December 3, 2022

What does regression analysis show us about analyzing complex measures?

Business

ID Salary Compa Midpoint Age Performance Rating Service Gender Raise Degree Gender1 Grade

1 60.2 1.056 57 34 85 8 0 5.7 0 M E

2 27.7 0.893 31 52 80 7 0 3.9 0 M B

3 35.5 1.145 31 30 75 5 1 3.6 1 F B

4 56.1 0.985 57 42 100 16 0 5.5 1 M E

5 48.9 1.018 48 36 90 16 0 5.7 1 M D

6 74.1 1.106 67 36 70 12 0 4.5 1 M F

Do not manipuilate Data set on this page, copy to another page to make changes

The ongoing question that the weekly assignments will focus on is: Are males and females paid the same for equal work (under the Equal Pay Act)?

Note: to simplfy the analysis, we will assume that jobs within each grade comprise equal work.

The column labels in the table mean:

ID – Employee sample number Salary – Salary in thousands

Age – Age in years Performance Rating – Appraisal rating (employee evaluation score)

Service – Years of service (rounded) Gender – 0 = male, 1 = female

Midpoint – salary grade midpoint Raise – percent of last raise

Grade – job/pay grade Degree (0= BSBA 1 = MS)

Gender1 (Male or Female) Compa-ratio – salary divided by midpoint

Week 4: Identifying relationships – correlations and regression

To Ensure full credit for each question, you need to show how you got your results. This involves either showing where the data you used is located

or showing the excel formula in each cell. Be sure to copy the appropriate data columns from the data tab to the right for your use this week.

1 What is the correlation between and among the interval/ratio level variables with salary? (Do not include compa-ratio in this question.)

a. Create the correlation table. Use Cell K08 for the Excel test outcome location.

i. What is the data input ranged used for this question:

ii. Create a correlation table in cell K08.

b. Technically, we should perform a hypothesis testing on each correlation to determine

if it is significant or not. However, we can be faithful to the process and save some

time by finding the minimum correlation that would result in a two tail rejection of the null.

We can then compare each correlation to this value, and those exceeding it (in either a

positive or negative direction) can be considered statistically significant.

i. What is the t-value we would use to cut off the two tails? T = ii. What is the associated correlation value related to this t-value? r = c. What variable(s) is(are) significantly correlated to salary?

d. Are there any surprises – correlations you though would be significant and are not, or non significant correlations you thought would be?

e. Why does or does not this information help answer our equal pay question?

2 Perform a regression analysis using salary as the dependent variable and all of the variables used in Q1. Add the

two dummy variables – gender and education – to your list of independent variables. Show the result, and interpret your findings by answering the following questions.

Suggestion: Add the dummy variables values to the right of the last data columns used for Q1.

What is the multiple regression equation predicting/explaining salary using all of our possible variables except compa-ratio?

a. What is the data input ranged used for this question:

b. Step 1: State the appropriate hypothesis statements: Use Cell M34 for the Excel test outcome location.

Ho:

What is your conclusion about the factors influencing the population salary values?

c. If we rejected the null hypothesis, we need to test the significance of each of the variable coefficients. Step 1: State the appropriate coefficient hypothesis statements: (Write a single pair, we will use it for each variable separately.)

Ho:

Ha:

d. Is gender a significant factor in salary?

e. Regardless of statistical significance, who gets paid more with all other things being equal? f. How do we know?

3 After considering the compa-ratio based results in the lectures and your salary based results, what else would you like to know before answering our question on equal pay? Why?

4 Between the lecture results and your results, what is your answer to the question