Question

In: Statistics and Probability

The National Basketball Association (NBA) records a variety of statistics for each team. Five of these...

The National Basketball Association (NBA) records a variety of statistics for each team. Five of these statistics are he percentage of games won (Win %), the percentage of field goals made (FG%), the percentage of three-point shots made (3P%), the percentage of the free throws made (FT%), the average number of offensive rebounds per game (RBOff), and the average number of defensive rebounds per game (RBDef). The data given in the table below show the values of these statistics for the 30 teams in the NA for one full season.

Team	Win%	FG%	3P%	FT%	RBOff	RBDef
Atlanta	60.5	45.4	37.0	74.1	9.9	31.3
Boston	59.0	46.0	36.6	77.7	7.7	31.0
Brooklyn	33.3	42.5	34.2	77.7	11.9	28.5
Charlotte	10.6	41.4	29.5	74.6	10.3	28.7
Chicago	75.8	45.2	37.5	72.2	13.9	32.8
Cleveland	31.8	42.2	34.6	71.6	12.7	29.5
Dallas	54.5	44.3	33.9	77.1	10.1	32.7
Denver	57.6	47.6	33.2	73.5	11.2	31.9
Detroit	37.9	43.8	34.6	75.2	11.7	28.5
Golden State	34.8	45.7	38.8	77.0	9.7	29.5
Houston	51.5	44.9	35.9	78.2	11.7	30.5
Indiana	63.6	43.8	36.8	78.2	12.5	31.4
LA Clippers	60.6	45.5	35.7	68.0	12.1	29.4
LA Lakers	62.1	45.7	32.6	75.6	12.1	34.1
Memphis	62.1	44.7	32.6	75.9	12.6	29.5
Miami	69.7	46.9	35.9	77.5	10.4	31.2
Milwaukee	47.0	44.3	34.5	77.4	12.4	30.0
Minnesota	39.4	43.3	33.2	77.1	12.1	31.7
New Orleans	31.8	45.1	33.3	75.7	11.0	30.2
New York	54.5	44.3	33.6	74.1	11.3	30.5
Oklahoma City	71.2	47.1	35.8	80.6	11.0	32.7
Orlando	56.1	44.1	37.5	66.0	11.2	31.2
Philadelphia	53.0	44.8	36.2	74.2	10.7	32.5
Phoenix	50.0	45.8	34.3	75.7	10.9	30.8
Portland	42.4	44.3	34.6	79.6	11.1	29.5
Sacramento	33.3	43.6	31.6	73.6	13.4	29.5
San Antonio	75.8	47.8	39.3	74.8	10.3	32.6
Toronto	34.8	44.0	34.0	77.0	10.6	31.4
Utah	54.5	45.6	32.3	75.4	13.0	31.1
Washington	30.3	44.1	32.0	72.7	11.7	29.9

a. Develop an estimated regression equation that can be used to predict the percentage of games won given the percentage of field goals made (to 4 decimals).

y^ = - _____ + _____ FG%

At the .05 level of significance, test for a significant relationship.

[- Select your answer -] There is a significant relationship / There is no significant relationship

b. Provide the interpretation for the slope of the estimated regression equation developed in part (a).

An increase in the percentage of field goals made will [ - Select your answer -] increase / decrease the percentage of games won.

c. Develop an estimated regression equation that can be used to predict the percentage of games won given the percentage of field goals made, the percentage of three-point shots made, the percentage of the free throws made, the average number of offensive rebounds per game, and the average number of defensive rebounds per game (to 4 decimals).

y^ = - ___ + ____ FG% + _____ 3P% + ____ FT% + _____ RBOff% + _____ RBDef%

d. For the estimated regression equation developed in part (c), remove any independent variables that are not significant at the .05 level of significance and develop a new estimated regression equation using the remaining independent variables (to 4 decimals).

y^ = - ___ + ___ [select your answer] (3P%, FT%, RBOff%, RBDef%,GF%) + ___ [ select your answer] (3P%, FT%, RBOff%, RBDef%,GF%) + ___ (3P%, FT%, RBOff%, RBDef%,GF%) + ___ (3P%, FT%, RBOff%, RBDef%,GF%)

e. Assuming the estimated regression equation developed in part (d) can be used for the 2012-2013 season, predict the percentage of the games won for a team with the following values for the four independent variables: FG= 45, 3P% = 35, RBOff% = 12, and RBDef = 30 (to 1 decimals).

y^ = ___ %

Solutions

Expert Solution

Y^ = -294.64 + 7.69 FG%

p value < 0.05, There is a significant relationship

b)slope is positive, increase in Win % as the FG% increases, for every 1 unit increase in FG%, there is 7.69 increase of Win%

y = -407.1775 + 4.9809 X1 + 2.3651 X2 + 0.003840 X3 + 3.4224 X4 + 3.6594 X5

y^ = - 407.1775 + 4.9809 FG% + 2.3651 3P% + 0.0038 FT% + 3.4224 RBOff% + 3.6594 RBDef%

Here removed X3 because its variable not significant at 0.05

Y = -406.8729 + 4.9816 X₁ + 2.3642 X₂ + 3.4199 X₄ + 3.6598 X₅

y^ = - 406.8729 + 4.9816 FG% + 2.3642 3P% + 3.4199 RBOff% + 3.6598 RBDef%

FG= 45, 3P% = 35, RBOff% = 12, and RBDef = 30

Y = -406.8729 + 4.9816 X₁ + 2.3642 X₂ + 3.4199 X₄ + 3.6598 X₅

Y = -406.8729 + 4.9816 (45) + 2.3642 (35) + 3.4199 (12) + 3.6598 (30)

Y = 50.8789

Y = 50.9%

orchestra answered 1 year ago

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