The personnel director for an space manufacturing company has

acquired complaints from the employees in a certain retailer regarding what they

perceive to be inequities throughout the annual wage for employees who’ve associated

effectivity rankings, years of service and associated certifications. The personnel director believes that an

employeeâs pay on this particular retailer should be positively correlated to their

prior effectivity rating, years of service and associated certifications. The personnel director has collected the knowledge

confirmed throughout the following desk pertaining to the employees all through the shop.

Employee

Current Annual Wage

(1000’s)

Widespread Effectivity Rating for

Earlier three Years

(5 stage scale)

Years of Service

Number of Associated

Certifications

1

48.2

2.18

9

6

2

55.three

three.31

20

6

three

53.7

three.18

18

7

4

61.eight

three.62

33

7

5

56.4

2.62

31

eight

6

52.5

three.75

13

6

7

54.zero

4.25

25

6

eight

55.7

three.43

30

4

9

45.1

1.93

5

6

10

67.9

4.5

47

eight

11

53.2

2.81

25

5

12

46.eight

three.06

11

6

13

58.three

5

23

eight

14

59.1

4.06

35

7

15

57.eight

4.12

39

5

16

48.6

2.31

21

4

17

49.2

three.87

7

6

18

63.zero

4.37

40

7

19

53.zero

2.5

35

6

20

50.9

2.81

23

4

21

55.4

three.68

33

5

22

51.eight

three.5

27

4

23

60.2

three

34

eight

24

50.1

2.43

15

5

The personnel director is raring about making a linear

regression model that may be utilized to estimate the annual wage an employee might

rely on to acquire based upon his or her earlier effectivity, years of service and/or

number of associated certifications. The

regression model shall be used as a basis for determining whether or not or not or not there

is any validity to the employeesâ complaints regarding wage inequities.

Perform each of the subsequent seven regression

analyses using a 95% confidence diploma.

Â·

Annual wage vs. years of service

Â·

Annual wage vs. number of associated

certifications

Â·

Annual wage vs. widespread effectivity

rating for the earlier three years and years of service

Â·

Annual wage vs. widespread effectivity

rating for the earlier three years and number of associated certifications

Â·

Annual wage vs. years of service and

number of associated certifications

Â·

Annual wage vs. widespread effectivity

rating for the earlier three years, years of service and number of associated

certifications

Hint: Seek advice from

the handouts posted on Blackboard pertaining to decoding regression

statistics as a technique to determine if a given regression model is appropriate. This an identical handout moreover provides steering

regarding strategies to decide on a preferred regression model from amongst numerous

acceptable regression fashions, along with fashions with differing numbers of

neutral variables.

Hint: For the wants

of this homework mission, the minimal distinction between the R2or

Adjusted R2 values for two acceptable fashions with differing numbers

of neutral variables that can favor deciding on the model with the larger

number of neutral variables is zero.03.

Please make certain that you just completely understand the tactic for selecting a

preferred model sooner than making an attempt to make use of this criterion.

Hint: Question 19 is

meant to have you ever ever present that you just simply understand strategies to determine which

univariate fashions are acceptable, after which select a preferred univariate model

from amongst the appropriate univariate fashions. Question 20 is supposed to have you ever ever present

that you just simply understand strategies to determine which bivariate fashions are acceptable, and

then select a preferred bivariate model from amongst the appropriate bivariate

fashions. Question 21 is supposed to have you ever ever present that you just simply

understand strategies to decide on a preferred model from amongst numerous acceptable

fashions which have differing numbers of neutral variables. Question 22 is supposed to have you ever ever

present that you just simply understand strategies to determine if the trivariate model is

acceptable, after which select a preferred model from amongst numerous acceptable

fashions.

