BUS308 Assignments Week 4 - Assignment.docx

30 July, 2024 | 12 Min Read

ID

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42 Salary

64.3 27.5 35.2 63.4 46.6

72.9 43

22.7 78.1 23.6

23.8 67

40.8

25

24

38.1 68.7 33.2 24.3 34.7 75.7

56.1 24

58.3 23.6 21.9 41.8 74.6 75.4 47.7

23.1 28

61.3

27.7 24

24.1 23.2 58.9 35.7 24.1 46.4

24.9 Comparatio

1.128 0.888 1.135 1.113 0.970 1.088 1.074 0.989 1.165 1.024 1.036 1.176 1.021 1.085 1.042 0.952 1.205 1.070 1.058 1.120 1.130 1.169 1.044 1.214 1.025 0.953 1.046 1.113 1.126 0.993 1.006 0.904 1.076 0.894 1.044 1.049 1.010 1.034 1.151 1.049 1.161

1.082 Midpoint

57

31

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57

48

67

40

23

67

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57

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67

48

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67

67

48

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57

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57

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23 Age

34

52

30

42

36

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49

30

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52

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44

27

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48

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22

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45

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32 Performance Rating

85

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90

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80

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95

100

90

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55

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85

70

95

65

65

75

70

95

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60

95

90

80

90

75

95

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80 100 Service

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12

8

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19

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1

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6

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2

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8 Gender

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1 Raise

5.7 3.9 3.6 5.5 5.7 4.5 5.7 5.8 4

4.7 4.8 4.5 4.7 6

4.9 5.7 3

5.6 4.6 4.8 6.3 3.8 3.3

3.8 4

6.2 3.9 4.4 5.4 4.3 3.9 5.6 5.5 4.9 5.3 4.3 6.2 4.5 5.5 6.3 4.3

5.7 Degree

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1

43 76 1.135 67 42 95 20 1 5.5 0

44 60.6 1.063 57 45 90 16 0 5.2 1

45 56.4 1.174 48 36 95 8 1 5.2 1

46 60.2 1.057 57 39 75 20 0 3.9 1

47 64.6 1.134 57 37 95 5 0 5.5 1

48 69.7 1.222 57 34 90 11 1 5.3 1

49 60.4 1.059 57 41 95 21 0 6.6 0

50 61.4 1.078 57 38 80 12 0 4.6 0

Gender1

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M

F Grade

E

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D

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C

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C

E

B

A

B

F

D

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C

A Do not manipuilate Data set on this page, copy to another page to make changes

The ongoing question that the weekly assignments will focus on is: Are males Note: to simplfy the analysis, we will assume that jobs within each grade compr

The column labels in the table mean:

ID – Employee sample number Salary – Salary in thousands

Age – Age in years Performance Rating - Appraisal rating (e

Service – Years of service (roundGender – 0 = male, 1 = female

Midpoint – salary grade midpoinRaise – percent of last raise

Grade – job/pay grade Degree (0= BS\BA 1 = MS)

Gender1 (Male or Female) Compa-ratio - salary divided by midpoin

#NAME?

The difference between raise in all female and male differ by a marg

F F

M E

F D

M E

M E

F E

M E

M E

and females paid the same for equal work (under the Equal Pay Act)? rise equal work.

employee evaluation score)

nt

gin of 0.24405 which is 24.4%

Week 4: Identifying relationships - correlations and regression

To Ensure full credit for each question, you need to show how you got your resu or showing the excel formula in each cell. Be sure to copy the appro

1 What is the correlation between and among the interval/ratio level var a. Create the correlation table.

i. What is the data input ranged used for this question: ii. Create a correlation table in cell K08.

b. Technically, we should perform a hypothesis testing on each correlaif it is significant or not. However, we can be faithful to the process a time by finding the minimum correlation that would result in a two tai We can then compare each correlation to this value, and those exceedi positive or negative direction) can be considered statistically significa i. What is the t-value we would use to cut off the two tails?

ii. What is the associated correlation value related to this t-value?    

c. What variable(s) is(are) significantly correlated to salary?

