Assignment on Multiple Linear Regression
The Excel file BankData shows the values of the following variables for randomly selected 93 employees of a large bank. This real data set was used in a court lawsuit against discrimination.
Let
Y= monthly salary in dollars (SALARY),
X1 = years of schooling at the time of hire (EDUCAT),
X2 = number of months of previous work experience (EXPER),
X3 = number of months since the individual was hired by the bank (MONTHS),
X4 = dummy variable coded 1 for males and 0 for females (MALE).
Let
μM = the average salary for all male bank employees,
μF = the average salary for all female bank employees.
Task 1. Extract monthly salaries for males and females. Using "t-Test: Two-Sample: Assuming Unequal Variances" in Data Analysis of Excel, conduct the hypothesis test to determine whether μ_M>μ_F, that is, there is evidence of wage discrimination for the bank employees.
Use a 1% level of significance. State the two hypotheses to be tested, the value of the test statistic, the p-value of the test, your conclusion and its interpretation.
Note. Two-Sample Hypothesis Tests are discussed on pages 215-219 in the textbook.
Task 2. Evidence ofμM>μF provides some support for a discrimination suit against the employer.
It is recognized, however, that a simple comparison of mean starting salaries might beinsufficient to conclude that the female employees have been discriminated against.
Obviously there are other factors that affect the starting salary to which the relation μM>μFmight be attributed. These factors have been identified as X1,X2 and X3.
Assume the following regression model,
Y=β0+β1 X1+β2 X2+β3 X3+β4 X4+ε,
and apply Regression in Data Analysis of Excel to find the estimated regression equation
Y ^=b0+b1 X1+b2 X2+b3 X3+b4 X4.
1. Clearly show the estimated regression equation. Assuming that the values of X1,X2 and X3 are fixed, what is the predicted average difference between the male and female salaries?
2. Is there a difference in the average salaries for all male and female employees after accounting for the effects of the three other independent variables?
Use a 1% level of significance to answer this question by conducting the t test.
State the two hypotheses to be tested, the value of the test statistic, the p-value of the test, your conclusion and its interpretation.
3. Using "Correlation" in Data Analysis of Excel, find the correlation matrix for Y,X1,X2 and X3 . Is there any problem with multicollinearity?
4. What salary would you predict for a male employee with 12 years educations, 10 months of previous work experience, and with time hired equal to 15 months?
What salary would you predict for a female employee with 12 years educations, 10 months of previous work experience, and with time hired equal to 15 months?
What is the difference between the two predicted salaries? Compare this difference with that found in Task 1.
Attachment:- Bank Data.rar