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

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

Test the significance of model Y vs X1, X2