Hint: For questions 24

and 25, you should use the regression equation associated to the favored

model chosen for question 22 as a technique to calculate the anticipated wage for

each of the 24 workers. In order to answer questions 24 and 25 you need

to recollect the truth that the anticipated wage value for each employee is simply

a level estimate (this concept was talked about in week one relative to the

suggest). Whereas a level estimate is a actual value, it is not

basically an appropriate value because the normal error value tells us there could also be

some potential diploma of error associated to using the favored regression model

to predict wage values. In order to answer questions 24 and 25 you will

should create an interval estimate (this concept was moreover talked about all through

week one relative to the suggest) for the anticipated wage for each of the 24

workers. To calculate the interval estimate for each employee, merely

multiply the standard error value for the favored regression model by 1.5 and

then subtract this value from the anticipated stage estimate wage value

to stipulate the lower prohibit of the interval estimate and add this value

to the anticipated stage estimate wage value to stipulate the upper prohibit for the

interval estimate. Upon getting created

an interval estimate for each employee, you will then wish to match each

employee’s current wage to their corresponding interval estimate as a technique to determine

if each employee’s current wage falls inside their predicted interval

estimate.

Use the outcomes for the

univariate regression analysis for annual wage vs. widespread effectivity rating

for the earlier three years as a technique to reply questions 1 via 14.

1. What

is the diploma of correlation between the dependent variable and the neutral

variable?

o zero.8198

o zero.6672

o zero.7862

o zero.6523

2. Does

the regression model confirm a optimistic correlation between the dependent

variable and the neutral variable as hypothesized?

o Positive

o No

three. What

is the required statistical significance for the regression model?

o zero.00

o zero.01

o zero.05

o zero.10

4. Is

the statistical significance of the model as a whole decrease than the required

statistical significance for the regression model?

o Positive

o No

5. What

is the exact confidence diploma for the regression model as a whole?

o 99.97%

o 95%

o 90.5%

o 80.2%

6. Is

the statistical significance of the linear relationship between the dependent

and neutral variables decrease than the required statistical significance for

the regression model?

o Positive

o No

7. Should

the coefficient of willpower or adjusted coefficient of willpower be

used to guage this regression model?

o Coefficient

of willpower

o Adjusted

coefficient of willpower

eight. What

share of the observed variation between the exact values of the dependent

variable and the suggest value of the dependent variable throughout the sample information set is

outlined by the regression model?

o 44.51%

o 66.72%

o 41.99%

o 76.24%

9. What

is the amount by which we will be off on widespread when predicting values for the

dependent variable using the regression model?

o $12,287

o $32,966

o $4,169

o $25,896

10. What is the

coefficient for the y-intercept for the regression model?

o 39.38

o 19.94

o 12.29

o 2.96

11. What is the

coefficient for the neutral variable for the regression model?

o 63.08

o 4.52

o 12.29

o 2.96

12. What is the

stage estimate for the anticipated wage for an employee with a imply

effectivity rating of three.9?

o $71,562

o $57,zero06

o $41,299

o $50,896

13. What is the

interval estimate for the anticipated wage for an employee with a imply

effectivity rating of three.9 based upon contemplating the standard

error?

o $61,913

– $71,562

o $57,zero06

– $64,159

o $52,837

– $61,175

o $54,896

– $60,873

14. What is the

95% confidence diploma interval estimate for the wage for an employee with an

widespread effectivity rating of three.9?

o $60,265

â 85,789

o $75,412

– $78,523

o $40,636

– $73,376

o $65,141

– $72,269

Perform a correlation

analysis between the dependent variable and each of the three neutral

variables. Use the outcomes of the

correlation analysis to answer questions 15 and 16.

15. Which

neutral variables proof a optimistic correlation with the dependent

variable?

o

Widespread

effectivity rating for the earlier three years

o

Years

of service

o

Amount

of associated certifications

o All

of the above

o None

of the above

16. Which

neutral variable evidences the perfect diploma of correlation with the

dependent variable?

o

Widespread

effectivity rating for the earlier three years

o

Years

of service

o

Amount

of associated certifications

o All

of the above

o None

of the above

Perform a correlation

analysis between each of the three pairs of neutral variables. Use the outcomes of the correlation analyses

to answer question 17.

