0
95
7
0
0
1
68
8
0
0
0
77
9
1
0
0
89
10
0
1
0
111
11
0
0
1
84
12
0
0
0
93
13
1
0
0
105
14
0
1
0
127
15
0
0
1
100
16
0
0
0
109
Regression Analysis: sales versus period, Q1, Q2, Q3
Analysis of Variance
Source DF Adj SS Adj MS F-Value P-Value
Regression 4 6779.00 1694.75 * *
period 1 5120.00 5120.00 * *
Q1 1 121.18 121.18 * *
Q2 1 1319.02 1319.02 * *
Q3 1 49.69 49.69 * *
Error 11 0.00 0.00
Total 15 6779.00
Model Summary
S R-sq R-sq(adj) R-sq(pred)
0 100.00% 100.00% 100.00%
Coefficients
Term Coef SE Coef T-Value P-Value VIF
Constant 45.00 0.00 * *
period 4.000 0.000 * * 1.06
Q1 8.000 0.000 * * 1.58
Q2 26.00 0.00 * * 1.54
Q3 -5.000 0.000 * * 1.51
Regression Equation
sales = 45.00 + 4.000 period + 8.000 Q1 + 26.00 Q2 - 5.000 Q3
period
Q1
Q2
Q3
sales
1
1
0
0
57
2
0
1
0
79
3
0
0
1
52
4
0
0
0
61
5
1
0
0
73
6
0
1
0
95
7
0
0
1
68
8
0
0
0
77
9
1
0
0
89
10
0
1
0
111
11
0
0
1
84
12
0
0
0
93
13
1
0
0
105
14
0
1
0
127
15
0
0
1
100
16
0
0
0
109