Question

Twenty-five volunteer athletes participated in a study of cross-disciplinary athletic abilities. The group comprised athletes from football, baseball, water polo, volleyball, and soccer. None had ever played organized basketball, but did acknowledge interest and some social participation in the game. Height (inches), weight (pounds), and speed in the 100-yard dash (seconds) were recorded for each subject. The basketball test consisted of the number of field goals that could be made in a 60-min. period. The data are given in Athlete.jmp on Blackboard. We are interested in predicting GOALMADE using some combination of WEIGHT, HEIGHT, DASH100.

3) Using JMP output from above, do any of the input variables (HEIGHT, WEIGHT, DASH100) exhibit collinearity?

4) Now, we want to determine if the variables WEIGHT and/or HEIGHT should be added to the model that already contains DASH100 to explain GOALMADE. Write the full and reduced models; then perform the appropriate test. (Please show your expanded ANOVA table, but you do not need to state your hypotheses explicitly.)

5) Finally (without running any more JMP output), determine if the variable DASH100 is useful in explaining GOALMADE when HEIGHT and WEIGHT are already in the model. State the test-statistic, p-value, and conclusion only

JMP DATA:

W H D G

130   71   11.5   15
149   74   12.23   19
170   70   12.26   11
177   71   12.65   15
188   69   10.26   12
210   73   12.76   17
223   72   11.89   15
170   75   12.32   19
145   72   10.77   16
132   74   11.31   18
211   71   12.91   13
212   72   12.55   15
193   73   11.72   17
146   72   12.94   16
158   71   12.21   15
154   75   11.81   20
193   71   11.9   15
228   75   11.22   19
217   78   10.89   22
172   79   12.84   23
188   72   11.01   16
144   75   12.18   20
164   76   12.37   21
188   74   11.98   19
231   70   12.23   13

Answer 1

3. Coefficients

Term	Coef	SE Coef	T-Value	P-Value	VIF
Constant	-67.36	5.22	-12.91	0.000
Weight	-0.01057	0.00505	-2.09	0.049	1.01
Height	1.2027	0.0627	19.19	0.000	1.01
Dash 100	-0.142	0.216	-0.66	0.519	1.01

Since the VIF value is 1.01, which is very close to 1, there is no collinearity between the variables

If the value of VIF is between 5 to 10, we can say the the variables are highly collinear

4.& 5. Full model -

Coefficients

Term	Coef	SE Coef	T-Value	P-Value	VIF
Constant	-67.36	5.22	-12.91	0.000
Weight	-0.01057	0.00505	-2.09	0.049	1.01
Height	1.2027	0.0627	19.19	0.000	1.01
Dash 100	-0.142	0.216	-0.66	0.519	1.01

Reduced Model -

Analysis of Variance

Source	DF	Adj SS	Adj MS	F-Value	P-Value
Dash 100	23	213.36	9.277	0.52	0.823
Error	1	18.00	18.000
Total	24	231.36

Since the p-value is more than 0.05 in the case of Dash100 only and we are using 95% confidence interval, Dash 100 only is enough to explain Goal Made