In: Statistics and Probability

Assume you have the following set of job evaluation factors:

A. Educational Requirements

B. Experience

C. Responsibility

D. Mental Effort

E. Physical Effort

F. Working Conditions

G. Work Leadership

A | B | C | D | E | F | G | |

Admin. Secretary I | 4 | 5 | 3 | 2 | 1 | 1 | 1 |

Technician II | 4 | 2 | 1 | 2 | 1 | 2 | 1 |

Engineer I | 5 | 1 | 2 | 3 | 2 | 2 | 1 |

Engineer IV | 6 | 4 | 4 | 5 | 1 | 1 | 3 |

Accounting Leader | 5 | 3 | 5 | 4 | 1 | 1 | 2 |

Consulting Engineer | 7 | 7 | 5 | 6 | 2 | 2 | 3 |

Assume further that you have made an attempt to statistically weigh your grade system by regressing the jobs overall pay grade on the level for each compensable factor with these results.

Dep Var: Job Grade

R-Squared: .9233

Standard error of estimate: .645

64 valid cases

Intercept: -2.54

F: 176.25

Prob: 0.000

Variable | Regression Coefficient | Standardized coefficient | T statistic | T probability |

Educational Requirements | 1.40 | .46 | 9.63 | .0000 |

Experience | .70 | .34 | 4.81 | .0000 |

Responsibility | .14 | .07 | 1.76 | .0838 |

Mental Effort | .09 | .03 | 1.26 | .1824 |

Physical Effort | .48 | .10 | 2.08 | .0416 |

Working Conditions | .46 | .15 | 3.04 | .0036 |

Work Leadership | .40 | .11 | 1.82 | .0721 |

a. based on the printout, does your job evaluation system do a good job of explaining your current grade structure? explain.

b. based on the handouts I gave you, which compensable factors would you keep and which would you drop based on the printout? Explain. Would you ever consider keeping a compensable factor that was not a statistically significant predictor? Explain.

c. if you assume you used all compensable factors, estimate the pay grade for the accounting leader to be sure to include all of your work. If the accounting leader is currently in pay grade 9 what would your conclusions be about actual versus predicted fit?

a.

The p-value (Prob: 0.000) for the significance test of the regression model is less than 0.05 significance level. Thus there is strong evidence that the model is significant and does a good job of explaining your current grade structure.

b.

The statistically significant predictors are the predictors with p-value (T probability) less than 0.05. Similarly, the statistically non-significant predictors are the predictors with p-value (T probability) greater than 0.05.

Thus, compensable factors which are statistically significant predictor in estimating Job Grade and which we keep in the model are Educational Requirements, Experience, Physical Effort and Working Conditions.

The compensable factors which are not statistically significant predictor in estimating Job Grade and which we drop in the model are Responsibility, Mental Effort and Work Leadership.

We can consider keeping a compensable factor that was not a statistically significant predictor as they may explain (although small) variation in the dependent variable Job Grade.

c.

The estimated regression equation is,

Job Grade = 1.40 * Educational Requirements + 0.7 * Experience + 0.14 * Responsibility + 0.09 * Mental Effort + 0.48 * Physical Effort + 0.46 * Working Conditions + 0.4 * Work Leadership

For the accounting leader,

Educational Requirements = 5,

Experience = 3,

Responsibility = 5,

Mental Effort = 4,

Physical Effort = 1,

Working Conditions = 1,

Work Leadership = 2

Job Grade = 1.40 * 5 + 0.7 * 3 + 0.14 * 5 + 0.09 * 4 + 0.48 * 1 + 0.46 * 1 + 0.4 * 2

= 11.9

Actual - predicted fit = 9 - 11.9 = -2.9

We conclude that the actual pay grade for the accounting leader is less than the predicted pay grade.

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