BUS308 Statistics for Managers – Week 5

Paper details:
Complete the problems included in the resources below and submit your work in an Excel document. Be sure to show all of your work and clearly label all calculations. All statistical calculations will use the Employee Salary Data Set and the Week 5 assignment sheet.

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?
See comments at the right of the data set.
ID    Salary    Compa    Midpoint    Age    Performance Rating    Service    Gender    Raise    Degree    Gender1    Grade
8    23    1.000    23    32    90    9    1    5.8    0    F    A        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)?
10    22    0.956    23    30    80    7    1    4.7    0    F    A        Note: to simplfy the analysis, we will assume that jobs within each grade comprise equal work.
11    23    1.000    23    41    100    19    1    4.8    0    F    A
14    24    1.043    23    32    90    12    1    6    0    F    A        The column labels in the  table mean:
15    24    1.043    23    32    80    8    1    4.9    0    F    A        ID – Employee sample number             Salary – Salary in thousands
23    23    1.000    23    36    65    6    1    3.3    1    F    A        Age – Age in years            Performance Rating  – Appraisal rating (Employee evaluation score)
26    24    1.043    23    22    95    2    1    6.2    1    F    A        Service – Years of service (rounded)            Gender:   0 = male, 1 = female
31    24    1.043    23    29    60    4    1    3.9    0    F    A        Midpoint – salary grade midpoint                Raise – percent of last raise
35    24    1.043    23    23    90    4    1    5.3    1    F    A        Grade – job/pay grade            Degree (0= BSBA 1 = MS)
36    23    1.000    23    27    75    3    1    4.3    1    F    A        Gender1 (Male or Female)            Compa – salary divided by midpoint
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

BUS308 Statistics for Managers – Week 5

Paper details:
Complete the problems included in the resources below and submit your work in an Excel document. Be sure to show all of your work and clearly label all calculations. All statistical calculations will use the Employee Salary Data Set and the Week 5 assignment sheet.

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?
See comments at the right of the data set.
ID    Salary    Compa    Midpoint    Age    Performance Rating    Service    Gender    Raise    Degree    Gender1    Grade
8    23    1.000    23    32    90    9    1    5.8    0    F    A        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)?
10    22    0.956    23    30    80    7    1    4.7    0    F    A        Note: to simplfy the analysis, we will assume that jobs within each grade comprise equal work.
11    23    1.000    23    41    100    19    1    4.8    0    F    A
14    24    1.043    23    32    90    12    1    6    0    F    A        The column labels in the  table mean:
15    24    1.043    23    32    80    8    1    4.9    0    F    A        ID – Employee sample number             Salary – Salary in thousands
23    23    1.000    23    36    65    6    1    3.3    1    F    A        Age – Age in years            Performance Rating  – Appraisal rating (Employee evaluation score)
26    24    1.043    23    22    95    2    1    6.2    1    F    A        Service – Years of service (rounded)            Gender:   0 = male, 1 = female
31    24    1.043    23    29    60    4    1    3.9    0    F    A        Midpoint – salary grade midpoint                Raise – percent of last raise
35    24    1.043    23    23    90    4    1    5.3    1    F    A        Grade – job/pay grade            Degree (0= BSBA 1 = MS)
36    23    1.000    23    27    75    3    1    4.3    1    F    A        Gender1 (Male or Female)            Compa – salary divided by midpoint
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