bus 308 week4 and 5

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Week 5

W 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 0.9915590747
R Square 0.9831893985
Adjusted R Square 0.9808437332
Standard Error 2.6575925726
Observations 50
ANOVA
df SS MS F Significance F
Regression 6 17762.2996738743 2960.383278979 419.1516111294 1.8121523852609E-36
Residual 43 303.7003261257 7.062798282
Total 49 18066
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept -1.7496212123 3.6183676583 -0.4835388157 0.6311664899 -9.0467550427 5.547512618 -9.0467550427 5.547512618
Midpoint 1.2167010505 0.0319023509 38.1382881163 8.66416336978111E-35 1.1523638283 1.2810382727 1.1523638283 1.2810382727
Age -0.0046280102 0.065197212 -0.0709847876 0.9437389875 -0.1361107191 0.1268546987 -0.1361107191 0.1268546987
Performace Rating -0.0565964405 0.0344950678 -1.6407110971 0.1081531819 -0.1261623747 0.0129694936 -0.1261623747 0.0129694936
Service -0.0425003573 0.0843369821 -0.5039350033 0.6168793519 -0.2125820912 0.1275813765 -0.2125820912 0.1275813765
Gender 2.420337212 0.8608443176 2.8115852804 0.0073966188 0.684279192 4.156395232 0.684279192 4.156395232
Degree 0.2755334143 0.7998023048 0.3445019009 0.732148119 -1.3374216547 1.8884884833 -1.3374216547 1.8884884833
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?

Data Set

See comments at the right of the data set.
ID Salary Compa Midpoint Age Performance Rating Service Gender Raise Degree Gender1 Grade 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)?
8 23 1.000 23 32 90 9 1 5.8 0 F A Note: to simplfy the analysis, we will assume that jobs within each grade comprise equal work.
10 22 0.956 23 30 80 7 1 4.7 0 F A
11 23 1.000 23 41 100 19 1 4.8 0 F A The column labels in the table mean:
14 24 1.043 23 32 90 12 1 6 0 F A ID – Employee sample number Salary – Salary in thousands
15 24 1.043 23 32 80 8 1 4.9 0 F A Age – Age in years Performance Rating – Appraisal rating (Employee evaluation score)
23 23 1.000 23 36 65 6 1 3.3 1 F A Service – Years of service (rounded) Gender: 0 = male, 1 = female
26 24 1.043 23 22 95 2 1 6.2 1 F A Midpoint – salary grade midpoint Raise – percent of last raise
31 24 1.043 23 29 60 4 1 3.9 0 F A Grade – job/pay grade Degree (0= BS\BA 1 = MS)
35 24 1.043 23 23 90 4 1 5.3 1 F A Gender1 (Male or Female) Compa - salary divided by midpoint
36 23 1.000 23 27 75 3 1 4.3 1 F A
37 22 0.956 23 22 95 2 1 6.2 1 F A
42 24 1.043 23 32 100 8 1 5.7 0 F A
3 34 1.096 31 30 75 5 1 3.6 0 F B
18 36 1.161 31 31 80 11 1 5.6 1 F B
20 34 1.096 31 44 70 16 1 4.8 1 F B
39 35 1.129 31 27 90 6 1 5.5 1 F B
7 41 1.025 40 32 100 8 1 5.7 0 F C
13 42 1.050 40 30 100 2 1 4.7 1 F C
22 57 1.187 48 48 65 6 1 3.8 0 F D
24 50 1.041 48 30 75 9 1 3.8 1 F D
45 55 1.145 48 36 95 8 1 5.2 0 F D
17 69 1.210 57 27 55 3 1 3 0 F E
48 65 1.140 57 34 90 11 1 5.3 1 F E
28 75 1.119 67 44 95 9 1 4.4 1 F F
43 77 1.149 67 42 95 20 1 5.5 1 F F
19 24 1.043 23 32 85 1 0 4.6 1 M A
25 24 1.043 23 41 70 4 0 4 0 M A
40 25 1.086 23 24 90 2 0 6.3 0 M A
2 27 0.870 31 52 80 7 0 3.9 0 M B
32 28 0.903 31 25 95 4 0 5.6 0 M B
34 28 0.903 31 26 80 2 0 4.9 1 M B
16 47 1.175 40 44 90 4 0 5.7 0 M C
27 40 1.000 40 35 80 7 0 3.9 1 M C
41 43 1.075 40 25 80 5 0 4.3 0 M C
5 47 0.979 48 36 90 16 0 5.7 1 M D
30 49 1.020 48 45 90 18 0 4.3 0 M D
1 58 1.017 57 34 85 8 0 5.7 0 M E
4 66 1.157 57 42 100 16 0 5.5 1 M E
12 60 1.052 57 52 95 22 0 4.5 0 M E
33 64 1.122 57 35 90 9 0 5.5 1 M E
38 56 0.982 57 45 95 11 0 4.5 0 M E
44 60 1.052 57 45 90 16 0 5.2 1 M E
46 65 1.140 57 39 75 20 0 3.9 1 M E
47 62 1.087 57 37 95 5 0 5.5 1 M E
49 60 1.052 57 41 95 21 0 6.6 0 M E
50 66 1.157 57 38 80 12 0 4.6 0 M E
6 76 1.134 67 36 70 12 0 4.5 1 M F
9 77 1.149 67 49 100 10 0 4 1 M F
21 76 1.134 67 43 95 13 0 6.3 1 M F
29 72 1.074 67 52 95 5 0 5.4 0 M F
Mean 45 1.06248 41.76 35.72 85.9 8.96 0.5 4.938 0.5 ERROR:#DIV/0! ERROR:#DIV/0!
StdDVA 19.20140301 0.0768250703 16.231186912 8.2512584074 11.4147237534 5.7177132578 0.5050762723 0.8672946443 0.5050762723 0 0
Max 77 1.21 67 52 100 22 1 6.6 1 0 0
Min 22 0.87 23 22 55 1 0 3 0 0 0
Diff 55 0.34 44 30 45 21 1 3.6 1 0 0
Male Mean 52 1.05624 48.64 38.92 87.6 10
StdDVA 17.7763888346 0.0837890605 14.6880904137 8.3860996099 8.6746757864 6.3574103743
Max 77 1.175 67 52 100 22
Min 24 0.87 23 24 70 1
Range 53 0.305 44 28 30 21
Female Mean 38 1.06872 34.88 32.52 84.2 7.92
StdDVA 18.2938969787 0.0703446989 14.9508082279 6.8806491942 13.5922772191 4.9067980055
Max 77 1.21 67 48 100 20
Min 22 0.956 23 22 55 2
Range 55 0.254 44 26 45 18

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