Chapter 13, Problem 47CE

A sports enthusiast created an equation to predict Victories (the team’s number of victories in the National Basketball Association regular season play) using predictors FGP (team field goal percentage), FTP (team free throw percentage), Points (team average points per game), Fouls (team average number of fouls per game), TrnOvr (team average number of turnovers per game), and Rbnds (team average number of rebounds per game). The fitted regression was Victories = −281 + 523 FGP + 3.12 FTP + 0.781 Points − 2.90 Fouls + 1.60 TrnOvr + 0.649 Rbnds (R2 = .802, F = 10.80, SE = 6.87). The strongest predictors were FGP (t = 4.35) and Fouls (t = −2.146). The other predictors were only marginally significant and FTP and Rbnds were not significant. The matrix of correlations is shown below. At the time of this analysis, there were 23 NBA teams. (a) Do the signs of the regression coefficients make sense? (b) Is the intercept meaningful? Explain. (c) Is the sample size a problem (using Evans’ Rule or Doane’s Rule)? (d) Why might collinearity account for the lack of significance of some predictors?

(Source: Data are from a research project by MBA student Michael S. Malloy.)