Question

In: Statistics and Probability

3. Fit a multiple regression model that relates the salary to education, work experience, and time spent at the bank so far.

SALARY EDUC EXPER TIME
39000 12 0 1
40200 10 44 7
42900 12 5 30
43800 8 6 7
43800 8 8 6
43800 12 0 7
43800 12 0 10
43800 12 5 6
44400 15 75 2
45000 8 52 3
45000 12 8 19
46200 12 52 3
48000 8 70 20
48000 12 6 23
48000 12 11 12
48000 12 11 17
48000 12 63 22
48000 12 144 24
48000 12 163 12
48000 12 228 26
48000 12 381 1
48000 16 214 15
49800 8 318 25
51000 8 96 33
51000 12 36 15
51000 12 59 14
51000 15 115 1
51000 15 165 4
51000 16 123 12
51600 12 18 12
52200 8 102 29
52200 12 127 29
52800 8 90 11
52800 8 190 1
52800 12 107 11
54000 8 173 34
54000 8 228 33
54000 12 26 11
54000 12 36 33
54000 12 38 22
54000 12 82 29
54000 12 169 27
54000 12 244 1
54000 15 24 13
54000 15 49 27
54000 15 51 21
54000 15 122 33
55200 12 97 17
55200 12 196 32
55800 12 133 30
56400 12 55 9
57000 12 90 23
57000 12 117 25
57000 15 51 17
57000 15 61 11
57000 15 241 34
60000 12 121 30
60000 15 79 13
61200 12 209 21
63000 12 87 33
63000 15 231 15
46200 12 12 22
50400 15 14 3
51000 12 180 15
51000 12 315 2
52200 12 29 14
54000 12 7 21
54000 12 38 11
54000 12 113 3
54000 15 18 8
54000 15 359 11
57000 15 36 5
60000 8 320 21
60000 12 24 2
60000 12 32 17
60000 12 49 8
60000 12 56 33
60000 12 252 11
60000 12 272 19
60000 15 25 13
60000 15 36 32
60000 15 56 12
60000 15 64 33
60000 15 108 16
60000 16 46 3
63000 15 72 17
66000 15 64 16
66000 15 84 33
66000 15 216 16
68400 15 42 7
69000 12 175 10
69000 15 132 24
81000 16 55 33
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.549576953
R Square 0.302034828
Adjusted R Square 0.278507912
Standard Error 6027.28285
Observations 93
ANOVA
df SS MS F Significance F
Regression 3 1399124701 466374900.2 12.83784192 4.80E-07
Residual 89 3233204332 36328138.56
Total 92 4632329032
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept 31794.79804 3834.248408 8.29231564 1.09E-12 24176.22813 39413.36796 24176.22813 39413.368
X Variable 1 1396.093359 277.1248641 5.037777335 2.45E-06 845.4521573 1946.734561 845.4521573 1946.73456
X Variable 2 14.84048274 6.970537846 2.129029792 0.036013792 0.990172517 28.69079297 0.990172517 28.690793
X Variable 3 206.290769 61.54401075 3.351922738 0.001179572 84.0041306 328.5774075 84.0041306 328.577407

3. Fit a multiple regression model that relates the salary to education, work experience, and time spent at the bank so far.

a - State what your model is.

b - Determine whether the independent variables are significant, or not, at a level of significance of 5%.

c - Which independent variable is most significant in explaining salary? Which is least significant?

d - Is your overall model significant? Provide statistical proof by conducting an F-test for overall fit of the regression. State the hypothesis to be tested, the p-value for your F-statistic, and your decision. How much weight of evidence is there in rejecting the null hypothesis?

Solutions

Expert Solution

SUMMARY OUTPUT
Regression Statistics
Multiple R 0.549576953
R Square 0.302034828
Adjusted R Square 0.278507912
Standard Error 6027.28285
Observations 93
ANOVA
df SS MS F Significance F
Regression 3 1399124701 466374900.2 12.83784192 4.80329E-07
Residual 89 3233204332 36328138.56
Total 92 4632329032
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept 31794.79804 3834.248408 8.29231564 1.08909E-12 24176.22813 39413.36796 24176.22813 39413.36796
EDUC 1396.093359 277.1248641 5.037777335 2.44893E-06 845.4521573 1946.734561 845.4521573 1946.734561
EXPER 14.84048274 6.970537846 2.129029792 0.036013792 0.990172517 28.69079297 0.990172517 28.69079297
TIME 206.290769 61.54401075 3.351922738 0.001179572 84.0041306 328.5774075 84.0041306 328.5774075

a)

Multuple regression:

SALARY =  31794.7980+1396.0934*EDUC+14.8405*EXPER+206.2908*TIME

b)

All independent variables are significanct at 5% significance level because all p values < 0.05

c)

Most significant variable is EDUCATION, Its P value is lessthan 0.00001

Least significant variable is EXPERIANCE, Its P value is between 0.01 < P value < 0.05

d)

Hypothesis:

H0: β1 = β2 = β3

Ha: At least one β is different

F stat = 12.8378

P value = 0

P value < 0.05

There is a strong evidence to conclude that Regression is significant at 5% significance level

orchestra answered 3 years ago
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