Score: Week 5  Correlation and Regression <1 point> 1.     Create a correlation table for the variables in our data set. (Use analysis ToolPak or StatPlus:mac LE function Correlation.) a.  Reviewing the data levels from week 1, what variables can be used in a Pearson's Correlation table (which is what Excel produces)? b. Place table here (C8): c. Using r = approximately .28 as the signicant r value (at p = 0.05) for a correlation between 50 values, what variables are significantly related to Salary? To compa? d. Looking at the above correlations - both significant or not - are there any surprises -by that I  mean any relationships you expected to be meaningful and are not and vice-versa? e. Does this help us answer our equal pay for equal work question? <1 point> 2 Below is a regression analysis for salary being predicted/explained by the other variables in our sample  (Midpoint,  age, performance rating, service,  gender, and degree variables. (Note: since salary and compa are different ways of  expressing an employee’s salary, we do not want to have both used in the same regression.) Plase interpret the findings. Ho: The regression equation is not significant. Ha: The regression equation is significant. Ho: The regression coefficient for each variable is not significant   Note: technically we have one for each input variable. Ha: The regression coefficient for each variable is significant   Listing it this way to save space. Sal SUMMARY OUTPUT Regression Statistics Multiple R 0.9915591 R Square 0.9831894 Adjusted R Square 0.9808437 Standard Error 2.6575926 Observations 50 ANOVA df SS MS F Significance F Regression 6 17762.3 2960.38 419.1516 1.812E-36 Residual 43 303.7003 7.0628 Total 49 18066 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept -1.749621 3.618368 -0.4835 0.631166 -9.046755 5.5475126 -9.04675504 5.54751262 Midpoint 1.2167011 0.031902 38.1383 8.66E-35 1.1523638 1.2810383 1.152363828 1.28103827 Age -0.004628 0.065197 -0.071 0.943739 -0.136111 0.1268547 -0.13611072 0.1268547 Performace Rating -0.056596 0.034495 -1.6407 0.108153 -0.126162 0.0129695 -0.12616237 0.01296949 Service -0.0425 0.084337 -0.5039 0.616879 -0.212582 0.1275814 -0.2125.

1. Score:
Week 5
Correlation and Regression

2. <1 point>
1.
Create a correlation table for the variables in our data set. (Use
analysis ToolPak or StatPlus:mac LE function Correlation.)
a.
Reviewing the data levels from week 1, what variables can be
used in a Pearson's Correlation table (which is what Excel
produces)?

3. b. Place table here (C8):

8. c.
Using r = approximately .28 as the signicant r value (at p =
0.05) for a correlation between 50 values, what variables are
significantly related to Salary?

9. To compa?

10. d.
Looking at the above correlations - both significant or not - are
there any surprises -by that I
mean any relationships you expected to be meaningful and are
not and vice-versa?

11. e.
Does this help us answer our equal pay for equal work question?

12. <1 point>
2
Below is a regression analysis for salary being
predicted/explained by the other variables in our sample
(Midpoint,
age, performance rating, service, gender, and degree variables.
(Note: since salary and compa are different ways of
expressing an employee’s salary, we do not want to have both

13. used in the same regression.)
Plase interpret the findings.

14. Ho: The regression equation is not significant.
Ha: The regression equation is significant.
Ho: The regression coefficient for each variable is not
significant

15. Note: technically we have one for each input variable.
Ha: The regression coefficient for each variable is significant
Listing it this way to save space.
Sal

16. SUMMARY OUTPUT

17. Regression Statistics
Multiple R
0.9915591

18. R Square
0.9831894
Adjusted R Square
0.9808437

19. Standard Error
2.6575926
Observations
50

20. ANOVA

21. df
SS
MS
F
Significance F
Regression
6
17762.3
2960.38
419.1516
1.812E-36

22. Residual
43
303.7003
7.0628
Total
49
18066

23. Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Lower 95.0%
Upper 95.0%
Intercept
-1.749621
3.618368
-0.4835

