Assignment : Forecasting
1. The sample data shown in table below are collected from a firm's shipping and production records to provide cost information about a firm's shipping department. The manager of the shipping department wants to identify the relationship between labor requirements (Y) and pounds shipped (X1), percentage of units shipped by truck (X2), and average shipment weight (X3) for capacity planning purposes in future periods. Answer the following questions based on the given data:
|
Week
|
Labor (hrs)
|
Pounds Shipped (1,000s)
|
% of Units Shipped by Truck
|
Average Shipment Weight (lbs)
|
|
|
Y
|
X1
|
X2
|
X3
|
|
1
|
100
|
5.1
|
90
|
30
|
|
2
|
85
|
3.8
|
99
|
17
|
|
3
|
108
|
4.9
|
58
|
24
|
|
4
|
116
|
6.1
|
16
|
23
|
|
5
|
92
|
4.5
|
54
|
18
|
|
6
|
63
|
3.3
|
42
|
15
|
|
7
|
79
|
5.3
|
12
|
18
|
|
8
|
101
|
5.2
|
32
|
21
|
|
9
|
88
|
4.0
|
56
|
15
|
|
10
|
71
|
4.2
|
64
|
13
|
|
11
|
122
|
6.1
|
78
|
38
|
|
12
|
85
|
3.9
|
90
|
14
|
|
13
|
50
|
3.8
|
74
|
10
|
|
14
|
114
|
5.9
|
89
|
25
|
|
15
|
104
|
4.5
|
90
|
21
|
|
16
|
111
|
6.0
|
40
|
23
|
|
17
|
110
|
8.1
|
55
|
24
|
|
18
|
100
|
2.9
|
64
|
19
|
|
19
|
82
|
4.0
|
35
|
16
|
|
20
|
85
|
4.8
|
58
|
17
|
a. If the manager wishes to use a single independent variable regression model, which model would you suggest and why? Explain what the slope, y-intercept, and R2 value mean for the model that you selected.
b. If the manager wishes to use two independent variables in the model, which model would you suggest and why?
c. Is it useful to include X1 in the model when X3 is already in the model? Explain why or why not.
d. Consider all one-independent variable, two-independent variable, and three-independent variable models and select the best model and explain your reasons.
e. Check the model assumptions for Y vs X1, X3 (normality, residual, and line-fit plots)
f. Develop a 95% prediction interval for labor requirements when average shipment weight is 35 lbs
g. Test the significance of model Y vs X1, X2
Note: Include all EXCEL regression output and any plots.
2. Amalgamated Products which produces chemical materials has the following demand pattern for one of its key products. Demand data is shown by quarter for three years:
|
Period/Qtr
|
Q1
|
Q2
|
Q3
|
Q4
|
|
1
|
1600
|
6050
|
4000
|
12000
|
|
2
|
2000
|
7100
|
3900
|
10200
|
|
3
|
2200
|
8000
|
5000
|
9800
|
a. Suggest an appropriate forecasting technique for this problem and provide reasons.
b. Build a model to forecast the demand for the product in future time periods.
c. Develop a 95% confidence interval for demand forecast in quarter 2 of year 4.
Note: Include all EXCEL regression output and any plots.