Question

ABC, Inc. is undergoing scrutiny for a possible wage discrimination suit. The following data is available: SALARY(monthly salary for each employee $), YEARS (years with the company), POSITION (position with company coded as: 1 = manual labor 2 = secretary 3 = lab technician 4 = chemist 5 = management EDUCAT (amount of education completed coded as: 1 = high school degree 2 = some college 3 = college degree 4 = graduate degree), GENDER (employee gender).

SALARY	YEARS	POSITION	EDUCAT	GENDER
1720	6	3	2	female
2400	4.9	1	1	male
1600	4.2	2	2	female
2900	3.7	4	3	female
1200	1.6	3	1	female
1000	0.3	3	1	female
2900	1	4	3	male
2400	1.8	4	3	male
1900	6.8	3	1	female
2200	1.2	4	3	male
1000	0.3	3	1	female
900	0.2	3	1	female
1250	0.6	3	1	female
950	0.5	3	1	female
2000	0.7	4	3	male
2000	1.9	4	3	male
1900	1.6	1	1	male
1000	1.4	3	1	female
1000	1.4	3	1	female
2800	3.4	4	3	female
2900	3.5	4	3	male
1550	3.1	3	1	female
1550	3	2	1	female
2200	2.5	4	3	male
1650	2.2	1	1	male
2200	2	4	3	male
900	0.5	3	1	female
1000	0.5	3	2	female
1220	2	3	1	female
2100	0.5	4	3	male
900	0.5	3	1	female
900	0.2	3	1	female
2000	0.5	4	3	male
2330	0.6	4	3	male
2400	0.3	4	3	male
900	1	1	1	male
1069	0.5	3	1	female
1400	0.5	1	1	male
1650	1	1	1	male
1200	0.3	1	1	male
3500	13.5	5	4	male
1750	11	5	3	female
4000	6.4	5	3	male
1800	7.2	2	1	female
4000	6.1	5	3	male
4600	5.8	5	4	male
1350	5.1	4	3	male

         

1. Using the selected model (i.e., “best” model) answer the following: a) Briefly summarize (present & calculate) the descriptive statistics of the data b)Interpret and evaluate the model coefficients for the management team and corporate lawyer of ABC, Inc. c) Test for significance of relationships (both individually and jointly for the overall model). Use a 10% level of significance. Please note if you are performing a two-tailed test or one-tailed test and justify. d) Demonstrate how ABC, Inc., could use the model for predicting employee salary. Include a sample computation. e) Verify model assumptions (e.g., residual plots) f) Identify any potential problems with the data or model & briefly discuss. g) Explicitly answer: Should ABC, Inc. be worried about possible wage discrimination charges? Deliberate about what additional variables to consider for the model.

Answer 1

a) Briefly summarize (present & calculate) the descriptive statistics of the data.

We have to find the descriptive statistics for Salary and Years.

Go to Megastat>Descriptive Statistics.

Select the Input Range and click OK.

Descriptive statistics for Salary is:

	SALARY
count	47
mean	1,873.17
sample standard deviation	900.56
sample variance	8,11,009.32
minimum	900
maximum	4600
range	3700
skewness	1.17
kurtosis	1.20
coefficient of variation (CV)	48.08%
1st quartile	1,134.50
median	1,720.00
3rd quartile	2,265.00
interquartile range	1,130.50
mode	1,000.00

Therefore, we can say that the average salary for an employee is $1,873.17. The minimum salary for an employee is $900 and the maximum salary for an employee is $4,600.

Descriptive statistics for Years is:

	YEARS
count	47
mean	2.634
sample standard deviation	2.911
sample variance	8.476
minimum	0.2
maximum	13.5
range	13.3
skewness	1.867
kurtosis	3.916
coefficient of variation (CV)	110.53%
1st quartile	0.500
median	1.600
3rd quartile	3.600
interquartile range	3.100
mode	0.500

Therefore, we can say that the average number of years an employee works in the company is 2.634 years. The minimum number of years an employee works in the company is 0.2 years and the maximum number of years an employee works in the company is 13.5 years.

b)Interpret and evaluate the model coefficients for the management team and corporate lawyer of ABC, Inc.

The model coefficients for the management team and corporate lawyer of ABC, Inc are:

Let x₁ represents the number of years an employee is working in the company.

Let x₂ represents the position of an employee.

Let x₃ represents the education of an employee.

Let x₄ represents the gender of an employee.

For x₄, suppose its value is 1 for Female and 0 for Male.

c) Test for significance of relationships (both individually and jointly for the overall model). Use a 10% level of significance. Please note if you are performing a two-tailed test or one-tailed test and justify.

Let us test for significance of relationship jointly for the overall model.

Go to Megastat>Correlation/Regression.

Select the Input Range and click OK.

For the Input Range, select the independent variable(s), X as Years, Position, Education and Gender column.

For the Input Range, select the dependent variable, Y as Salary column.

The output is as follows:

	R²	0.700
	Adjusted R²	0.671	n	47
	R	0.837	k	4
	Std. Error	516.205	Dep. Var.	SALARY
ANOVA table
Source	SS	df	MS	F	p-value
Regression	2,61,14,770.0905	4	65,28,692.5226	24.50	1.64E-10
Residual	1,11,91,658.5478	42	2,66,468.0607
Total	3,73,06,428.6383	46
Regression output					confidence interval
variables	coefficients	std. error	t (df=42)	p-value	95% lower	95% upper
Intercept	945.2355
YEARS	102.0659	29.4081	3.471	.0012	42.7179	161.4138
POSITION	111.6250	139.0671	0.803	.4267	-169.0237	392.2738
EDUCAT	300.8649	195.4214	1.540	.1312	-93.5113	695.2412
GENDER	-579.7620	239.3983	-2.422	.0198	-1,062.8873	-96.6367

At a significance level of 0.1, we can say that the result is significant as the p-value(0.000) is less than the significance level.

