Professional basketball has truly become a sport that generates interest among fans around the world. More and more players come from outside the United States to play in the National Basketball Association (NBA). You want to develop a regression model to predict the number of wins achieved by each NBA team, based on field goal (shots made) percentage for the team and for the opponent. The data are stored in NBA2010.
a. State the multiple regression equation.
b. Interpret the meaning of the slopes in this equation.
c. Predict the number of wins for a team that has a field goal percentage of 45% and an opponent field goal percentage of 44%.
d. Perform a residual analysis on your results and determine whether the regression assumptions are valid.
e. Is there a significant relationship between number of wins and the two independent variables (field goal percentage for the team and for the opponent) at the 0.05 level of significance?
f. Determine the p-value in (e) and interpret its meaning.
g. Interpret the meaning of the coefficient of multiple determination in this problem.
h. Determine the adjusted r2.
i. At the 0.05 level of significance, determine whether each independent variable makes a significant contribution to the regression model. Indicate the most appropriate regression model for this set of data.
j. Determine the p-values in (i) and interpret their meaning.
k. Compute and interpret the coefficients of partial determination.