GSB519 Homework WEEK9

INBA (30 points, 2 points each and 4 point for Q14)

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 and three-point field goal percentage. The data are stored in NBA.xlsx .

1) Estimate the following multiple regression model (copy and paste the results from either Minitab or Excel).

2) Interpret the meanings of the coefficients of the regression model.

3) Predict the mean number of wins for a team that has a field goal percentage of 45% and a three-point field goal percentage of 35%.

4) Perform a residual analysis on your results and determine whether the regression assumptions are valid.

5) Using t-test, show if the field goal percent or the three point field goal percent are significant at the 0.05 significance level for the following hypothesis? (Use the p-values to explain without using t-table)

a.

b.

6) Interpret the meaning of the coefficient of multiple determination (r²) in this problem.

7) Show how to calculate the adjusted r². Explain the difference between r² and adjusted r².

8) At the 0.05 level of significance, perform a F test to determine whether the regression model has any significant variable. Setup your hypothesis and perform the test using p-value to explain.

9) Show how to compute the 95% confidence interval of the estimated coefficients and explain their meanings.

10) The conference is a character variable. Using a dummy variable, find if the number of wins matters with the conference. Using t test, prove if the conference is an important variable on the number of wins at 5% significance level.

11) Let's estimate the following with interactive dummy variable. Carefully explain the meanings of the coefficient for the variables related with dummy variables.

12) Suppose, the Chicago bulls has 45% field goal and 35% of three-point field goal, what are the predicted wins from the regression models in 1), 11) and 12)?

13) Compare R square and adjusted R square for the three regression models 1),11), and 12). Explain which model is the best in terms of the goodness-to-fit.

14)Using the NBA data, develop the best model to predict the number of wins using the variables given. You can add/remove any variables or even combine variables if necessary. There two criteria to evaluate the model.

First, the highest adjusted r square among any alternative models.

Second, all included independent variables are significant at least at 10 % and have meaningful signs and magnitude.

You need to demonstrate why your model is the best comparing to other possible models. Full/Partial credit is possible for this question. (4 points)

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