Please help me answer this. Quarterly revenues (in $1,000,000\'s) for a national
ID: 3312177 • Letter: P
Question
Please help me answer this.
Quarterly revenues (in $1,000,000's) for a national restaurant chain for a five-year period were as follows:
Based on these data, develop a multiple regression model that can capture both a trend and seasonal components. Carefully explain how you built the model and interpret each slope. Based on this model, what revenues would you predict for the third quarter of Year 6 (the following year)?
Quarter Year 1 Year 2 Year 3 Year 4 Year 5 1 33 42 54 70 85 2 36 40 53 67 82 3 35 42 54 70 87 4 38 47 62 77 99Explanation / Answer
Result:
Based on these data, develop a multiple regression model that can capture both a trend and seasonal components. Carefully explain how you built the model and interpret each slope. Based on this model, what revenues would you predict for the third quarter of Year 6 (the following year)?
Your answer
To capture quarterly trend, create 3 dummy variables.
If the time series exhibits linear trend, then add a year time trend variable
Data are prepared like follows:
revenue
Qr1
Qr2
Qr3
t
33
1
0
0
1
36
0
1
0
1
35
0
0
1
1
38
0
0
0
1
42
1
0
0
2
40
0
1
0
2
42
0
0
1
2
47
0
0
0
2
54
1
0
0
3
53
0
1
0
3
54
0
0
1
3
62
0
0
0
3
70
1
0
0
4
67
0
1
0
4
70
0
0
1
4
77
0
0
0
4
85
1
0
0
5
82
0
1
0
5
87
0
0
1
5
99
0
0
0
5
Regression Analysis
R²
0.972
Adjusted R²
0.964
n
20
R
0.986
k
4
Std. Error
3.784
Dep. Var.
revenue
ANOVA table
Source
SS
df
MS
F
p-value
Regression
7,401.7750
4
1,850.4438
129.24
1.97E-11
Residual
214.7750
15
14.3183
Total
7,616.5500
19
Regression output
confidence interval
variables
coefficients
std. error
t (df=15)
p-value
95% lower
95% upper
Intercept
24.4750
2.4668
9.922
5.54E-08
19.2171
29.7329
Qr1
-7.8000
2.3932
-3.259
.0053
-12.9010
-2.6990
Qr2
-9.0000
2.3932
-3.761
.0019
-14.1010
-3.8990
Qr3
-7.0000
2.3932
-2.925
.0105
-12.1010
-1.8990
t
13.3750
0.5983
22.355
6.25E-13
12.0998
14.6502
Predicted values for: revenue
95% Confidence Interval
95% Prediction Interval
Qr1
Qr2
Qr3
t
Predicted
lower
upper
lower
upper
Leverage
0
0
1
6
97.725
92.467
102.983
88.097
107.353
0.425
The trend line is
Revenue=24.4750-7.8*qr1-9.0*Qr2-7.0*Qr3+13.375*t
For quarter 1, there is a decrease of 7.8 (in $1,000,000's) in revenue.
For quarter 2, there is a decrease of 9.0 (in $1,000,000's) in revenue.
For quarter 3, there is a decrease of 7.0 (in $1,000,000's) in revenue.
Predicted revenue for the third quarter of Year 6 =97.725 (in $1,000,000's).
revenue
Qr1
Qr2
Qr3
t
33
1
0
0
1
36
0
1
0
1
35
0
0
1
1
38
0
0
0
1
42
1
0
0
2
40
0
1
0
2
42
0
0
1
2
47
0
0
0
2
54
1
0
0
3
53
0
1
0
3
54
0
0
1
3
62
0
0
0
3
70
1
0
0
4
67
0
1
0
4
70
0
0
1
4
77
0
0
0
4
85
1
0
0
5
82
0
1
0
5
87
0
0
1
5
99
0
0
0
5
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