24. 0.631166
-9.046755
5.5475126
-9.04675504
5.54751262
Midpoint
1.2167011
0.031902
38.1383
8.66E-35
1.1523638
1.2810383
1.152363828
1.28103827
Age
-0.004628
0.065197
-0.071
0.943739
-0.136111

25. 0.1268547
-0.13611072
0.1268547
Performace Rating
-0.056596
0.034495
-1.6407
0.108153
-0.126162
0.0129695
-0.12616237
0.01296949
Service
-0.0425
0.084337
-0.5039
0.616879
-0.212582
0.1275814
-0.21258209

26. 0.12758138
Gender
2.4203372
0.860844
2.81159
0.007397
0.6842792
4.1563952
0.684279192
4.15639523
Degree
0.2755334
0.799802
0.3445
0.732148
-1.337422
1.8884885
-1.33742165
1.88848848

27. Note: since Gender and Degree are expressed as 0 and 1, they
are considered dummy variables and can be used in a multiple
regression equation.

28. Interpretation:
For the Regression as a whole:

29. What is the value of the F statistic:
What is the p-value associated with this value:

30. Is the p-value <0.05?
Do you reject or not reject the null hypothesis:

31. What does this decision mean for our equal pay question:

32. For each of the coefficients:
Intercept
Midpoint
Age
Perf. Rat.
Service
Gender
Degree
What is the coefficient's p-value for each of the variables:

33. Is the p-value < 0.05?
Do you reject or not reject each null hypothesis:
What are the coefficients for the significant variables?

34. Using only the significant variables, what is the equation?
Salary =
Is gender a significant factor in salary:

35. If so, who gets paid more with all other things being equal?
How do we know?

37. <1 point>
3
Perform a regression analysis using compa as the dependent
variable and the same independent
variables as used in question 2. Show the result, and interpret
your findings by answering the same questions.
Note: be sure to include the appropriate hypothesis statements.

38. Regression hypotheses
Ho:

39. Ha:
Coefficient hyhpotheses (one to stand for all the separate
variables)
Ho:

40. Ha:

41. Place D94 in output box.

53. Interpretation:
For the Regression as a whole:
What is the value of the F statistic:

54. What is the p-value associated with this value:
Is the p-value < 0.05?

55. Do you reject or not reject the null hypothesis:
What does this decision mean for our equal pay question:

56. For each of the coefficients:
Intercept
Midpoint
Age
Perf. Rat.
Service
Gender
Degree

57. What is the coefficient's p-value for each of the variables:
Is the p-value < 0.05?

58. Do you reject or not reject each null hypothesis:
What are the coefficients for the significant variables?

59. Using only the significant variables, what is the equation?
Compa =
Is gender a significant factor in compa:

60. If so, who gets paid more with all other things being equal?
How do we know?

61. <1 point>
4
Based on all of your results to date,

62. Do we have an answer to the question of are males and females
paid equally for equal work?
If so, which gender gets paid more?

63. How do we know?
Which is the best variable to use in analyzing pay practices -
salary or compa? Why?
What is most interesting or surprising about the results we got
doing the analysis during the last 5 weeks?

65. <2 points>
5
Why did the single factor tests and analysis (such as t and
single factor ANOVA tests on salary equality) not provide a
complete answer to our salary equality question?
What outcomes in your life or work might benefit from a
multiple regression examination rather than a simpler one
variable test?

67. See comments at the right of the data set.
ID
Salary
Compa
Midpoint
Age
Performance Rating
Service

68. Gender
Raise
Degree
Gender1
Grade
8
23
1.000
23
32
90
9
1
5.8
0
F
A
The ongoing question that the weekly assignments will focus on
is: Are males and females paid the same for equal work (under
the Equal Pay Act)?

