Question

Assignment on Multiple Linear Regression

The Excel file BankData shows the values of the following variables for randomly selected 93 employees of a bank. This real data set was used in a court lawsuit against discrimination. Let = starting monthly salary in dollars (SALARY), = years of schooling at the time of hire (EDUCAT), = number of months of previous work experience (EXPER), = number of months that the individual was hired (MONTHS), = dummy variable coded 1 for males and 0 for females (MALE). Let = the mean starting salary for all male bank employees, and = the mean starting salary for all female bank employees. Using the t-test studied in Section 10.2, you could find some evidence of and provide some support for a discrimination suit against the employer. It is recognized, however, that a simple comparison of the mean starting salaries might be insufficient to conclude that the female employees have been discriminated against. Obviously there are other factors that affect the starting salary to which the relation might be attributed. These factors have been identified as and defined above. Assume the following regression model, , and apply Regression in Data Analysis of Excel (see pages 312 – 314) to find the estimated regression equation . 1. Clearly show the estimated regression equation. Assuming that the values of and are fixed, what is the estimated average difference between the starting salaries of all male and female employees? 2. What starting salary would you predict for a male employee with 12 years educations, 10 months of previous work experience, and with the time hired equal to 15 months? What starting salary would you predict for a female employee with 12 years educations, 10 months of previous work experience, and with the time hired equal to 15 months? What is the difference between the two predicted salaries? Compare this difference with that found in Task 1. 3. Is there a significant difference in the average starting salaries for male and female employees after accounting for the effects of the three other independent variables? Use a 5% level of significance to answer this question. Clearly show the null and alternative hypotheses to be tested, the value of the test statistic, the p-value of the test, your conclusion and its interpretation; see pages 322 – 323 and 333-335.

SALARY	EDUCAT	EXPER	MONTHS	GENDER
3900	12	0	1	0
4020	10	44	7	0
4290	12	5	30	0
4380	8	6	7	0
4380	8	8	6	0
4380	12	0	7	0
4380	12	0	10	0
4380	12	5	6	0
4440	15	75	2	0
4500	8	52	3	0
4500	12	8	19	0
4620	12	52	3	0
4800	8	70	20	0
4800	12	6	23	0
4800	12	11	12	0
4800	12	11	17	0
4800	12	63	22	0
4800	12	144	24	0
4800	12	163	12	0
4800	12	228	26	0
4800	12	381	1	0
4800	16	214	15	0
4980	8	318	25	0
5100	8	96	33	0
5100	12	36	15	0
5100	12	59	14	0
5100	15	115	1	0
5100	15	165	4	0
5100	16	123	12	0
5160	12	18	12	0
5220	8	102	29	0
5220	12	127	29	0
5280	8	90	11	0
5280	8	190	1	0
5280	12	107	11	0
5400	8	173	34	0
5400	8	228	33	0
5400	12	26	11	0
5400	12	36	33	0
5400	12	38	22	0
5400	12	82	29	0
5400	12	169	27	0
5400	12	244	1	0
5400	15	24	13	0
5400	15	49	27	0
5400	15	51	21	0
5400	15	122	33	0
5520	12	97	17	0
5520	12	196	32	0
5580	12	133	30	0
5640	12	55	9	0
5700	12	90	23	0
5700	12	117	25	0
5700	15	51	17	0
5700	15	61	11	0
5700	15	241	34	0
6000	12	121	30	0
6000	15	79	13	0
6120	12	209	21	0
6300	12	87	33	0
6300	15	231	15	0
4620	12	12	22	1
5040	15	14	3	1
5100	12	180	15	1
5100	12	315	2	1
5220	12	29	14	1
5400	12	7	21	1
5400	12	38	11	1
5400	12	113	3	1
5400	15	18	8	1
5400	15	359	11	1
5700	15	36	5	1
6000	8	320	21	1
6000	12	24	2	1
6000	12	32	17	1
6000	12	49	8	1
6000	12	56	33	1
6000	12	252	11	1
6000	12	272	19	1
6000	15	25	13	1
6000	15	36	32	1
6000	15	56	12	1
6000	15	64	33	1
6000	15	108	16	1
6000	16	46	3	1
6300	15	72	17	1
6600	15	64	16	1
6600	15	84	33	1
6600	15	216	16	1
6840	15	42	7	1
6900	12	175	10	1
6900	15	132	24	1
8100	16	55	33	1

Answer 1

1) This Is the Regression Output from Excel

Factor	Coefficients	SE	T-Stat	P-Value
Intercept	3526.20	327.68	10.76	0.00
EDUCAT	90.02	24.69	3.65	0.00
EXPER	1.27	0.59	2.16	0.03
MONTHS	23.40	5.20	4.50	0.00
GENDER	722.38	117.81	6.13	0.00

the Regreesion Equation will be

Pred_SALARY=3526.2+ (90.01*EDUCAT)+(1.27*EXPER)+(23.4*MONTHS)+(722.3*GENDER).

1.1) From above Output we have got Predicted salaries and from that we got the estimated average difference between the starting salaries of all male and female employees is 818.02 dollar ( since estimated average starting salary of Male is 5956.87 and for female 5138.85).

2) From above regreesion equation predicted salary for male is 5692.32 dollar provided that 12 years educations, 10 months of previous work experience, and with the time hired equal to 15 months.

and For Female 4970.02 dollar provided that  12 years educations, 10 months of previous work experience, and with the time hired equal to 15 months

2.1) the difference between two salaries is 722.30 dollar

2.2) If we compare this result with Task 1result then the difference for salary in male and female is 264.55 and 168.83 dollar respectively.

3) we will use t test to compare means so our null hypothesis will be

H0: There is no significant difference between actual and pred salary for male.

and H1: There is significant difference between actual and pred salary for male.

so after performing t test we got the t test statistic with p value as shown below

t Stat	0.00
P(T<=t) one-tail	0.50

Here P > alpha (0.05) so we accept H0 .. There is no significant difference between actual and pred salary for male.?

similarly for female same hypothesis

H0: There is no significant difference between actual and pred salary for female.

and H1: There is significant difference between actual and pred salary for female.

t Stat	0.00
P(T<=t) one-tail	0.50

Here P > alpha (0.05) so we accept H0 .... There is no significant difference between actual and pred salary for female.?