Score: | Week 5 | Correlation and Regression | |||||||||||||||||||||||||

<1 point> | 1. | Create a correlation table for the variables in our data set. (Use analysis ToolPak or StatPlus:mac LE function Correlation.) | |||||||||||||||||||||||||

a. | 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): | |||||||||||||||||||||||||||

c. | 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? | |||||||||||||||||||||||||||

To compa? | |||||||||||||||||||||||||||

d. | 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? | |||||||||||||||||||||||||||

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

<1 point> | 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.) | |||||||||||||||||||||||||||

Plase 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 | Note: technically we have one for each input variable. | ||||||||||||||||||||||||||

Ha: The regression coefficient for each variable is significant | Listing it this way to save space. | ||||||||||||||||||||||||||

Sal | |||||||||||||||||||||||||||

SUMMARY OUTPUT | |||||||||||||||||||||||||||

Regression Statistics | |||||||||||||||||||||||||||

Multiple R | 0.9915591 | ||||||||||||||||||||||||||

R Square | 0.9831894 | ||||||||||||||||||||||||||

Adjusted R Square | 0.9808437 | ||||||||||||||||||||||||||

Standard Error | 2.6575926 | ||||||||||||||||||||||||||

Observations | 50 | ||||||||||||||||||||||||||

ANOVA | |||||||||||||||||||||||||||

df | SS | MS | F | Significance F | |||||||||||||||||||||||

Regression | 6 | 17762.3 | 2960.38 | 419.1516 | 1.812E-36 | ||||||||||||||||||||||

Residual | 43 | 303.7003 | 7.0628 | ||||||||||||||||||||||||

Total | 49 | 18066 | |||||||||||||||||||||||||

Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Lower 95.0% | Upper 95.0% | ||||||||||||||||||||

Intercept | -1.749621 | 3.618368 | -0.4835 | 0.631166 | -9.046755 | 5.5475126 | -9.04675504 | 5.54751262 | |||||||||||||||||||

Midpoint | 1.2167011 | 0.031902 | 38.1383 | 8.66E-35 | 1.1523638 | 1.2810383 | 1.152363828 | 1.28103827 | |||||||||||||||||||

Age | -0.004628 | 0.065197 | -0.071 | 0.943739 | -0.136111 | 0.1268547 | -0.13611072 | 0.1268547 | |||||||||||||||||||

Performace Rating | -0.056596 | 0.034495 | -1.6407 | 0.108153 | -0.126162 | 0.0129695 | -0.12616237 | 0.01296949 | |||||||||||||||||||

Service | -0.0425 | 0.084337 | -0.5039 | 0.616879 | -0.212582 | 0.1275814 | -0.21258209 | 0.12758138 | |||||||||||||||||||

Gender | 2.4203372 | 0.860844 | 2.81159 | 0.007397 | 0.6842792 | 4.1563952 | 0.684279192 | 4.15639523 | |||||||||||||||||||

Degree | 0.2755334 | 0.799802 | 0.3445 | 0.732148 | -1.337422 | 1.8884885 | -1.33742165 | 1.88848848 | |||||||||||||||||||

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: | Intercept | Midpoint | Age | Perf. Rat. | Service | Gender | Degree | ||||||||||||||||||||

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? | Salary = | ||||||||||||||||||||||||||

Is gender a significant factor in salary: | |||||||||||||||||||||||||||

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

How do we know? | |||||||||||||||||||||||||||

<1 point> | 3 | 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. | |||||||||||||||||||||||||||

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: | Intercept | Midpoint | Age | Perf. Rat. | Service | Gender | Degree | ||||||||||||||||||||

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? | Compa = | ||||||||||||||||||||||||||

Is gender a significant factor in compa: | |||||||||||||||||||||||||||

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

How do we know? | |||||||||||||||||||||||||||

<1 point> | 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? | |||||||||||||||||||||||||||

<2 points> | 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? | |||||||||||||||||||||||||||

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