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Assignment on Multiple Linear Regression                                     &nb

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

= 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 by the bank (MONTHS),

= dummy variable coded 1 for males and 0 for females (MALE).

Let um = the mean salary for all male bank employees, and uf = the mean salary for all female bank employees. Using the t-test studied in Section 10.2, you could find some evidence of um > uf and provide some support for a discrimination suit against the employer. It is recognized, however, that a simple comparison of the mean salaries might be insufficient to conclude that the female employees have been discriminated against. Obviously there are other factors that affect the salary to which the relation um > uf might be attributed. These factors have been identified as x1, x2 and x3 defined above.

Assume the following regression model,

y = B0 + B1x1 + B2x2 + B3x3 + B4x4 + E

and apply Regression in Data Analysis of Excel to find the estimated regression equation

1. Clearly show the estimated regression equation. Assuming that the values of x1, x2 and x3 are fixed, what is the estimated average difference between the salaries of all male and female employees?

2. What 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 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 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.

     The detailed example of using Regression in Data Analysis of Excel is shown on pages 312 – 314.

     Use Microsoft Word to write a managerial report with your name shown on the first page. The report should include your Excel output from Regression (copy and paste it), so do not attach any separate Excel file.

SALARY EDUCAT EXPER MONTHS        MALE

4620      12          11.5       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          17.5       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          35.5       32                        1

6000      15          56          12                        1          

6000      15          64          33                        1

6000      15          108        16                        1          

6000      16          45.5       3                          1

6300      15          72          17                        1

6600      15          64          16                        1

6600      15          84          33                        1

6600      15          215.5    16                        1

6840      15          41.5       7                          1

6900      12          175        10                        1

6900      15          132        24                        1

8100      16          54.5       33                        1

3900      12          0            1                          0

4020      10          44          7                          0          

4290      12          5            30                        0

4380      8            6.2         7                          0

4380      8            7.5         6                          0

4380      12          0            7                          0

4380      12          0            10                        0

4380      12          4.5         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          132.5    30                        0

5640      12          55          9                          0

5700      12          90          23                        0

5700      12          116.5    25                        0

5700      15          51          17                        0

5700      15          61          11                        0

5700      15          241        34                        0

6000      12          121        30                        0

6000      15          78.5       13                        0

6120      12          208.5    21                        0

6300      12          86.5       33                        0

6300      15          231        15                        0

Solutions

Expert Solution

(1) the estimated regression eqution is given as

y=3526.42+90.02x1+1.27x2+23.41x3+722.47x4

SALARY EDUCAT Exper Month MALE
y x1 x2 x3 x4

estimated difference between male and femal is regression coefficient of x4 and it is 722.47

(2)

for male x1=12,x2=10, x3=15 and x4=1,

the y=3526.42+90.02*12+1.27*10+23.41*15+722.47*1=5692.98

for female x1=12,x2=10, x3=15 and x4=0,

the y=3526.42+90.02*12+1.27*10+23.41*15+722.47*0=4970.51

difference =5692.98-4970.51=722.47 which is same

(3)null hypothesis H0:4=0 and alternate hypothesis Ha:

t=4/SE(4)=722.46/117.82=6.13 with df=88

and p-value=0.000

following information has been generated using ms-excel

SUMMARY OUTPUT
Regression Statistics
Multiple R 0.714754304
R Square 0.510873714
Adjusted R Square 0.488640701
Standard Error 507.4215001
Observations 93
ANOVA
df SS MS F Significance F
Regression 4 23665351.39 5916338 22.97816 5.07217E-13
Residual 88 22657938.93 257476.6
Total 92 46323290.32
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 3526.422111 327.7254214 10.76029 1E-17 2875.136716 4177.707506
X Variable 1 90.02031094 24.69356079 3.645497 0.000451 40.94704888 139.093573
X Variable 2 1.268990015 0.587736851 2.159113 0.033562 0.100986552 2.436993477
X Variable 3 23.40623577 5.200862805 4.500452 2.07E-05 13.07061404 33.74185749
X Variable 4 722.4606714 117.8215905 6.131819 2.41E-08 488.3150236 956.6063192

orchestra answered 1 year ago
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