Question

6. Determine whether ANTIBIO has statistically significant predictive value when entered as the last predictor in the equation. Conduct a statistical test and include all steps of a hypothesis test.

7. Determine whether the three predictors together have statistically significant predictive value. Conduct a statistical test and include all steps of a hypothesis test.

8. Calculate the coefficient of determination and interpret.

9. Suppose x1 = PROTEIN, x2 = ANTIBIO and x3 = SUPPLEM, and you enter these predictors in the model in the order of x1, x2, x3. Find SSR(x2 | x1) and SSR(x3 | x1, x2). What do they mean?

10. Test whether adding ANTIBIO and SUPPLEM provides any additional predic- tive value, given that PROTEIN is already in the model. Include all steps of a statistical test.

<data>

STEER   PROTEIN   ANIBIO   SUPPLEM   TIME  
1   10   1   3   88  
2   10   1   5   82  
3   10   1   7   81  
4   10   2   3   82  
5   10   2   5   83  
6   10   2   7   75  
7   15   1   3   80  
8   15   1   5   80  
9   15   1   7   75  
10   15   2   3   77  
11   15   2   5   76  
12   15   2   7   72  
13   20   1   3   79  
14   20   1   5   74  
15   20   1   7   75  
16   20   2   3   74  
17   20   2   5   70  
18   20   2   7   69  

using MINITAB

Coefficients

Term	Coef	SE Coef	T-Value	P-Value	VIF
Constant	102.71	2.31	44.46	0.000
PROTEIN	-0.8333	0.0987	-8.44	0.000	1.00
ANIBIO	-4.000	0.806	-4.96	0.000	1.00
SUPPLEM	-1.375	0.247	-5.57	0.000	1.00

Regression Equation

TIME

=

102.71 - 0.8333 PROTEIN - 4.000 ANIBIO - 1.375 SUPPLEM

Model Summary

S	R-sq	R-sq(adj)	R-sq(pred)
1.70957	90.07%	87.94%	83.44%

Analysis of Variance

Source	DF	Adj SS	Adj MS	F-Value	P-Value
Regression	3	371.08	123.694	42.32	0.000
PROTEIN	1	208.33	208.333	71.28	0.000
ANIBIO	1	72.00	72.000	24.64	0.000
SUPPLEM	1	90.75	90.750	31.05	0.000
Error	14	40.92	2.923
Total	17	412.00

Fits and Diagnostics for Unusual Observations

Obs	TIME	Fit	Resid	Std Resid
5	83.000	79.500	3.500	2.28	R

Answer 1