managerial statistics

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Data

ID Salary Compa Midpoint Age Performance Rating Service Gender Raise Degree Gender1 Gr
1 64.4 1.130 57 34 85 8 0 5.7 0 M E 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)?
2 27.4 0.884 31 52 80 7 0 3.9 0 M B Note: to simplfy the analysis, we will assume that jobs within each grade comprise equal work.
3 35.6 1.148 31 30 75 5 1 3.6 1 F B
4 62.3 1.093 57 42 100 16 0 5.5 1 M E The column labels in the table mean:
5 48.7 1.014 48 36 90 16 0 5.7 1 M D ID – Employee sample number Salary – Salary in thousands
6 75 1.120 67 36 70 12 0 4.5 1 M F Age – Age in years Performance Rating - Appraisal rating (employee evaluation score)
7 41.8 1.046 40 32 100 8 1 5.7 1 F C Service – Years of service (rounded) Gender – 0 = male, 1 = female
8 23.7 1.029 23 32 90 9 1 5.8 1 F A Midpoint – salary grade midpoint Raise – percent of last raise
9 76.8 1.147 67 49 100 10 0 4 1 M F Grade – job/pay grade Degree (0= BS\BA 1 = MS)
10 24 1.044 23 30 80 7 1 4.7 1 F A Gender1 (Male or Female) Compa - salary divided by midpoint
11 23.9 1.041 23 41 100 19 1 4.8 1 F A
12 62.5 1.096 57 52 95 22 0 4.5 0 M E
13 42.7 1.067 40 30 100 2 1 4.7 0 F C
14 23.4 1.016 23 32 90 12 1 6 1 F A
15 23.3 1.012 23 32 80 8 1 4.9 1 F A
16 48.7 1.217 40 44 90 4 0 5.7 0 M C
17 65.1 1.142 57 27 55 3 1 3 1 F E
18 34.6 1.116 31 31 80 11 1 5.6 0 F B
19 24.5 1.065 23 32 85 1 0 4.6 1 M A
20 34.9 1.125 31 44 70 16 1 4.8 0 F B
21 76.5 1.142 67 43 95 13 0 6.3 1 M F
22 57.8 1.204 48 48 65 6 1 3.8 1 F D
23 22.7 0.987 23 36 65 6 1 3.3 0 F A
24 56.5 1.177 48 30 75 9 1 3.8 0 F D
25 24.5 1.064 23 41 70 4 0 4 0 M A
26 23.2 1.010 23 22 95 2 1 6.2 0 F A
27 46.8 1.171 40 35 80 7 0 3.9 1 M C
28 76.6 1.144 67 44 95 9 1 4.4 0 F F
29 75.9 1.133 67 52 95 5 0 5.4 0 M F
30 47.4 0.987 48 45 90 18 0 4.3 0 M D
31 25.3 1.101 23 29 60 4 1 3.9 1 F A
32 27.2 0.878 31 25 95 4 0 5.6 0 M B
33 66 1.158 57 35 90 9 0 5.5 1 M E
34 28.1 0.907 31 26 80 2 0 4.9 1 M B
35 22.5 0.980 23 23 90 4 1 5.3 0 F A
36 22.7 0.985 23 27 75 3 1 4.3 0 F A
37 23.4 1.017 23 22 95 2 1 6.2 0 F A
38 58.5 1.026 57 45 95 11 0 4.5 0 M E
39 35.5 1.144 31 27 90 6 1 5.5 0 F B
40 24.8 1.078 23 24 90 2 0 6.3 0 M A
41 45.8 1.144 40 25 80 5 0 4.3 0 M C
42 22.2 0.965 23 32 100 8 1 5.7 1 F A
43 77.4 1.155 67 42 95 20 1 5.5 0 F F
44 58.8 1.032 57 45 90 16 0 5.2 1 M E
45 51.2 1.066 48 36 95 8 1 5.2 1 F D
46 61.3 1.076 57 39 75 20 0 3.9 1 M E
47 64.3 1.128 57 37 95 5 0 5.5 1 M E
48 67.6 1.186 57 34 90 11 1 5.3 1 F E
49 61.3 1.075 57 41 95 21 0 6.6 0 M E
50 66.1 1.159 57 38 80 12 0 4.6 0 M E

