Question

In: Statistics and Probability

A large grocery retailer tracks productivity and costs of its facilities closely. Data in the Grocery...

A large grocery retailer tracks productivity and costs of its facilities closely. Data in the Grocery retailer file were obtained from a single distribution center for a one-year period. Each data point for each variable represents one week of activity. The variables included are total labor hours required to handle a shipment (Y) in the first column, the number of cases shipped (X₁) in the second column, the indirect costs of the total labor hours as a percentage (X₂) in the third column, and a qualitative predictor called holiday (X₃: 1 if holiday week, 0 otherwise) in the last column.

Interpret the meaning of the estimated
1. intercept term,
2. coefficient of X₁
3. coefficient of X₂.
4. coefficient of X₃.

LaborHours NoShipped IndLaborCost HolidayWeek
4264 305657 7.17 0

4496 328476 6.20 0

4317 317164 4.61 0

4292 366745 7.02 0

4945 265518 8.61 1

4325 301995 6.88 0

4110 269334 7.23 0

4111 267631 6.27 0

4161 296350 6.49 0

4560 277223 6.37 0

4401 269189 7.05 0

4251 277133 6.34 0

4222 282892 6.94 0

4063 306639 8.56 0

4343 328405 6.71 0

4833 321773 5.82 1

4453 272319 6.82 0

4195 293880 8.38 0

4394 300867 7.72 0

4099 296872 7.67 0

4816 245674 7.72 1

4867 211944 6.45 1

4114 227996 7.22 0

4314 248328 8.50 0

4289 249894 8.08 0

4269 302660 7.26 0

4347 273848 7.39 0

4178 245743 8.12 0

4333 267673 6.75 0

4226 256506 7.79 0

4121 271854 7.89 0

3998 293225 9.01 0

4475 269121 8.01 0

4545 322812 7.21 0

4016 252225 7.85 0

4207 261365 6.14 0

4148 287645 6.76 0

4562 289666 7.92 0

4146 270051 8.19 0

4555 265239 7.55 0

4365 352466 6.94 0

4471 426908 7.25 0

5045 369989 9.65 1

4469 472476 8.20 0

4408 414102 8.02 0

4219 302507 6.72 0

4211 382686 7.23 0

4993 442782 7.61 1

4309 322303 7.39 0

4499 290455 7.99 0

4186 411750 7.83 0

4342 292087 7.77 0

Solutions

Expert Solution

Using Excel, go to Data, select Data Analysis, choose Regression. Put values of No. Shipped, IndLaborCost and HolidayWeek in X input range and LabourHours in Y input range.

	Coefficients	Standard Error	t Stat	P-value
Intercept	4149.887	195.565	21.220	0.000
No Shipped	0.001	0.000	2.159	0.036
IndLaborCost	-13.166	23.092	-0.570	0.571
HolidayWeek	623.554	62.641	9.954	0.000

1. Intercept = 4149.887

This means labour hours will be 4149.887 when value of all the independent variables (No. Shipped, IndLaborCost and HolidayWeek) is 0.

2. Coefficient of X1 = 0.001

This means with one unit increase in no. of cases shipped, labour hours increase by 0.001.

3. Coefficient of X2 = -13.166

This means with one unit increase in indirect costs, labour hours decrease by 13.166.

4. Coefficient of X3 = 623.554

This means that labours hours would increase by 623.554 if its a holiday week.

orchestra answered 1 year ago

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