Discussion:
Q1) Two candidates for governor participated in a televised debate. A political pollster recorded the preferences of 500 registered voters in a random sample prior to and after the debate:
Preference After Debate
Preference Prior Candidate A Candidate B Total
To Debate
Candidate A 269 21 290
Candidate B 36 174 210
Total 305 195 500
a. At the 0.01 level of significance, is there evidence of a difference in the proportion of voters who favored Candidate A prior to and after the debate?
b. Compute the p-value in (a) and interpret its meaning.
Q2) Professional basketball has truly become a sport that generates interest among fans around the world. More and more players come from outside the U.S. to play in the 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 is stored in the attached file: NBA2009.
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 level of 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.
| Team |
Wins |
Points Scored |
Points Allowed |
Point Difference |
Field Goal% |
Field Goal % Allowed |
Field Goal % Difference |
Own Turnovers |
Opponent Turnovers |
Turnover Difference |
Offensive Rebound % |
Defensive Rebound % |
| Atlanta |
47 |
98.1 |
96.5 |
1.6 |
45.8% |
45.4% |
0.4% |
12.8 |
13.7 |
-0.9 |
26.0% |
71.6% |
| Boston |
62 |
100.9 |
93.4 |
7.5 |
45.6% |
43.1% |
2.5% |
15.6 |
14.6 |
1.0 |
27.9% |
75.6% |
| Charlotte |
35 |
93.6 |
94.9 |
-1.3 |
45.5% |
45.4% |
0.1% |
15.6 |
14.7 |
0.9 |
27.7% |
73.0% |
| Chicago |
41 |
102.2 |
102.5 |
-0.3 |
45.7% |
45.8% |
-0.1% |
14.5 |
14.4 |
0.1 |
28.0% |
70.9% |
| Cleveland |
66 |
100.3 |
91.4 |
8.9 |
46.8% |
43.1% |
3.7% |
12.7 |
13.9 |
-1.2 |
27.7% |
74.6% |
| Dallas |
53 |
101.7 |
99.8 |
1.9 |
46.2% |
45.5% |
0.7% |
12.7 |
13.0 |
-0.3 |
26.6% |
74.6% |
| Denver |
54 |
104.3 |
100.9 |
3.4 |
47.0% |
44.0% |
3.0% |
15.3 |
15.4 |
-0.1 |
27.5% |
71.7% |
| Detroit |
39 |
94.2 |
94.7 |
-0.5 |
45.4% |
45.1% |
0.3% |
11.9 |
11.8 |
0.1 |
27.9% |
74.0% |
| Golden State |
29 |
106.6 |
112.3 |
-5.7 |
45.8% |
46.8% |
-1.0% |
14.6 |
15.0 |
-0.4 |
26.1% |
68.1% |
| Houston |
53 |
98.4 |
94.4 |
4.0 |
45.3% |
44.4% |
0.9% |
14.1 |
12.3 |
1.8 |
26.4% |
75.3% |
| Indiana |
36 |
105.1 |
106.2 |
-1.1 |
45.5% |
45.8% |
-0.3% |
14.5 |
14.0 |
0.5 |
25.4% |
74.5% |
| L. A. Clippers |
19 |
95.1 |
103.0 |
-7.9 |
44.1% |
47.3% |
-3.2% |
14.9 |
13.3 |
1.6 |
25.1% |
71.2% |
| L.A. Lakers |
65 |
106.9 |
99.3 |
7.6 |
47.4% |
44.7% |
2.7% |
13.5 |
15.5 |
-2.0 |
29.4% |
73.0% |
| Memphis |
24 |
93.9 |
99.3 |
-5.4 |
45.4% |
47.3% |
-1.9% |
15.3 |
14.6 |
0.7 |
25.8% |
73.5% |
| Miami |
43 |
98.3 |
98.0 |
0.3 |
45.7% |
45.5% |
0.2% |
12.5 |
15.2 |
-2.7 |
24.6% |
72.9% |
| Milwaukee |
34 |
99.3 |
100.4 |
-1.1 |
44.5% |
45.8% |
-1.3% |
14.1 |
16.5 |
-2.4 |
27.8% |
74.0% |
| Minnesota |
24 |
97.8 |
102.7 |
-4.9 |
44.1% |
47.4% |
-3.3% |
14.2 |
12.5 |
1.7 |
27.7% |
75.0% |
| New Jersey |
34 |
98.1 |
100.5 |
-2.4 |
44.8% |
46.2% |
-1.4% |
13.1 |
13.5 |
-0.4 |
25.2% |
73.5% |
| New Orleans |
49 |
95.8 |
94.3 |
1.5 |
45.7% |
45.0% |
0.7% |
12.5 |
13.3 |
-0.8 |
24.6% |
74.9% |
| New York |
32 |
105.2 |
107.8 |
-2.6 |
44.5% |
48.0% |
-3.5% |
14.3 |
14.5 |
-0.2 |
24.4% |
72.7% |
| Oklahoma City |
23 |
97.0 |
103.1 |
-6.1 |
44.7% |
47.5% |
-2.8% |
16.2 |
13.9 |
2.3 |
28.6% |
73.9% |
| Orlando |
59 |
101.0 |
94.4 |
6.6 |
45.7% |
43.3% |
2.4% |
13.9 |
13.1 |
0.8 |
24.0% |
75.9% |
| Philadelphia |
41 |
97.4 |
97.3 |
0.1 |
45.9% |
46.2% |
-0.3% |
14.1 |
15.6 |
-1.5 |
31.3% |
71.4% |
| Phoenix |
46 |
109.4 |
107.5 |
1.9 |
50.4% |
46.7% |
3.7% |
15.7 |
14.2 |
1.5 |
27.7% |
71.7% |
| Portland |
54 |
99.4 |
94.1 |
5.3 |
46.5% |
46.0% |
0.5% |
12.9 |
13.2 |
-0.3 |
32.6% |
75.0% |
| Sacramento |
17 |
100.6 |
100.3 |
0.3 |
44.7% |
48.3% |
-3.6% |
15.4 |
14.4 |
1.0 |
24.5% |
69.9% |
| San Antonio |
54 |
97.0 |
93.3 |
3.7 |
46.6% |
45.3% |
1.3% |
11.7 |
13.7 |
-2.0 |
22.1% |
78.0% |
| Toronto |
33 |
99.0 |
101.9 |
-2.9 |
45.8% |
46.5% |
-0.7% |
13.4 |
13.3 |
0.1 |
24.0% |
73.7% |
| Utah |
48 |
103.6 |
100.9 |
2.7 |
47.5% |
46.4% |
1.1% |
14.8 |
16.1 |
-1.3 |
28.2% |
72.7% |
| Washington |
19 |
96.1 |
103.5 |
-7.4 |
45.0% |
46.2% |
-1.2% |
14.0 |
13.9 |
0.1 |
27.7% |
71.4% |