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 sometime 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 the variables used in Q1 along with your two dummy variables - gender and education.  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:

Ha:

Step 2: Significance (Alpha):

Step 3: Test Statistic and test:

Why this test?

Step 4: Decision rule:

Step 5: Conduct the test - place test function in cell M34

Step 6: Conclusion and Interpretation

What is the p-value:

What is your decision: REJ or NOT reject the null?

Why?

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:

Step 2: Significance (Alpha):

Step 3: Test Statistic and test:

Why this test?

Step 4: Decision rule:

Step 5: Conduct the test

Note, in this case the test has been performed and is part of the Regression output above.

Step 6: Conclusion and Interpretation

Place the t and p-values in the following table

Identify your decision on rejecting the null for each variable.  If you reject the null, place the coefficient in the table.

Midpoint Age Perf. Rat. Seniority Raise Gender Degree

t-value:

P-value:

Rejection Decision:

If Null is rejected, what is the variable's coefficient value?

Using the intercept coefficient and only the significant variables, what is the equation?

Salary = 

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 of equal pay for equal work for males and females?  Why?

5 What does regression analysis show us about analyzing complex measures?