17. Which pair

of neutral variable evidences a stage of collinearity that should be set off

for concern when performing multivariate linear regression (i.e., evidences a

diploma of correlation in further of zero.5)?

o

Widespread

effectivity rating for the earlier three years vs. years of service

o

Widespread

effectivity rating for the earlier three years vs. number of associated certifications

o

Years

of service vs. number of associated certifications

o All

of the above

o None

of the above

Use the regression

statistics pertaining to all seven regression analyses as a technique to reply

questions 15 via 23.

18.

Of

the seven regression fashions, which model every accounts for the underside

share of the observed variation between the exact values of the dependent

variable and the suggest value of the dependent variable throughout the sample information set

and evidences the perfect diploma of error for predicting values for the

dependent variable?

o

Annual

wage vs. widespread effectivity rating for the earlier three years

o

Annual

wage vs. years of service

o

Annual

wage vs. number of associated certifications

o

Annual

wage vs. widespread effectivity rating for the earlier three years and years of service

o

Annual

wage vs. widespread effectivity rating for the earlier three years and number of

associated certifications

o

Annual

wage vs. years of service and number of associated certifications

o

Annual

wage vs. widespread effectivity rating for the earlier three years, years of service

and number of associated certifications

19.

If

you may have been to ponder solely the three regression fashions which is likely to be based upon a

single neutral variable, which of the subsequent fashions could possibly be your

preferred model?

o

Annual

wage vs. widespread effectivity rating for the earlier three years

o

Annual

wage vs. years of service

o

Annual

wage vs. number of associated certifications

20.

If

you may have been to ponder solely the three regression fashions which is likely to be based upon two

neutral variables, which of the subsequent fashions could possibly be your preferred

model?

o

Annual

wage vs. widespread effectivity rating for the earlier three years and years of service

o

Annual

wage vs. widespread effectivity rating for the earlier three years and number of

associated certifications

o

Annual

wage vs. years of service and number of associated certifications

21.

If

you may have been to match the favored regression model based upon a single

neutral variable with the favored regression model based upon two

neutral variables, which model could possibly be preferred normal?

o

Hottest

regression model based upon a single neutral variable

o

Hottest

regression model based upon two neutral variables

22.

When

you ponder all seven regression fashions, which is the final preferred regression

model?

o

Annual

wage vs. widespread effectivity rating for the earlier three years

o

Annual

wage vs. years of service

o

Annual

wage vs. number of associated certifications

o

Annual

wage vs. widespread effectivity rating for the earlier three years and years of service

o

Annual

wage vs. widespread effectivity rating for the earlier three years and number of

associated certifications

o

Annual

wage vs. years of service and number of associated certifications

o

Annual

wage vs. widespread effectivity rating for the earlier three years, years of service

and number of associated certifications

23.

Do

any of the regression fashions present a greater confidence diploma for the model as a

whole, or a lower regular error in comparison with the final preferred model?

o

Positive

o

No

The personnel is raring about evaluating each employeeâs

exact wage to their predicted wage as a technique to determine if there are any

prevailing wage inequities. Suppose

the personnel director considers an employeeâs current wage to be truthful and

reasonably priced whether or not it’s inside plus or minus 1.5 regular errors of the price

estimated by the regression model chosen in response to question 22. For each specific particular person employee, calculate his

or her estimated wage using the regression model chosen in response to

question 22, as correctly calculate his or her greater and reduce limits for a very good

reasonably priced wage, as a technique to reply questions 24 and 25.

24.

Of

the 24 workers, what variety of employeesâ current wage is below what’s

considered truthful and reasonably priced?

o

zero

o

1

o

2

o

three

o

4

o

5

25.

Of

the 24 workers, what variety of employeesâ current wage is above what’s

considered truthful and reasonably priced?

o

zero

o

1

o

2

o

three

o

4

o

5