d. Are there any surprises - correlations you though would be significa

e. Why does or does not this information help answer our equal pay qu

2 Perform a regression analysis using salary as the dependent variable a our two dummy variables - gender and education. Show the result, an Suggestion: Add the dummy variables values to the right of the last da

What is the multiple regression equation predicting/explaining compa-

a. What is the data input ranged used for this question:

b. Step 1: State the appropriate hypothesis statements:

Ho: All dependant variable are not statiscally signif

Ha: At least one dependant variable are statiscally s

Step 2:Significance (Alpha): 0.05

Step 3:Test Statistic and test:Regression

Why this test?An equation showing relationships,

Step 4:Decision rule: If p-value is < 0.05, we r

Step 5:Conduct the test - place test function in cell M3

What is the p-value: 2.69E-35

What is your decision: REJ or NOT reject the null?Reject the Null Hypothes

Why?The p-value is < 0.05, we

Step 6:Conclusion and Interpretation

What does this decision mean? ble is statiscally significan

c. If we rejected the null hypothesis, we need to test the sign

Step 1: State the appropriate coefficient hypothesis statem Ho: All dependant variable are not statiscally signif

Ha: At least one dependant variable are statiscally s

Step 2:Significance (Alpha): 0.05

Step 3:Test Statistic and test:Regression

Why this test?An equation showing relationships,

Step 4:Decision rule: If p-value is < 0.05, we r

Step 5:Conduct the test for each variable, complete an

Midpoint Age Perf. Rat. Service

t-value: P-value: Rejection Decision:

3.96E+01 0.83 -0.23 0.09

6.92E-35 0.41 0.82 0.28

Yes No No No

1.2

If Null is rejected, what is the variable’s coefficient value?

Step 6:Conclusion and Interpretation

Using the intercept coefficient and only the significant va Salary = 1.2006*midpoint+3.665065*Gender

d. Is gender a significant factor in compa-ratio?

e. Regardless of statistical significance, who gets paid more

f. How do we know? Because we are unable to obtain en

Since 0 is assigned for male and 1 is assigned for fema

3 After considering the compa-ratio based results in the lectures and you before answering our question on equal pay? Why? Hours worked The equal pay question can be answered better if more variables c

4 Between the lecture results and your results, what is your answer to th of equal pay for equal work for males and females? Why?

5 What does regression analysis show us about analyzing complex meas

ults. This involves either showing where the data you used is located

opriate data columns from the data tab to the right for your use this week.

riables withsalary? (Do not use compa-ratio in this question.)

S1:Z51

ation to determine

and save some il rejection of the null. ing it (in either a ant.

T = #NAME? r = #NAME?

Midpoint, Age and Service ant and are not, or non significant correlations you thought would be?

uestion? According to our chart, gender is not as sig

and the variables used in Q1 along with nd interpret your findings by answering the following questions. ata columns used for Q1.

a-ratio using all of our possible variables except salary?

S1:Z51 SUMMARY OUTPUT

Regression Statistics

ficant to the Salary Multiple R significant to the Salary R Square

Adjusted R Square Standard Error , we need to see the relationships to understand them. Observations reject the null hypthesis

34

Regression

sis Residual e reject the null Total

nt to the Salary Intercept

Midpoint

nificance of each of the variable coefficients. Age

ments: Performance Rating ficant to the Salary Service significant to the Salary Gender

Raise Degree , we need to see the relationships to understand them. reject the null hypthesis nd use the table below.

Raise Gender

0.3 4.28

0.76 0

No Yes

3.67

ariables, what is the equation?

