Human Resources Management:

The ABX Company is interested in conducting a study of the factors that affect absenteeism among its production employees. Data on 77 employees of the ABX Company have been collected. The variable ABSENT is the number of distinct occasions that the worker was absent during 2018. (Each occasion consists of one or more consecutive days of absence.) The following possible explanatory variables are:

However, there is evidence to suggest that an inverse relationship exists between ABSENT and SENIOR. Therefore, use the reciprocal of SENIOR in the model. Furthermore, the variable SATIS has five categories (coded 1 = Very Dissatisfied (VD), 2 = Somewhat Dissatisfied (SD), 3 = Neutral (N), 4 = Somewhat Satisfied (SS), 5 = Very Satisfied (VS)). Recode the SATIS variable for regression analysis such that “Very Satisfied” serves as the reference level. These data are available in the worksheet entitled “ABSENT7R”.

(a) State the model equation.

[A] ABSENT = 𝛽₀ + 𝛽₁COMPLX + 𝛽₂SENIOR + 𝛽₃SATIS

[B] ABSENT = 𝛽₀ + 𝛽₁COMPLX + 𝛽₂( 1 / SENIOR) + 𝛽₃VD + 𝛽₄SD + 𝛽₅N + 𝛽₆SS + 𝛽₆VS

[C] ABSENT = ABSENT = 𝛽₀ + 𝛽₁COMPLX + 𝛽₂( 1 / SENIOR) + 𝛽₃SATIS

[D] ABSENT = 𝛽₀ + 𝛽₁COMPLX + 𝛽₂SENIOR + 𝛽₃VD + 𝛽₄SD + 𝛽₅N + 𝛽₆SS

[E] ABSENT = 𝛽₀ + 𝛽₁COMPLX + 𝛽₂( 1 / SENIOR) + 𝛽₃VD + 𝛽₄SD + 𝛽₅N + 𝛽₆SS

[F] ABSENT = 𝛽₀ + 𝛽₁COMPLX + 𝛽₂SENIOR + 𝛽₃VD + 𝛽₄SD + 𝛽₅N + 𝛽₆SS + 𝛽₆VS

Run the regression with the explanatory variables described here. Answer the following questions.

(b) Is there a difference in average absenteeism for employees in different supervisor satisfaction groups? Perform a hypothesis test to answer this question. Use a 5% level of significance.

State the hypotheses to be tested.

[A] H₀: 𝛽₃ = 𝛽₄ = 𝛽₅ = 𝛽₆ = 0
H_a: At least one of the coefficients is not equal to 0.

[B] H₀: None of the coefficients are equal to 0.
H_a: 𝛽₃ = 𝛽₄ = 𝛽₅ = 𝛽₆ = 0

[C] H₀: 𝛽₃ = 𝛽₄ = 𝛽₅ = 𝛽₆ = 0
H_a: None of the coefficients are equal to 0.

[D] H₀: At least one of the coefficients is not equal to 0.
H_a: 𝛽₃ = 𝛽₄ = 𝛽₅ = 𝛽₆ = 0

Interpret the hypotheses you specified above.

[A]H₀: At least one explanatory variable is important in explaining/predicting absenteeism.
H_a: None of the explanatory variables are important in explaining/predicting absenteeism.

[B] H₀: None of the explanatory variables are important in explaining/predicting absenteeism.
H_a: All of the explanatory variables are important in explaining/predicting absenteeism.

[C] H₀: There is no significant difference in absenteeism among the different satisfaction groups after accounting for job complexity and seniority.
H_a: There is a significant difference in absenteeism among the different satisfaction groups after accounting for job complexity and seniority.H₀: There is a significant difference in absenteeism among the different satisfaction groups after accounting for job complexity and seniority.

[D] H_a: There is no significant difference in absenteeism among the different satisfaction groups after accounting for job complexity and seniority.H₀: None of the explanatory variables are important in explaining/predicting absenteeism.
H_a: At least one explanatory variable is important in explaining/predicting absenteeism.

State the decision rule.

[A] Reject H₀ if p < 0.025.
Do not reject H₀ if p ≥ 0.025.

[B] Reject H₀ if p > 0.025.
Do not reject H₀ if p ≤ 0.025.

[C] Reject H₀ if p < 0.05.
Do not reject H₀ if p ≥ 0.05.

[D] Reject H₀ if p > 0.05.
Do not reject H₀ if p ≤ 0.05.