1. The sample data shown in table below are collected from a firms shipping and production records to provide cost information about a firms 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

1. 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.
2. If the manager wishes to use two independent variables in the model, which model would you suggest and why?
3. Is it useful to include X1 in the model when X3 is already in the model? Explain why or why not.
4. Consider all one-independent variable, two-independent variable, and three-independent variable models and select the best model and explain your reasons.
5. Check the model assumptions for Y vs X1, X3 (normality, residual, and line-fit plots)
6. Develop a 95% prediction interval for labor requirements when average shipment weight is 35 lbs
7. 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. Weekly demand data is show below:

Week	Demand
1	1000
2	1250
3	800
4	1900
5	1640
6	2200
7	1870
8	2670
9	3210
10	2850
11	2200
12	2980
13	3790
14	4210
15	4716

1. Apply the Holts Model in forecasting the demand for period 16
2. What are the optimal values for alpha and beta if the decision-maker wishes to restrict both values to be between 0.25 and 0.65
3. What is the value of the minimized error term in this context?
4. Show all related EXCEL plots

Note: Include all EXCEL regression output and any plots