Therefore, we can say there is a relationship between Salary and Years, Position, Education and Gender of an employee.

The regression equation for the model is:

y = 945.2355 + 102.0659*x₁ + 111.6250*x₂ + 300.8649*x₃ - 579.7620*x₄

_Or

Salary = 945.2355 + 102.0659*Years+ 111.6250*Position + 300.8649*Education  - 579.7620*Gender

Let us test for significance of relationship for Salary and Years.

Go to Megastat>Correlation/Regression.

Select the Input Range and click OK.

For the Input Range, select the independent variable(s), X as Years column.

For the Input Range, select the dependent variable, Y as Salary column.

The output is as follows:

	r²	0.276	n	47
	r	0.526	k	1
	Std. Error	774.603	Dep. Var.	SALARY
ANOVA table
Source	SS	df	MS	F	p-value
Regression	1,03,06,021.8929	1	1,03,06,021.8929	17.18	.0001
Residual	2,70,00,406.7454	45	6,00,009.0388
Total	3,73,06,428.6383	46
Regression output					confidence interval
variables	coefficients	std. error	t (df=45)	p-value	95% lower	95% upper
Intercept	1,444.9179
YEARS	162.5837	39.2293	4.144	.0001	83.5719	241.5955

At a significance level of 0.1, we can say that the result is significant as the p-value(0.0001) is less than the significance level.

Therefore, we can say there is a relationship between Salary and Years of an employee.

The regression equation for the model is:

y = 1,444.9179 + 162.5837*x₁

_Or

Salary = 1,444.9179 + 162.5837*Years

Let us test for significance of relationship for Salary and Position.

Go to Megastat>Correlation/Regression.

Select the Input Range and click OK.

For the Input Range, select the independent variable(s), X as Position column.

For the Input Range, select the dependent variable, Y as Salary column.

The output is as follows:

	r²	0.331	n	47
	r	0.575	k	1
	Std. Error	744.827	Dep. Var.	SALARY
ANOVA table
Source	SS	df	MS	F	p-value
Regression	1,23,41,902.8476	1	1,23,41,902.8476	22.25	2.35E-05
Residual	2,49,64,525.7907	45	5,54,767.2398
Total	3,73,06,428.6383	46
Regression output					confidence interval
variables	coefficients	std. error	t (df=45)	p-value	95% lower	95% upper
Intercept	487.8999
POSITION	436.9645	92.6425	4.717	2.35E-05	250.3728	623.5561

At a significance level of 0.1, we can say that the result is significant as the p-value(0.0000) is less than the significance level.

Therefore, we can say there is a relationship between Salary and Position of an employee.

The regression equation for the model is:

y = 487.8999 + 436.9645*x₂

_Or

Salary = 487.8999 + 436.9645*Position

Let us test for significance of relationship for Salary and Education.

Go to Megastat>Correlation/Regression.

Select the Input Range and click OK.

For the Input Range, select the independent variable(s), X as Education column.

For the Input Range, select the dependent variable, Y as Salary column.

The output is as follows:

	r²	0.591	n	47
	r	0.769	k	1
	Std. Error	581.968	Dep. Var.	SALARY
ANOVA table
Source	SS	df	MS	F	p-value
Regression	2,20,65,549.6728	1	2,20,65,549.6728	65.15	2.71E-10
Residual	1,52,40,878.9655	45	3,38,686.1992
Total	3,73,06,428.6383	46
Regression output					confidence interval
variables	coefficients	std. error	t (df=45)	p-value	95% lower	95% upper
Intercept	571.7059
EDUCAT	664.8785	82.3728	8.072	2.71E-10	498.9712	830.7858

At a significance level of 0.1, we can say that the result is significant as the p-value(0.0000) is less than the significance level.

Therefore, we can say there is a relationship between Salary and Education of an employee.

The regression equation for the model is:

y = 571.7059 + 664.8785*x₃

_Or

Salary = 571.7059 + 664.8785*Education

Let us test for significance of relationship for Salary and Gender.

Go to Megastat>Correlation/Regression.

Select the Input Range and click OK.

For the Input Range, select the independent variable(s), X as Gender column.

For the Input Range, select the dependent variable, Y as Salary column.

( I am not able to attach the output due to characters limit per question)

At a significance level of 0.1, we can say that the result is significant as the p-value(0.0000) is less than the significance level.

Therefore, we can say there is a relationship between Salary and Gender of an employee.

The regression equation for the model is:

y = 2,340.8333 - 955.6594*x₄

_Or

Salary = 2,340.8333 - 955.6594*Gender

d) Demonstrate how ABC, Inc., could use the model for predicting employee salary. Include a sample computation.

The model for predicting employee salary has a regression equation:

y = 945.2355 + 102.0659*x₁ + 111.6250*x₂ + 300.8649*x₃ + 239.3983*x₄

_Or

Salary = 945.2355 + 102.0659*Years+ 111.6250*Position + 300.8649*Education  - 579.7620*Gender

A sample computation:

Let us say, we want to predict an employee salary who is a female, working for the company from the past 10 years as a secretary and has a graduate degree.

In simple words, we are given with:

Years = 10

Position = 2

Education = 4

Gender = 1

Therefore, the predicted salary for this employee is:

Salary = 945.2355 + 102.0659*10+ 111.6250*2 + 300.8649*4 - 579.7620*1

Salary = $2,812.841866

Therefore, the predicted salary for an employee who is a female, working for the company from the past 10 years as a secretary and has a graduate degree is $2,812.841866.