Sheet1

Sal Compa G Mid Age EES SR G Raise Deg SUMMARY OUTPUT SUMMARY OUTPUT
24 1.045 1 23 32 90 9 1 5.8 1
24.2 1.053 1 23 30 80 7 1 4.7 1 Regression Statistics Regression Statistics
23.4 1.018 1 23 41 100 19 1 4.8 1 Multiple R 0.7050179484 Multiple R 0.9931286935
23.4 1.017 1 23 32 90 12 1 6 1 R Square 0.4970503076 R Square 0.9863046018
22.6 0.983 1 23 32 80 8 1 4.9 1 Adjusted R Square 0.4132253589 Adjusted R Square 0.9840220355
22.9 0.995 1 23 36 65 6 1 3.3 0 Standard Error 0.0561252686 Standard Error 2.4352822665
23.1 1.003 1 23 22 95 2 1 6.2 0 Observations 50 Observations 50
23.3 1.011 1 23 29 60 4 1 3.9 1
22.7 0.985 1 23 23 90 4 1 5.3 0 ANOVA ANOVA
23.5 1.023 1 23 27 75 3 1 4.3 0 df SS MS F Significance F df SS MS F Significance F
23 1.002 1 23 22 95 2 1 6.2 0 Regression 7 0.1307500775 0.0186785825 5.9296225662 0.0000782906 Regression 7 17938.424611863 2562.632087409 432.1033638177 5.29906273684337E-37
24 1.042 1 23 32 100 8 1 5.7 1 Residual 42 0.1323019225 0.0031500458 Residual 42 249.085188137 5.9305997175
35.5 1.145 1 31 30 75 5 1 3.6 1 Total 49 0.263052 Total 49 18187.5098
34.7 1.119 1 31 31 80 11 1 5.6 0
35.5 1.146 1 31 44 70 16 1 4.8 0 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
35.2 1.136 1 31 27 90 6 1 5.5 0 Intercept 0.9486238772 0.0817167716 11.6086803119 0 0.7837127557 1.1135349987 0.7837127557 1.1135349987 Intercept -4.8714544587 3.54570071 -1.3739045839 0.1767599037 -12.0269681853 2.2840592678 -12.0269681853 2.2840592678
40.4 1.01 1 40 32 100 8 1 5.7 1 Mid 0.0034995027 0.0006492568 5.3900133356 0.0000029767 0.0021892495 0.0048097559 0.0021892495 0.0048097559 Mid 1.2284155048 0.0281713308 43.6051641629 1.32019333894083E-36 1.1715634576 1.2852675521 1.1715634576 1.2852675521
42.7 1.068 1 40 30 100 2 1 4.7 0 Age 0.0005527738 0.0014459446 0.3822925256 0.7041721007 -0.0023652605 0.0034708081 -0.0023652605 0.0034708081 Age 0.0368279425 0.0627397124 0.5869957178 0.5603489282 -0.0897859231 0.1634418081 -0.0897859231 0.1634418081
53.4 1.112 1 48 48 65 6 1 3.8 1 EES -0.0018462553 0.0010252155 -1.8008461371 0.0789105539 -0.0039152239 0.0002227133 -0.0039152239 0.0002227133 EES -0.0821579785 0.0444842245 -1.8469014451 0.0718147225 -0.171930778 0.007614821 -0.171930778 0.007614821
51.5 1.072 1 48 30 75 9 1 3.8 0 SR -0.0004182288 0.0018278101 -0.2288141345 0.820123898 -0.004106899 0.0032704414 -0.004106899 0.0032704414 SR -0.0778484529 0.079308905 -0.9815852701 0.3319249969 -0.2379003029 0.0822033971 -0.2379003029 0.0822033971
49.8 1.037 1 48 36 95 8 1 5.2 1 G 0.0646649961 0.0183396697 3.5259629624 0.001034866 0.0276540443 0.101675948 0.0276540443 0.101675948 G 2.9145083112 0.7957605113 3.6625445343 0.000693549 1.3085985836 4.5204180389 1.3085985836 4.5204180389
