# Winning at Basketball Darren Bloomingdale Michelle Bomer Peter Martin Josh Patsey Matt Mason.

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Winning at Basketball Darren Bloomingdale Michelle Bomer Peter Martin Josh Patsey Matt Mason

The Problem… Does Field Goal percentage and average turnovers per game effect the number of games won during a single season? Thought it was interesting because the Suns are for sale. New owners might be interested in team performance.

Our Data (espn.com) TeamsWins Season Field Goal Percentage (FG%) Average Turnovers Per Game (TO) Correlati on yx1x2 x1x2 Minnesota Timber wolves580.46112.2 5.6242 San Antonio Spurs570.44214 6.188 Dallas Mavericks520.4611.8 5.428 Memphis Grizzlies500.44614.4 6.4224 Houston Rockets450.44215.8 6.9836 Denver Nuggets430.44414.6 6.4824 Utah Jazz420.43615.3 6.6708 Los Angeles Lakers560.45413.4 6.0836 Sacramento Kings550.46313.5 6.2505 Portland Trailblazers410.44813.8 6.1824 Golden State Warriors370.44214.1 6.2322 Seattle SuperSonics370.44513.8 6.141 Phoenix Suns290.44314.6 6.4678

Results Fitted Regression Equation: ŷ = 203 – 293x1 – 26.6x2 + 55.4x1x2 Refitted regression equation ŷ = 74.5 - 17.4 X2 + 34.4 X1X2 where x1=FG%, & x2=TO/Game Hypothesis H0: β1 = β2 = β3 = β4 = 0 H1: At least on β 0.

Regression Analysis The regression equation is Wins = 74.5 - 17.4 TO/Game + 34.4 Correlation Predictor Coef StDev T P Constant 74.53 22.15 3.37 0.002 TO/Game -17.404 3.984 -4.37 0.000 Correlat 34.36 10.07 3.41 0.002 S = 8.439 R-Sq = 46.8% R-Sq(adj) = 42.7% Analysis of Variance Source DF SS MS F P Regression 2 1630.16 815.08 11.44 0.000 Residual Error 26 1851.84 71.22 Total 28 3482.00 Source DF Seq SS TO/Game 1 801.59 Correlat 1 828.57 Unusual Observations Obs TO/Game Wins Fit StDev Fit Residual St Resid 21 13.0 21.00 39.90 3.10 -18.90 -2.41R 21 13.0 21.00 39.90 3.10 -18.90 -2.41R 22 13.6 61.00 41.57 1.95 19.43 2.37R 22 13.6 61.00 41.57 1.95 19.43 2.37R R denotes an observation with a large standardized residual

Matrix of scatter plots for the FG% TO/Game data

Normal Probability Plot of the residuals

Residuals Versus the fitted values

Residuals vs. the Fitted Values Response is ln(Wins)

Conclusion Best fits the data is: ŷ = 74.5 - 17.4* TO/Game + 34.4* FG%*TO/Game R 2 value of only 46.8% suggests this model is a poor fit Plots of the transformations indicated that the residuals are not completely random

To answer the question… Yes - field goal percentage and the average number of turnovers per game, during a season, have an effect on the number of games a team wins that season, however additional factors and possibly correlations are necessary to model the data well enough to make future predictions. For future research we suggest another model that includes such factors as Free Throw %, Rebounds, Blocks, Steals or Assists.

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