Question

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

TEAM	Wins	Field Goal %	Three-Point Field Goal %	Points Per Game	Rebound	Freedraw	Turnover
Houston Rockets	65	46	36.2	112.4	43.5	19.6	13.8
Toronto Raptors	59	47.2	35.8	111.7	44	17.3	13.4
Golden State Warriors	58	50.3	39.1	113.5	43.5	16.6	15.4
Boston Celtics	55	45	37.7	104	44.5	16	14
Philadelphia 76ers	52	47.2	36.9	109.8	47.4	17.1	16.5
Cleveland Cavaliers	50	47.6	37.2	110.9	42.1	18.1	13.7
Portland Trail Blazers	49	45.2	36.6	105.6	45.5	16.7	13.5
Indiana Pacers	48	47.2	36.9	105.6	42.3	14.9	13.3
New Orleans Pelicans	48	48.3	36.2	111.7	44.3	16.1	14.9
Oklahoma City Thunder	48	45.3	35.4	107.9	45.1	17.3	14
Utah Jazz	48	46.2	36.6	104.1	43.3	16.8	14.7
Minnesota Timberwolves	47	47.6	35.7	109.5	42	19.4	12.5
San Antonio Spurs	47	45.7	35.2	102.7	44.2	16.1	13.1
Denver Nuggets	46	47	37.1	110	44.5	17.1	15
Miami Heat	44	45.5	36	103.4	43.5	14.7	14.4
Milwaukee Bucks	44	47.8	35.5	106.5	39.8	18.3	13.8
Washington Wizards	43	46.7	37.5	106.6	43.1	16.8	14.6
LA Clippers	42	47.1	35.4	109	43.9	19	14.7
Detroit Pistons	39	45	37.3	103.8	43.7	14.7	13.4
Charlotte Hornets	36	45	36.9	108.2	45.5	20.2	12.7
Los Angeles Lakers	35	46.1	34.5	108.1	46.4	16.6	15.8
New York Knicks	29	46.4	35.2	104.5	44	14.9	14.7
Brooklyn Nets	28	44.1	35.6	106.6	44.4	17.4	15.2
Chicago Bulls	27	43.5	35.5	102.9	44.7	14.6	14
Sacramento Kings	27	45	37.5	98.8	40.9	12.3	13.7
Orlando Magic	25	45.2	35.1	103.4	41.6	15.5	14.5
Atlanta Hawks	24	44.6	36	103.4	41.9	15.8	15.5
Dallas Mavericks	24	44.4	36	102.3	41.3	14.2	12.3
Memphis Grizzlies	22	44.4	35.2	99.3	40.5	16.6	15
Phoenix Suns	21	44.2	33.4	103.9	44.1	17.7	15.7

1) At the 0.05 level of significance, perform a F test to determine whether the regression model has any significant variable. Use p-value to explain.

Answer 1

Solution:

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

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.

Also, it is observed that the independent variable or explanatory variable Three-Point Field Goal is not a statistically significant variable because the p-value for this coefficient of this variable is given as 0.1018 which is greater than the alpha value 0.05.