# 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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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