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Chapter 9: Problem 28

A common (and hotly debated) saying among sports fans is "Defense wins championships." Is offensive scoring ability or defensive stinginess a better indicator of a team's success? To investigate this question we'll use data from the \(2015-2016\) National Basketball Association (NBA) regular season. The data \(^{6}\) stored in NBAStandings2016 include each team's record (wins, losses, and winning percentage) along with the average number of points the team scored per game (PtsFor) and average number of points scored against them ( PtsAgainst). (a) Examine scatterplots for predicting \(\operatorname{WinPct}\) using PtsFor and predicting WinPct using PtsAgainst. In each case, discuss whether conditions for fitting a linear model appear to be met. (b) Fit a model to predict winning percentage (WinPct) using offensive ability (PtsFor). Write down the prediction equation and comment on whether PtsFor is an effective predictor. (c) Repeat the process of part (b) using PtsAgainst as the predictor. (d) Compare and interpret \(R^{2}\) for both models. (e) The Golden State Warriors set an NBA record by winning 73 games in the regular season and only losing 9 (WinPct \(=0.890\) ). They scored an average of 114.9 points per game while giving up an average of 104.1 points against. Find the predicted winning percentage for the Warriors using each of the models in (b) and (c). (f) Overall, does one of the predictors, PtsFor or PtsAgainst, appear to be more effective at explaining winning percentages for NBA teams? Give some justification for your answer.

Short Answer

Expert verified
This answer would be based on the analysis of scatterplots, evaluation of linear regression models, comparison and interpretation of \(R^{2}\) values, and application & review of the models based on data for Golden State Warriors.

Step by step solution

01

Scatterplot & Linear Model Conditions

Plot the scatterplots for both \(WinPct\) vs \(PtsFor\) and \(WinPct\) vs \(PtsAgainst\). Check if the conditions for a linear model are met - Linearity, Independence, Normality and Equal Variance (LINE condition)
02

Linear Model: Offensive Ability as Predictor

Use a linear regression tool to fit a model using \(PtsFor\) as the predictor for \(WinPct\). Document the prediction equation. Also, comment on whether \(PtsFor\) is an effective predictor based on the output statistics including the p-value, confidence intervals and other regression diagnostics.
03

Linear Model: Defensive Ability as Predictor

Repeat the process in step 2 but replace \(PtsFor\) with \(PtsAgainst\) as the predictor. Document the prediction equation.
04

Compare the Models

Compare and interpret \(R^{2}\) for both models. A higher \(R^{2}\) value tends to indicate a better fit to the data.
05

Predict Winning Percentage For The Warriors

Plug in the data for the Golden State Warriors (scored an average of 114.9 points per game and average of 104.1 points against per game) into both models to predict their winning percentage.
06

Evaluate Effectiveness of Predictors

Based on all the previous analyses, finally conclude which predictor, \(PtsFor\) or \(PtsAgainst\), appears to be more effective at explaining winning percentages for NBA teams, citing the reasons for your decision.

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