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 2010–11 National Basketball Association (NBA) regular season. The data stored in NBAStandings 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 (1) predicting WinPct using PtsFor and (2) 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) The eventual NBA champion Dallas Mavericks averaged scoring 100.2 points per game while giving up an average of 96.0 points against. Find the predicted winning percentage for the Mavericks using each of the models in (b) and (c).
(e) Overall, which predictor, PtsFor or PtsAgainst, appears to be more effective at explaining winning percentages for NBA teams? Give some justification for your answer.
(f) Compare and interpret R² for both models.