After watching his Michigan Men’s Basketball Team fall short against the Arizona Wildcats, coach… 1 answer below »
 September 24, 2021 /
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Problem Description:
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 xaxis: height, yaxis: 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 
Pvalue 
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: sportsreference.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 