Question

Question 100)

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.

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

Wini=b0+b1FieldGoali+b2Threepoint+ei

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 level of significance using the following hypothesis? (Use the p-values to explain without using t-table)

a. Ho: β1=0, Ha:β1≠0

b. Ho: β2=0, Ha:β2≠0 $N+0gAAAABJRU5ErkJggg==$

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

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

9) 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.

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

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Answer 1

A required 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 is given as below:

Regression Statistics
Multiple R	0.692945243
R Square	0.48017311
Adjusted R Square	0.441667414
Standard Error	9.132542725
Observations	30
ANOVA
	df	SS	MS	F	Significance F
Regression	2	2080.109911	1040.054956	12.47018402	0.000145913
Residual	27	2251.890089	83.40333662
Total	29	4332
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	-263.4928464	63.09278893	-4.176275147	0.000277207	-392.9485546	-134.0371381
Field Goal %	4.409542804	1.242684914	3.548399723	0.001442028	1.859764005	6.959321604
Three-Point Field Goal %	2.806937603	1.656982407	1.694005676	0.101771186	-0.592909427	6.206784632

5)
p-value of Fied Goal (b1) = 0.00144 < alpha
hence it is significant

whereas p-value of Three-point fireld goal(b2) is 0.1018 > alpha
hence it is not significant

7)

r^2 = 0.4802

this means 48.02 % of variation in the number of wins can be explained by this model

8)
adjusted R^2 = 0.4417
= 1 - (1-R^2)(n-1)/(n-k-1)
= 1 - (1- 0.480173)*29/27
= 0.441667

r^2 always increases when we increase more independent variables
but adjusted r^2 penalizes for adding more independent variables
hence for multiple regression, adjusted r^2 is more useful

9)

From this regression model, the p-value or overall model is given as 0.0001459 which is very less than alpha value 0.05,
so we reject the null hypothesis that the given regression model is not statistically significant.
There is sufficient evidence to conclude that this regression model is statistically significant for prediction of the wins for a team.

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