69. 10
22
0.956
23
30
80
7
1
4.7
0
F
A
Note: to simplfy the analysis, we will assume that jobs within
each grade comprise equal work.
11
23
1.000
23
41
100
19
1
4.8
0
F
A

70. 14
24
1.043
23
32
90
12
1
6
0
F
A
The column labels in the table mean:

71. 15
24
1.043
23
32
80
8
1
4.9
0
F
A
ID – Employee sample number
Salary – Salary in thousands
23
23
1.000
23
36
65
6
1
3.3
1
F
A

72. Age – Age in years
Performance Rating – Appraisal rating (Employee evaluation
score)
26
24
1.043
23
22
95
2
1
6.2
1
F
A
Service – Years of service (rounded)
Gender: 0 = male, 1 = female
31
24
1.043
23
29

73. 60
4
1
3.9
0
F
A
Midpoint – salary grade midpoint
Raise – percent of last raise
35
24
1.043
23
23
90
4
1
5.3
1
F
A
Grade – job/pay grade
Degree (0= BSBA 1 = MS)

74. 36
23
1.000
23
27
75
3
1
4.3
1
F
A
Gender1 (Male or Female)
Compa - salary divided by midpoint
37
22
0.956
23
22
95
2
1
6.2

75. 1
F
A
42
24
1.043
23
32
100
8
1
5.7
0
F
A

76. 3
34
1.096
31
30
75
5
1
3.6
0
F
B

77. 18
36
1.161
31
31
80
11
1
5.6
1
F
B
20
34
1.096
31
44
70
16
1
4.8

78. 1
F
B
39
35
1.129
31
27
90
6
1
5.5
1
F
B

79. 7
41
1.025
40
32
100
8
1
5.7
0
F
C

80. 13
42
1.050
40
30
100
2
1
4.7
1
F
C
22
57
1.187
48
48
65
6
1
3.8

81. 0
F
D
24
50
1.041
48
30
75
9
1
3.8
1
F
D

82. 45
55
1.145
48
36
95
8
1
5.2
0
F
D

83. 17
69
1.210
57
27
55
3
1
3
0
F
E
48
65
1.140
57
34
90
11
1
5.3

84. 1
F
E
28
75
1.119
67
44
95
9
1
4.4
1
F
F

85. 43
77
1.149
67
42
95
20
1
5.5
1
F
F

86. 19
24
1.043
23
32
85
1
0
4.6
1
M
A
25
24
1.043
23
41
70
4
0
4

87. 0
M
A
40
25
1.086
23
24
90
2
0
6.3
0
M
A

88. 2
27
0.870
31
52
80
7
0
3.9
0
M
B

89. 32
28
0.903
31
25
95
4
0
5.6
0
M
B
34
28
0.903
31
26
80
2
0
4.9

90. 1
M
B
16
47
1.175
40
44
90
4
0
5.7
0
M
C

91. 27
40
1.000
40
35
80
7
0
3.9
1
M
C

92. 41
43
1.075
40
25
80
5
0
4.3
0
M
C
5
47
0.979
48
36
90
16
0
5.7

93. 1
M
D
30
49
1.020
48
45
90
18
0
4.3
0
M
D

94. 1
58
1.017
57
34
85
8
0
5.7
0
M
E

95. 4
66
1.157
57
42
100
16
0
5.5
1
M
E
12
60
1.052
57
52
95
22
0
4.5

96. 0
M
E
33
64
1.122
57
35
90
9
0
5.5
1
M
E

97. 38
56
0.982
57
45
95
11
0
4.5
0
M
E

98. 44
60
1.052
57
45
90
16
0
5.2
1
M
E
46
65
1.140
57
39
75
20
0
3.9

99. 1
M
E
47
62
1.087
57
37
95
5
0
5.5
1
M
E

100. 49
60
1.052
57
41
95
21
0
6.6
0
M
E

101. 50
66
1.157
57
38
80
12
0
4.6
0
M
E
6
76
1.134
67
36
70
12
0
4.5

102. 1
M
F
9
77
1.149
67
49
100
10
0
4
1
M
F

103. 21
76
1.134
67
43
95
13
0
6.3
1
M
F

104. 29
72
1.074
67
52
95
5
0
5.4
0
M
F