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 2018–2019 National Basketball Association (NBA) regular season. The data stored in NBAS tandings 2019 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 WinPct using Pts For and predicting WinPct using Pts Against. 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 R² for both models.

(e) The eventual NBA playoff champion Toronto Raptors won 58 games in the regular season while losing only 24 games (WinPct = 0.707). They scored an average of 114.4 points per game while giving up an average of 108.4 points against. Find the predicted winning percentage for the Raptors 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.