68.3 1.198 1 57 27 55 3 1 3 1 Raise 0.0146549564 0.0139088976 1.0536389608 0.2980722322 -0.0134143354 0.0427242483 -0.0134143354 0.0427242483 Raise 0.6763294824 0.6035087689 1.1206622295 0.2687988764 -0.5416005215 1.8942594864 -0.5416005215 1.8942594864
65.4 1.148 1 57 34 90 11 1 5.3 1 Deg 0.0014675988 0.0161098249 0.0910996125 0.9278465471 -0.0310433441 0.0339785418 -0.0310433441 0.0339785418 Deg 0.0345044482 0.6990072742 0.0493620731 0.9608647532 -1.3761493419 1.4451582383 -1.3761493419 1.4451582383
78.4 1.17 1 67 44 95 9 1 4.4 0
75.9 1.133 1 67 42 95 20 1 5.5 0
24 1.044 0 23 32 85 1 0 4.6 1
23.3 1.012 0 23 41 70 4 0 4 0
24.1 1.049 0 23 24 90 2 0 6.3 0
27.5 0.887 0 31 52 80 7 0 3.9 0 t-Test: Two-Sample Assuming Equal Variances
27.1 0.875 0 31 25 95 4 0 5.6 0
27.7 0.895 0 31 26 80 2 0 4.9 1 Variable 1 Variable 2
40.8 1.019 0 40 44 90 4 0 5.7 0 Mean 1.06684 1.04836
43.9 1.097 0 40 35 80 7 0 3.9 1 Variance 0.00430164 0.00648099
41 1.025 0 40 25 80 5 0 4.3 0 Observations 25 25
48.7 1.014 0 48 36 90 16 0 5.7 1 Pooled Variance 0.005391315
49.4 1.029 0 48 45 90 18 0 4.3 0 Hypothesized Mean Difference 0
64.4 1.13 0 57 34 85 8 0 5.7 0 df 48
64.5 1.132 0 57 42 100 16 0 5.5 1 t Stat 0.8898352784
58.9 1.033 0 57 52 95 22 0 4.5 0 P(T<=t) one-tail 0.188996287
57.9 1.016 0 57 35 90 9 0 5.5 1 t Critical one-tail 1.6772241961
59 1.035 0 57 45 95 11 0 4.5 0 P(T<=t) two-tail 0.3779925741
63.3 1.111 0 57 45 90 16 0 5.2 1 t Critical two-tail 2.0106347576
56.8 0.996 0 57 39 75 20 0 3.9 1
58 1.017 0 57 37 95 5 0 5.5 1
62.4 1.094 0 57 41 95 21 0 6.6 0
63.8 1.12 0 57 38 80 12 0 4.6 0
79 1.179 0 67 36 70 12 0 4.5 1
77 1.149 0 67 49 100 10 0 4 1
74.8 1.116 0 67 43 95 13 0 6.3 1
76 1.135 0 67 52 95 5 0 5.4 0

questions

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 0.991559075
R Square 0.983189399
Adjusted R Square 0.980843733
Standard Error 2.657592573
Observations 50
ANOVA
df SS MS F Significance F
Regression 6 17762.29967 2960.383279 419.1516111 1.81215E-36
Residual 43 303.7003261 7.062798282
Total 49 18066
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept -1.749621212 3.618367658 -0.483538816 0.63116649 -9.046755043 5.547512618 -9.046755043 5.547512618
Midpoint 1.216701051 0.031902351 38.13828812 8.66416E-35 1.152363828 1.281038273 1.152363828 1.281038273
Age -0.00462801 0.065197212 -0.070984788 0.943738987 -0.136110719 0.126854699 -0.136110719 0.126854699
Performace Rating -0.056596441 0.034495068 -1.640711097 0.108153182 -0.126162375 0.012969494 -0.126162375 0.012969494
Service -0.042500357 0.084336982 -0.503935003 0.616879352 -0.212582091 0.127581377 -0.212582091 0.127581377
Gender 2.420337212 0.860844318 2.81158528 0.007396619 0.684279192 4.156395232 0.684279192 4.156395232
Degree 0.275533414 0.799802305 0.344501901 0.732148119 -1.337421655 1.888488483 -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: 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?