Fred G. Hire is the manager of human resources at Crescent Tool and Die Inc. As
ID: 3269058 • Letter: F
Question
Fred G. Hire is the manager of human resources at Crescent Tool and Die Inc. As part of his yearly report to the CEO, he is required to present an analysis of the salaried employees. Because there are over 1,000 employees, he does not have the staff to gather information on each salaried employee, so he selects a random sample of 30. For each employee, he records monthly salary; service at Crescent, in months; gender (1 = male, 0 = female); and whether the employee has a technical or clerical job. Those working technical jobs are coded 1, and those who are clerical 0.
A. Using salary as the dependent variable and the other four variables as independent variables, write out the regression equation.
B. What is the value of R2? Comment on this value.
C. What is the label that you would give the variable, gender?
D. Conduct a global test of hypothesis to determine whether any of the independent variables are different from 0.
E. Conduct an individual test for Age to determine whether it can be dropped from the equation.
F. Rerun the regression equation, using only the independent variables that are significant. Write out your new regression equation. Hint: You may need to rearrange some of your variables in Excel. You can insert a new column and then cut and paste.
G. Using the following information: Length of Service = 115, Age 40, Gender 1, and Job 1; estimate the employee’s salary. Remember, you will not be using all of the variables!
Employee Salary Service Age Gender Job 1 $ 1,769.0 93 42 1 0 2 $ 1,740.0 104 33 1 0 3 $ 1,941.0 104 42 1 1 4 $ 2,367.0 126 57 1 1 5 $ 2,467.0 98 30 1 1 6 $ 1,640.0 99 49 1 1 7 $ 1,756.0 94 35 1 0 8 $ 1,706.0 96 46 0 1 9 $ 1,767.0 124 56 0 0 10 $ 1,200.0 73 23 0 1 11 $ 1,706.0 110 67 0 1 12 $ 1,985.0 90 36 0 1 13 $ 1,555.0 104 53 0 0 14 $ 1,749.0 81 29 0 0 15 $ 2,056.0 106 45 1 0 16 $ 1,729.0 113 55 0 1 17 $ 2,186.0 129 46 1 1 18 $ 1,858.0 97 39 0 1 19 $ 1,819.0 101 43 1 1 20 $ 1,350.0 91 35 1 1 21 $ 2,030.0 100 40 1 0 22 $ 2,550.0 123 59 1 0 23 $ 1,544.0 88 30 0 0 24 $ 1,766.0 117 60 1 1 25 $ 1,937.0 107 45 1 1 26 $ 1,691.0 105 32 0 1 27 $ 1,623.0 86 33 0 0 28 $ 1,791.0 131 56 0 1 29 $ 2,001.0 95 30 1 1 30 $ 1,874.0 98 47 1 0Explanation / Answer
Answer:
Regression Analysis
R²
0.433
Adjusted R²
0.342
n
30
R
0.658
k
4
Std. Error
236.529
Dep. Var.
Salary
ANOVA table
Source
SS
df
MS
F
p-value
Regression
1,066,830.3889
4
266,707.5972
4.77
.0054
Residual
1,398,650.9778
25
55,946.0391
Total
2,465,481.3667
29
Regression output
confidence interval
variables
coefficients
std. error
t (df=25)
p-value
95% lower
95% upper
Intercept
651.8575
345.3017
1.888
.0707
-59.3046
1,363.0197
Service
13.4219
5.1253
2.619
.0148
2.8662
23.9776
Age
-6.7102
6.3494
-1.057
.3007
-19.7870
6.3667
Gender. Male
205.6455
90.2657
2.278
.0315
19.7399
391.5512
Job
-33.4530
89.5474
-0.374
.7119
-217.8794
150.9734
Salary = 651.8575+13.4219* Service -6.7102* Age +205.6455* Gender. Male -33.4530* Job
B. What is the value of R2? Comment on this value.
R2 =0.433
43.3% of variance in alary is explained by the regression model.
C. What is the label that you would give the variable, gender?
Gender. male
D. Conduct a global test of hypothesis to determine whether any of the independent variables are different from 0.
Calculated F=4.77, P=0.0054 which is < 0.05 level of significance.
We conclude that atleast one of the independent variables are different from 0.
E. Conduct an individual test for Age to determine whether it can be dropped from the equation.
Calculated t= -1.057, P=0.3007which is > 0.05 level of significance. Age is not significant
Age can be dropped from the equation.
F. Rerun the regression equation, using only the independent variables that are significant. Write out your new regression equation. Hint: You may need to rearrange some of your variables in Excel. You can insert a new column and then cut and paste.
Regression Analysis
R²
0.405
Adjusted R²
0.361
n
30
R
0.636
k
2
Std. Error
233.071
Dep. Var.
Salary
ANOVA table
Source
SS
df
MS
F
p-value
Regression
998,778.6683
2
499,389.3342
9.19
.0009
Residual
1,466,702.6983
27
54,322.3222
Total
2,465,481.3667
29
Regression output
confidence interval
variables
coefficients
std. error
t (df=27)
p-value
95% lower
95% upper
Intercept
784.1862
316.8193
2.475
.0199
134.1267
1,434.2458
Service
9.0212
3.1063
2.904
.0073
2.6476
15.3949
Gender. Male
224.4063
87.3520
2.569
.0160
45.1748
403.6379
Salary = 784.1862 +9.0212 * Service +224.4063 * Gender. Male
G. Using the following information: Length of Service = 115, Age 40, Gender 1, and Job 1; estimate the employee’s salary.
Estimated Salary = 784.1862 +9.0212 * 115 +224.4063 * 1
=$2046.03
Regression Analysis
R²
0.433
Adjusted R²
0.342
n
30
R
0.658
k
4
Std. Error
236.529
Dep. Var.
Salary
ANOVA table
Source
SS
df
MS
F
p-value
Regression
1,066,830.3889
4
266,707.5972
4.77
.0054
Residual
1,398,650.9778
25
55,946.0391
Total
2,465,481.3667
29
Regression output
confidence interval
variables
coefficients
std. error
t (df=25)
p-value
95% lower
95% upper
Intercept
651.8575
345.3017
1.888
.0707
-59.3046
1,363.0197
Service
13.4219
5.1253
2.619
.0148
2.8662
23.9776
Age
-6.7102
6.3494
-1.057
.3007
-19.7870
6.3667
Gender. Male
205.6455
90.2657
2.278
.0315
19.7399
391.5512
Job
-33.4530
89.5474
-0.374
.7119
-217.8794
150.9734
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