Question

Suppose an athletic director would like to develop a regression model to predict the point differential for games played by the college's men's basketball team. A point differential is the difference between the final points scored by two competing teams. A positive differential is a win, and a negative differential is a loss. For a random sample of home and away games, the point differential was calculated, along with the number of assists, rebounds, and turnovers. The data are given in the accompanying table. Complete parts a through d below.

Point_Differential   Assists   Rebounds   Turnovers   Location
38   19   42   9   Home
15   21   28   7   Home
45   22   47   11   Home
13   11   40   7   Away
-11   10   31   13   Away
11   19   45   11   Home
11   16   33   16   Away
4   16   28   18   Away
20   9   34   17   Home
40   16   41   9   Away
43   12   28   9   Home
17   17   36   13   Home
12   21   21   9   Away
11   14   33   19   Home
14   20   36   18   Home
9   12   41   14   Home
-1   8   31   8   Away
11   15   27   10   Away
-15   10   47   11   Away
-4   12   21   9   Home
5   13   28   12   Home
16   12   25   8   Home
-2   16   27   12   Away
-3   6   33   12   Home
2   13   36   20   Away
2   7   43   13   Away
-4   14   31   12   Home
-14   17   24   12   Home
-20   18   18   9   Away
-10   4   22   8   Away
-2   6   21   9   Away
-4   10   32   8   Away
23   16   38   8   Home
38   19   42   15   Home
0   9   42   16   Away
7   12   39   13   Home
13   8   46   22   Away
17   17   27   13   Home
19   14   39   13   Home
9   19   41   14   Away
7   16   39   16   Away
-11   12   23   9   Away
37   19   45   10   Away
34   15   39   12   Home
3   13   31   7   Away
28   19   38   14   Home
2   17   25   12   Home
8   10   33   21   Away
4   16   36   11   Home
26   14   49   12   Away

a. Using technology, construct a regression model using all of the independent variables. (Let variable Loc be the dummy variable for the location. Assign a 1 to a home game.)

Complete the regression equation for the model below, where y=Point Differential,x1=Assists,x2=Rebounds,x3=Turnovers,and x4=Loc.

y=_+(_)x1+(_)x2+(_)x3+(_)x4

Interpret the meaning of the regression coefficient for the dummy variable. Select the correct choice below and fill in the answer box to complete your choice

a. the team scores an average of _ more points in home games than away games

b. the home game point differential averages _ fewer points per game than away games.

c. the team scores an average of _ fewer points in home games than away games.

d. the home game point differential averages _ more points per game than away games.

A test for the significance of the overall regression model shows that it is significant using alpha=0.05. Using the p-values, identify which independent variables are significant with alpha=0.05

a. Loc

b. turnovers

c. assists

d. rebounds

Answer 1

using Excel

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.677668649
R Square	0.459234798
Adjusted R Square	0.41116678
Standard Error	12.12086343
Observations	50
ANOVA
	df	SS	MS	F	Significance F
Regression	4	5614.430136	1403.607534	9.553853439	1.11438E-05
Residual	45	6611.189864	146.9153303
Total	49	12225.62
	Coefficients	Standard Error	t Stat	P-value	Lower 95%
Intercept	-36.11425613	9.758677132	-3.700732757	0.000583685	-55.76924081
Assist	1.14798184	0.421965171	2.720560654	0.009231476	0.29810036
Rebounds	0.95310592	0.226909971	4.200370383	0.00012434	0.49608578
Turnover	-0.476659788	0.480003058	-0.993034899	0.326002856	-1.443435573
l0cation	7.321215599	3.607416452	2.029489996	0.048347253	0.055505898

a)

y^ = -36.1143 +1.14798 x1 + 0.9531 x2 -0.4766597888 x3 +7.321215599 x4

b)

option D) d. the home game point differential averages 7.3212 more points per game than away games.

c)

if p-value < 0.05 (alpha), then that variable is significant

here

a. Loc,   c. assists, d. rebounds are significant

b) turnover is not significant

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