You can use excel. X University has contacted us in an effort to better understa

Question

You can use excel.

X University has contacted us in an effort to better understand the outcome of business students seeking a Bachelor of Business degree in Australia. In particular, they wish to seek what is a larger driver of student outcomes, student satisfaction with their program or the prerequisites of students arriving at the university. We have collected information on the average salary of business graduates from 39 universities across Australia.  

a. Is the coefficient estimate for the ATAR requirement statistically different than zero at the 5% level of significance? Set-up the correct hypothesis test using the results found in the table in Part (G) using both the critical value and p-value approach. Interpret the coefficient estimate of the slope.  

b. Interpret the remaining slope coefficient estimates. Discuss whether the signs are what you are expecting and explain your reasoning.

c. Interpret the value of the Adjusted R2. Is there a large difference between the R2 and the Adjusted R2? If so, what may explain the reasoning for this?

d.Based on the results of the regressions, what other factors would have influenced graduate salary? Provide a couple possible examples and indicate their predicted relationship with graduate salary if they were included.

Business School Salary Satisfaction ATAR G8 ATN VIC QLD SA NSW WA OTHER Australian Catholic University 37251 84 59 0 0 1 0 0 0 0 0 Australian National University 50385 80 82 1 0 0 0 0 0 0 1 Bond University 41729 86 50 0 0 0 1 0 0 0 0 Charles Darwin University 55675 83 60 0 0 0 0 0 0 0 1 Charles Sturt University 55136 79 65 0 0 1 0 0 0 0 0 CQUniversity 49456 84 52 0 0 0 1 0 0 0 0 Curtin University 42062 81 70 0 1 0 0 0 0 1 0 Deakin University 41551 86 53 0 0 1 0 0 0 0 0 Edith Cowan University 44343 89 55 0 0 0 0 0 0 1 0 Federation University Australia 41638 82 50 0 0 1 0 0 0 0 0 Flinders University 41464 84 60 0 0 0 0 1 0 0 0 Griffith University 40960 84 59 0 0 0 1 0 0 0 0 James Cook University 39881 81 49 0 0 0 1 0 0 0 0 La Trobe University 39612 82 50 0 0 1 0 0 0 0 0 Macquarie University 40692 80 80 0 0 0 0 0 1 0 0 Monash University 43928 85 82 1 0 1 0 0 0 0 0 Murdoch University 42078 76 70 0 0 0 0 0 0 1 0 Queensland University of Technology 43006 89 62 0 1 0 1 0 0 0 0 RMIT University 41897 75 70 0 1 1 0 0 0 0 0 Southern Cross University 44297 79 61 0 0 0 0 0 1 0 0 Swinburne University of Technology 39930 87 60 0 0 1 0 0 0 0 0 University of Adelaide 42946 80 80 1 0 1 0 0 0 0 0 University of Canberra 47485 82 68 0 0 0 0 0 0 0 1 University of Melbourne 57296 86 95 1 0 1 0 0 0 0 0 University of New England 55778 88 73 0 0 0 0 0 1 0 0 University of New South Wales 49665 78 96 1 0 0 0 0 1 0 0 University of Newcastle 45869 84 61 0 0 0 1 0 0 0 0 University of Notre Dame Australia 43728 84 70 0 0 0 0 0 0 1 0 University of Queensland 43860 83 81 0 0 0 1 0 0 0 0 University of South Australia 42939 88 65 0 1 0 0 1 0 0 0 University of Southern Queensland 52027 83 59 0 0 0 1 0 0 0 0 University of Sydney 52414 77 95 1 0 0 0 0 1 0 0 University of Tasmania 44345 75 65 1 0 0 0 0 0 0 1 University of Technology, Sydney 41782 84 69 0 1 0 0 0 1 0 0 University of the Sunshine Coast 34000 89 52 0 0 0 0 0 1 0 0 University of Western Australia 49003 79 80 1 0 0 0 0 0 1 0 University of Wollongong 46703 91 70 0 0 0 0 0 1 0 0 Victoria University 36321 73 50 0 0 1 0 0 0 0 0 Western Sydney University 40806 84 65 0 0 0 0 0 1 0 0

Explanation / Answer

SUMMARY OUTPUT

Regression Statistics

Multiple R

0.632738048

R Square

0.400357437

Adjusted R Square

0.179778711

Standard Error

4924.743851

Observations

39

ANOVA

df

SS

MS

F

Significance F

Regression

10

469592055

46959205

2.151349341

0.053929079

Residual

29

703339958

24253102

Total

39

1172932013

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Lower 95.0%

Upper 95.0%

Intercept

8703.902

19271.94

0.451636

0.65489

-30712

48119

-30712

48119.441

Satisfaction

195.0207

205.6479

0.948323

0.3508

-225.58

615.62

-225.58

615.61794

ATAR

290.0331

101.9312

2.84538

0.00806

81.5603

498.51

81.56

498.50579

G8

-1765.05

3238.397

-0.54504

0.58989

-8388.3

4858.2

-8388.3

4858.2146

ATN

-2802.5

2570.932

-1.09007

0.28466

-8060.6

2455.6

-8060.6

2455.646

VIC

677.5906

4021.503

0.168492

0.86737

-7547.3

8902.5

-7547.3

8902.4883

QLD

2666.21

4026.109

0.66223

0.51305

-5568.1

10901

-5568.1

10900.527

SA

0

0

65535

#NUM!

0

0

0

0

NSW

-426.99

4088.043

-0.10445

0.91753

-8788

7934

-8788

7933.9971

WA

487.4321

4284.824

0.113758

0.91021

-8276

9250.9

-8276

9250.8802

OTHER

6109.693

4648.842

1.31424

0.19907

-3398.3

15618

-3398.3

15617.641

a)H0 = the regression coefficient of ATAR is not significant that is 2=0

H1 = the regression coefficient of ATAR is significant that is 20

The p-value of regression coefficient of ATAR is 0.00806

Since the p-value =0.00806 < 0.05, we reject the null hypothesis and hence conclude that ATAR is significant in the model.

b) The p-value of all the other slope coefficients is greater than 0.05, which indicates that they are not significant in the model.

The regression coefficients of G8, ATN and NSW are negative. This indicates that for a unit change in the variables, it reduces the salary.

c) R-square = 0.4003

Adjusted R-square =0.179

R-square gives importance to all the independent variables which are significant and not significant in the model.

But adjusted R-square gives importance only to the significant variables that is which doesn’t produce much standard error.

In this model, there are many insignificant variables. Therefore, there is a large difference between adjusted R square and R square.

d)There is a possibility of multicollinearity. Dealing this problem would give a better model.   

SUMMARY OUTPUT

Regression Statistics

Multiple R

0.632738048

R Square

0.400357437

Adjusted R Square

0.179778711

Standard Error

4924.743851

Observations

39

ANOVA

df

SS

MS

F

Significance F

Regression

10

469592055

46959205

2.151349341

0.053929079

Residual

29

703339958

24253102

Total

39

1172932013

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