Question

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.

Report the residual plot against predicted Y values (Y). Also report the normal probability plot. Do they indicate any violations of the regression assumptions: Linearity, normality, homoscedasticity, independence of error terms?

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

Answer 1

The plots are:

Linearity, normality, homoscedasticity, independence of error terms conditions are all met.

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