Yes with all other things being equal? Female

nough information to determine if men or females are being payed more but we know the salary is not ale

ur saalary based results, what else would you like to know

d on a weekly basis. Do men work more hours than women? could be incl

he question

Female compa ratio is higher than 1 which means that the females are getting payed more then the m

sures? Regression analysis is also used to under

Salary Midpoint Age ormance Ra Service Gender Raise Degree

Salary 1

Midpoint 0.99 1

Age 0.55 0.57 1

Performance R 0.18 0.19 0.14 1

Service 0.45 0.47 0.57 0.23 1

Gender -0.35 -0.43 -0.39 -0.15 -0.18 1

Raise -0.04 -0.03 -0.18 0.67 0.1 -0.07 1

Degree 0.05 0.06 -0.01 -0.06 0.08 0.04 -0.07 1

I believed that age and service would be significant bu

gnificant and issue for equal pay as age and midpoint are however, no conclusion can be done if ma

0.99 0.98 0.98

2.62 50

df SS MS F Significance F

7 17185.9 2455.13 357.28 0

42 288.61

49 17474.51 6.87

Coefficients tandard Erro t Stat P-value Lower 95%Upper 95%Lower 95.0%Upper 95.0%

-8.01 3.82 -2.1 0.04 -15.71 -0.31 -15.71 -0.31

1.2 0.03 39.59 6.92E-35 1.14 1.26 1.14 1.26

0.06 0.07 0.83 0.41 -0.08 0.19 -0.08 0.19

-0.01 0.05 -0.23 0.82 -0.11 0.09 -0.11 0.09

-0.09 0.09 -1.09 0.28 -0.27 0.08 -0.27 0.08

3.67 0.86 4.28 0 1.94 5.39 1.94 5.39

0.2 0.65 0.3 0.76 -1.12 1.51 -1.12 1.51

-0.68 0.75 -0.91 0.37 -2.2 0.84 -2.2 0.84

Degree

-0.91

0.37

No

t equal because we keep rejecting the null market value however, it does not allow us to say that they get payed more or less than male which m

rstand which among the independent variables are related to the dependent variable, and to e

ID

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44 Salary

64.3 27.5 35.2 63.4 46.6 72.9 43

22.7 78.1 23.6

23.8 67

40.8

25

24

38.1 68.7 33.2 24.3 34.7 75.7

56.1 24

58.3 23.6 21.9 41.8 74.6 75.4 47.7

23.1 28

61.3

27.7 24

24.1 23.2 58.9 35.7 24.1 46.4

24.9 76

60.6 Comparatio

1.128 0.888 1.135 1.113 0.970 1.088 1.074 0.989 1.165 1.024 1.036 1.176 1.021 1.085 1.042 0.952 1.205 1.070 1.058 1.120 1.130 1.169 1.044 1.214 1.025 0.953 1.046 1.113 1.126 0.993 1.006 0.904 1.076 0.894 1.044 1.049 1.010 1.034 1.151 1.049 1.161 1.082 1.135

1.063 Midpoint

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57 Age

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45 Performa nce

Rating

85

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100

90

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100

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95

100

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55

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85

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90 Service

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8 20

16 Gender

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0 Raise

5.7 3.9 3.6 5.5 5.7 4.5 5.7 5.8 4

4.7 4.8 4.5

4.7 6

4.9

5.7 3

5.6 4.6 4.8 6.3 3.8 3.3

3.8 4

6.2 3.9 4.4 5.4 4.3 3.9 5.6 5.5 4.9 5.3 4.3 6.2 4.5 5.5 6.3 4.3 5.7 5.5

5.2 Degree

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45 56.4 1.174 48 36 95 8 1 5.2 1

46 60.2 1.057 57 39 75 20 0 3.9 1

47 64.6 1.134 57 37 95 5 0 5.5 1

48 69.7 1.222 57 34 90 11 1 5.3 1

49 60.4 1.059 57 41 95 21 0 6.6 0

50 61.4 1.078 57 38 80 12 0 4.6 0

make us conclude that further study will be required to answer thisd question. explore the forms of these relationships. In restricted circumstances, regression analysis can be used

Gender1 Grade

M E

M B

F B

M E

M D

M F

F C

F A

M F

F A

F A

M E

F C

F A

F A

M C

F E

F B

M A

F B

M F

F D

F A

F D

M A

F A

M C

F F

M F

M D

F A

M B

M E

M B

F A

F A

F A

M E

F B

M A

M C

F A

F F

M E

F D

M E

M E

F E

M E

M E

d to infer causal relationships between the independent and dependent variables.

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