Problem Set Week 5 five Correlation and Regression

Problem Set Week 5 five Correlation and Regression

1.    

Create a correlation table for the variables in our data set. (Use analysis ToolPak or StatPlus:mac LE function Correlation.)

Reviewing the data levels from week 1, what variables can be used in a Pearson's Correlation table (which is what Excel produces)?

b. Place table here (C8):

Using r = approximately .28 as the signicant r value (at p = 0.05) for a correlation between 50 values, what variables are significantly related to Salary?

Looking at the above correlations - both significant or not - are there any surprises -by that I mean any relationships you expected to be meaningful and are not and vice-versa?

Does this help us answer our equal pay for equal work question?

2

Below is a regression analysis for salary being predicted/explained by the other variables in our sample (Midpoint, age, performance rating, service,  gender, and degree variables. (Note: since salary and compa are different ways of expressing an employee’s salary, we do not want to have both used in the same regression.)

Please interpret the findings.

Ho: The regression equation is not significant.

Ha: The regression equation is significant.

Ho: The regression coefficient for each variable is not significant

Ha: The regression coefficient for each variable is significant

Note: technically we have one for each input variable.

Listing it this way to save space.

SUMMARY OUTPUT

Regression Statistics

Multiple R

0.991559075

R Square

0.983189399

Adjusted R Square

0.980843733

Standard Error

2.657592573

Observations

50

ANOVA

df

SS

MS

F

Significance F

Regression

6

17762.3

2960.383

419.15161

1.8122E-36

Residual

43

303.70033

7.062798

Total

49

18066

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Lower 95.0%

Upper 95.0%

Intercept

-1.74962121

3.6183677

-0.48354

0.6311665

-9.046755

5.54751262

-9.046755043

5.547512618

Midpoint

1.216701051

0.0319024

38.13829

8.664E-35

1.15236383

1.28103827

1.152363828

1.281038273

Age

-0.00462801

0.0651972

-0.07098

0.943739

-0.1361107

0.1268547

-0.136110719

0.126854699

Performace Rating

-0.05659644

0.0344951

-1.64071

0.1081532

-0.1261624

0.01296949

-0.126162375

0.012969494

Service

-0.04250036

0.084337

-0.50394

0.6168794

-0.2125821

0.12758138

-0.212582091

0.127581377

Gender

2.420337212

0.8608443

2.811585

0.0073966

0.68427919

4.15639523

0.684279192

4.156395232

Degree

0.275533414

0.7998023

0.344502

0.7321481

-1.3374217

1.88848848

-1.337421655

1.888488483

Note: since Gender and Degree are expressed as 0 and 1, they are considered dummy variables and can be used in a multiple regression equation.

Interpretation:

For the Regression as a whole:

What is the value of the F statistic:

What is the p-value associated with this value:

Is the p-value <0.05?

Do you reject or not reject the null hypothesis:

What does this decision mean for our equal pay question:

For each of the coefficients:

What is the coefficient's p-value for each of the variables:

Is the p-value < 0.05?

Do you reject or not reject each null hypothesis:

What are the coefficients for the significant variables?

Using only the significant variables, what is the equation?

Is gender a significant factor in salary:

If so, who gets paid more with all other things being equal?

How do we know?

Perform a regression analysis using compa as the dependent variable and the same independent

variables as used in question 2.  Show the result, and interpret your findings by answering the same questions.

Note: be sure to include the appropriate hypothesis statements.

Regression hypotheses

Ho:

Ha:

Coefficient hyhpotheses (one to stand for all the separate variables)

Ho:

Ha:

Place D94 in output box.

What is the value of the F statistic:

What is the p-value associated with this value:

Is the p-value < 0.05?

Do you reject or not reject the null hypothesis:

What does this decision mean for our equal pay question:

What is the coefficient's p-value for each of the variables:

Is the p-value < 0.05?

Do you reject or not reject each null hypothesis:

What are the coefficients for the significant variables?

Using only the significant variables, what is the equation?

Is gender a significant factor in compa:

If so, who gets paid more with all other things being equal?

How do we know?

4.

Based on all of your results to date,

Do we have an answer to the question of are males and females paid equally for equal work?

If so, which gender gets paid more?

How do we know?

Which is the best variable to use in analyzing pay practices - salary or compa?  Why?

What is most interesting or surprising about the results we got doing the analysis during the last 5 weeks?

5

Why did the single factor tests and analysis (such as t and single factor ANOVA tests on salary equality) not provide a complete answer to our salary equality question?

What outcomes in your life or work might benefit from a multiple regression examination rather than a simpler one variable test?