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After watching his Michigan Men’s Basketball Team fall short against the Arizona Wildcats, coach… 1 answer below »

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After watching his Michigan Men’s Basketball Team fall short against the Arizona Wildcats, coach John Beilein wishes to explore the correlation between height and rebounding ability to see whether or not he should try playing with a bigger lineup. Using the given dataset (Lab1_Data.xls), answer the following questions.

 

a)      (1 point) Using Minitab, construct a scatter plot of the data and paste the graph (with x-axis: height, y-axis: rebounding percentage).

 

b)      (1 point) Assuming a linear relationship between two indices, make a wild guess of the slope of linear regression equation (explanatory variable: height, response variable: rebounding percentage) only based on the scatter plot in (a). Please provide a brief explanation of how you obtained the answer.

 

The following questions, (c)-(d), should be answered using Excel (To obtain the full credit for these questions, make sure that the Excel sheet used for calculation is attached when you submit the assignment).

c)      (2 points) Obtain the least squares estimate of the slope coefficient.

 

d)     (2 points) Obtain the least squares estimate of the intercept.

 

e)      (1 point) State the simple linear regression equation based on your answers in (c) and (d).

 

f)       (2 points) Use Minitab to fit a simple linear regression model relating height (x) to rebounding percentage (y). Paste the Minitab output and identify the regression equation, the least squares estimate of the slope coefficient, and the least squares estimate of the intercept (You may want to utilize Minitab outputs to confirm your answers in (c)-(e)).

 

g)      (1 point) Add a linear regression line to the scatter plot obtained in (a) and paste the result.

 

SUMMARY OUTPUT

 
   

Regression Statistics

Multiple R

0.717082622

R Square

0.514207487

Adjusted R Square

0.473724777

Standard Error

4.112177482

Observations

14

 

ANOVA

         

 

df

SS

MS

F

Significance F

Regression

1

214.789242

214.789242

12.70190395

0.003895294

Residual

12

202.9200437

16.91000364

   

Total

13

417.7092857

 

 

 

 

 

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Lower 95.0%

Upper 95.0%

Intercept

-77.75821678

24.93052993

-3.118995745

0.008871349

-132.0771752

-23.43925838

-132.0771752

-23.43925838

Height (in.)

1.146416084

0.321668

3.563973056

0.003895294

0.44556172

1.847270448

0.44556172

1.847270448

 

RESIDUAL OUTPUT

     
       

Observation

Predicted Rebounding %

Residuals

Standard Residuals

1

3.637325175

2.262674825

0.572705491

2

4.783741259

0.616258741

0.155981214

3

11.66223776

-3.662237762

-0.926948784

4

10.51582168

-4.415821678

-1.117688364

5

16.2479021

3.052097902

0.77251632

6

13.95506993

2.24493007

0.568214118

7

11.66223776

-1.962237762

-0.496661884

8

11.66223776

-5.762237762

-1.45847966

9

16.2479021

-1.047902098

-0.265234438

10

12.80865385

4.791346154

1.212737342

11

9.369405594

0.130594406

0.033054742

12

7.076573427

7.123426573

1.80301008

13

16.2479021

2.352097902

0.595339361

14

8.22298951

-5.72298951

-1.448545537

 

 

PROBABILITY OUTPUT

 
   

Percentile

Rebounding %

3.571428571

2.5

10.71428571

5.4

17.85714286

5.9

25

5.9

32.14285714

6.1

39.28571429

8

46.42857143

9.5

53.57142857

9.7

60.71428571

14.2

67.85714286

15.2

75

16.2

82.14285714

17.6

89.28571429

18.6

96.42857143

19.3

 

 

 

 

 

Height and Rebounding Ability

   

Original source: sports-reference.com, Accesed 1/10/2014

 
     
     
     

Player

Height (in.)

Rebounding %

Nik Stauskas

78

6.3

Glenn Robinson

78

9.1

Zak Irvin

78

7.2

Cole McConnell

77

20.3

Mitch McGary

82

20.6

Caris LeVert

78

5.1

Jordan Morgan

80

7.1

Jon Horford

82

15.9

Derrick Walton

73

5.8

Sean Lonergan

77

13.6

Max Bielfeldt

79

19

Spike Albrecht

71

10.3

Andrew Dakich

74

7.7

Brad Anlauf

76

6.2

 

 

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