The logistics department within a firm in the Twin Cities area wants to understand its cost drivers better. Since labor hours (y) form a crucial component of the department's cost, the goal is to identify factors that affect labor hours.

The logistics department has collected sample data for 20 weeks (in collaboration with the accounting department). The data provided in the enclosed Excel file includes information on labor hrs (y), pounds shipped in lbs (x1), % of units shipped by truck (x2), and average shipment weight in lbs (x3).

Week	Labor Hours (Y)	Pounds Shipped in lbs (X1)	Percentage of Units Shipped by Truck (X2)	Average Shipment Weight in lbs (X3)
1	100	5100	90	20
2	85	3800	99	22
3	108	5300	58	19
4	116	7500	16	15
5	92	4500	54	20
6	63	3300	42	26
7	79	5300	12	25
8	101	5900	32	21
9	88	4000	56	24
10	71	4200	64	29
11	122	6800	78	10
12	85	3900	90	30
13	50	3800	74	28
14	114	7500	89	14
15	104	4500	90	21
16	111	6000	40	20
17	110	8100	55	16
18	100	2900	64	19
19	82	4000	35	23
20	85	4800	58	25

a) Fit a multiple regression equation in excel linking labor hrs (y) to pounds shipped (x1), % of units shipped by truck (x2), and average shipment weight (x3). Provide the equation below based on your excel output. Note: Attach excel output showing the regression results when submitting the exam(3 points)

b) Estimate and interpret the 99% Confidence Interval for the coefficient ₃ in the above equation. (3 points)

c) Using the multiple linear regression equation obtained in a), what is the average labor hrs for a week in which 7100 pounds were shipped with 25% of the units being shipped by truck and the average shipment weight being 30 lbs.(2 points)