PLEASE HELP! ANSWER #5 Salary AgeEmployees Supervised S137,624.14 40 $121,427.85
ID: 3324985 • Letter: P
Question
PLEASE HELP! ANSWER #5
Salary AgeEmployees Supervised S137,624.14 40 $121,427.8535 129,698.40 54 S129,236.51 47 5143,318.11 49 S125,504.59 55 S146,765.01 50 127,260.60 56 5140,695.97 46 S143,647.16 43 5115,120.62 57 S134,346.35 57 5135,158.38 48 127,784.69 57 $139,108.7552 5146,236.83 46 5124,124.40 36 S132,625.07 43 S134,22946 35 117,669.48 58 S132,578.73 48 S139,453.55 56 134,417.38 37 S122,653.40 56 $127,997.92 36 137,109.90 44 130,722.02 36 117,623.28 50 5123,194.16 43 S137,173.84 52 S131,408.94 38 The following data are the results from an annual survey on the salaries of managers in the state of NJ. Besides the annual salary reported by the manager you also have the age of the manager at the time of the survey and the number of employees said manager directly supervises Assume the samples are representative of the population of NJ managers 550 485 518 516 573 502 587 509 562 574 460 537 540 511 556 584 496 530 536 470 530 Using multiple regression analysis to estimate the annual salaries: 1. Test for the overall and individual relationships at the 0.01 level of significance. Int t the results 8 pts.] 2. What should be your equation to estimate the annual salary? Explain your answer 8 pts.] 3. Interpret the coefficients of your equation 8 pts.] 4. What is the expected annual salary f a manager that supervises an and it is 55 of 400 employees 537 490 511 548 average s old? 8 pts.] 470 492 548 525 5. What is the expected annual salary for a manager that supervises an and it is 35 years old? Interpret results from 5 & 4 average of 400 employees 8 pts.] 6. Interpret the coefficient of determination of your regression analysis 8 pts.]Explanation / Answer
Solution:
Required regression output for the given data is summarised as below:
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.99997406
R Square
0.999948121
Adjusted R Square
0.999944415
Standard Error
62.7550972
Observations
31
ANOVA
df
SS
MS
F
Significance F
Regression
2
2125404256
1062702128
269844.479
1.02303E-60
Residual
28
110269.6623
3938.202225
Total
30
2125514525
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
408.343927
202.1019643
2.020484701
0.052991456
-5.643174551
822.3310286
Age
-4.062891528
1.494498876
-2.71856446
0.011126574
-7.124233657
-1.001549398
Employees Supervised
249.8584252
0.342913905
728.633111
1.9237E-61
249.1559979
250.5608525
Regression equation for the prediction of salary is given as below:
Expected Annual Salary in $ = 408.343927 – 4.0629*Age + 249.8584*Employees supervised
Question 4
Here, we are given
Age = 55
Employees supervised = 400
Expected Annual Salary in $ = 408.343927 – 4.0629*Age + 249.8584*Employees supervised
Expected Annual Salary in $ = 408.343927 - 4.0629*55 + 249.8584*400
Expected Annual Salary in $ = 100128.2444
Question 5
Here, we are given
Age = 35
Employees supervised = 400
Expected Annual Salary in $ = 408.343927 – 4.0629*Age + 249.8584*Employees supervised
Expected Annual Salary in $ = 408.343927 - 4.0629*35 + 249.8584*400
Expected Annual Salary in $ = 100209.5024
From question 4 and 5, it is observed that as the age of manager decreases, the expected annual Salary is increases, keeping number of employees supervised constant.
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.99997406
R Square
0.999948121
Adjusted R Square
0.999944415
Standard Error
62.7550972
Observations
31
ANOVA
df
SS
MS
F
Significance F
Regression
2
2125404256
1062702128
269844.479
1.02303E-60
Residual
28
110269.6623
3938.202225
Total
30
2125514525
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
408.343927
202.1019643
2.020484701
0.052991456
-5.643174551
822.3310286
Age
-4.062891528
1.494498876
-2.71856446
0.011126574
-7.124233657
-1.001549398
Employees Supervised
249.8584252
0.342913905
728.633111
1.9237E-61
249.1559979
250.5608525
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