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.

Report the p-value of the t-ratio test for X2. Write down the null and alternative hypothesis for this single slope. State your conclusion (Reject or Fail to reject)?


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

The hypothesis being tested is:

H0: β2 = 0

H1: β2 ≠ 0

The p-value is 0.5584.

Since the p-value (0.5584) is greater than the significance level (0.05), we fail to reject the null hypothesis.

Therefore, we cannot conclude that the slope is significant.

R² 0.678
Adjusted R² 0.659
R   0.824
Std. Error   143.423
n   54
k   3
Dep. Var. Y
ANOVA table
Source SS   df   MS F p-value
Regression 21,69,505.41952067 3   7,23,168.47317356 35.16 2.29E-12
Residual 10,28,507.41381266 50   20,570.14827625
Total 31,98,012.83333333 53  
Regression output confidence interval
variables coefficients std. error    t (df=50) p-value 95% lower 95% upper
Intercept 4,192.6803
X1 0.0006 0.00035117 1.844 .0711 -0.0001 0.0014
X2 -13.5918 23.0686 -0.589 .5584 -59.9264 32.7429
X3 627.1743 62.4860 10.037 1.42E-13 501.6676 752.6811

orchestra answered 1 year ago
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