Eastern Conference Team (NBA) Free Throw Percentage Win Percentage Indiana .779

Question

Eastern Conference Team (NBA)

Free Throw Percentage

Win Percentage

Indiana

.779

.683

Miami

.760

.659

Toronto

.782

.585

Chicago

.779

.585

Washington

.731

.537

Brooklyn

.753

.537

Charlotte

.737

.524

Atlanta

.781

.463

New York

.761

.451

Cleveland

.751

.402

Detroit

.670

.354

Boston

.777

.305

Orlando

.763

.280

Philadelphia

.710

.232

Milwaukee

.747

.183

Use the above chart to answer the following questions.

1) Calculate the sample correlation coefficient, r.

2) At a=.01 can you conclude there is a significant linear correlation between free throw percentage and percent of games won?

3) Use the calculator to produce the line of best fit.

4) Using the line of best fit, estimate the percent of games an Eastern Conference NBA team would win if they had a free through percentage of 60%. Is this a reasonable estimate? Why or why not?

5) Given the analysis you did above, would you advise an NBA coach to drill your players on free throws to improve your win percentage? Why or why not?

Eastern Conference Team (NBA)

Free Throw Percentage

Win Percentage

Indiana

.779

.683

Miami

.760

.659

Toronto

.782

.585

Chicago

.779

.585

Washington

.731

.537

Brooklyn

.753

.537

Charlotte

.737

.524

Atlanta

.781

.463

New York

.761

.451

Cleveland

.751

.402

Detroit

.670

.354

Boston

.777

.305

Orlando

.763

.280

Philadelphia

.710

.232

Milwaukee

.747

.183

Explanation / Answer

1) We calculate this in Excel with the function CORREL which gives the value of r =0.3913

2) Test statistic to check whether it is significant correlation

Test statistic = t= r*sqrt(n-2)/sqrt(1-r^2) =0.3913*sqrt(15-2)/sqrt(1-0.3913^2) = 1.5331

P(T<t) = 0.9262

Hence we accept the hypothesis that there there is no significant linear correlation at alpha =0.01

3) Please find below Linear regression resuts from Excel:

SUMMARY OUTPUT Regression Statistics Multiple R 0.391327 R Square 0.153137 Adjusted R Square 0.087994 Standard Error 0.147815 Observations 15 ANOVA df SS MS F Significance F Regression 1 0.051362 0.051362 2.350771 0.149191 Residual 13 0.28404 0.021849 Total 14 0.335402 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept -1.02755 0.965746 -1.06399 0.306697 -3.11391 1.058821 -3.11391 1.058821 Free Throw Percentage 1.967307 1.283119 1.533222 0.149191 -0.8047 4.739317 -0.8047 4.739317

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