In: Math

Absenteeism is a major problem for some companies and in some industries. Suppose a study was conducted on absenteeism in the warehousing industry. Observations on several variables that might be related to absenteeism were collected on 35 major warehouses in the Pacific Northwest.

Absent: The average number of absences per employee for the year (does not include vacation days or confirmed sick days)

Wage: The average annual wage paid to the warehouse employees (does not include manager salaries)

Pct U: Union membership. The percentage of employees who belong to a union at the warehouse.

Good R: 1 if the employee group self-reported a “good” relationship with management; 0 if the employee group self-reported otherwise.

Perform a complete
multiple regression analysis to find a model that might be useful
for predicting the average number of absences per employee for the
year. Perform ALL steps as outlined in class. **Use Minitab
and show all your work.** Use alpha = .10 for any required
tests (and show all steps for any required test). STAPLE MULTIPLE
PAGES and include all required computer output.

Absent | Wage | Pct U | Good R |

5.4 | 42000 | 57.1 | 1 |

4.1 | 39350 | 41.5 | 1 |

11.5 | 31000 | 52.6 | 0 |

2.1 | 28000 | 65.1 | 0 |

5.9 | 30000 | 68.8 | 1 |

12.9 | 28000 | 46.4 | 0 |

3.5 | 40000 | 38.9 | 1 |

2.6 | 35820 | 17.2 | 1 |

8.6 | 29500 | 12.9 | 0 |

2.7 | 29500 | 18.1 | 0 |

6.6 | 36500 | 64.4 | 1 |

2.1 | 39600 | 63.7 | 1 |

3.8 | 31200 | 12.2 | 1 |

4.3 | 32000 | 11.8 | 0 |

4.3 | 29600 | 25.8 | 0 |

2.2 | 37560 | 53.2 | 1 |

8.6 | 32000 | 22.8 | 0 |

10.8 | 22980 | 49.8 | 0 |

2.9 | 32000 | 39.1 | 0 |

5.3 | 42320 | 32.6 | 1 |

8.2 | 29500 | 67.7 | 0 |

2.8 | 36500 | 10.8 | 1 |

2.4 | 37970 | 25.5 | 1 |

2.8 | 35180 | 31.8 | 1 |

5 | 29630 | 35 | 0 |

9.5 | 39800 | 41.9 | 1 |

4.3 | 41000 | 52.9 | 1 |

8.9 | 32890 | 64.4 | 0 |

7.2 | 27500 | 69.7 | 0 |

5.6 | 27500 | 61.8 | 1 |

2.4 | 40826 | 52.1 | 1 |

2.7 | 31970 | 57.4 | 0 |

13.4 | 29990 | 15.2 | 0 |

14.8 | 31450 | 38.7 | 0 |

10.7 | 36900 | 69.4 | 1 |

Regression Analysis: Absent versus Wage, Pct U, Good R

Analysis of Variance

Source DF Adj SS Adj
MS F-Value P-Value

Regression 3 91.837
30.612 2.61 0.069

Wage 1
2.264 2.264
0.19 0.664

Pct U 1
8.673 8.673
0.74 0.397

Good R 1 24.989
24.989 2.13 0.155

Error 31 363.750 11.734

Total 34 455.587

Model Summary

S R-sq
R-sq(adj) R-sq(pred)

3.42547 20.16%
12.43% 3.16%

Coefficients

Term
Coef SE Coef T-Value P-Value VIF

Constant
8.82 5.55
1.59 0.122

Wage -0.000077
0.000176 -0.44 0.664 2.25

Pct U
0.0260 0.0303
0.86 0.397 1.01

Good R
-2.55 1.75
-1.46 0.155 2.27

Regression Equation

Absent = 8.82 - 0.000077 Wage + 0.0260 Pct U - 2.55 Good R

Fits and Diagnostics for Unusual Observations

Std

Obs Absent Fit Resid Resid

33 13.40 6.91 6.49 2.01 R

34 14.80 7.41 7.39 2.23 R

R Large residual

Regression Equation

**Absent = 8.82 - 0.000077 Wage + 0.0260 Pct U - 2.55 Good
R**

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