Question

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The Question:

For some Mechanical Engineer students, data for 224 student’s GPAs in their first 4 semesters of college were compared using several predictors, namely HSM, HSS, HSE, SATM, and SATV. Here significant level α is 0.05.

Then, the researcher fit a regression model and got the following results (intercept is included in the model):

ANOVA Table

Source	DF	Sum of Squares	Mean Squares	F ratio
Model(Reg)	(A)	(D)	(E)	(F)
Error(Residual)	(B)	105.65	0.4846433	Prob>F
Total	(C)	135.46		<0.001

             

Parameter Estimates Table

Term	Estimate	Std Error	t Ratio	Prob>|t|
Intercept	0.2187920884	0.40332538	0.54	0.5880
HSM	0.1464842907	0.03900487	(G)	0.0002
HSS	0.0274662163	0.03728366	0.74	0.4621
HSE	0.0770581216	0.03929423	1.96	0.0511
SATM	0.0009273573	0.00067983	1.36	0.1739
SATV	­.0004012914	0.00058484	-0.69	0.4933

1. What are the values for (A), (B), (C), (D), (E), (F) and (G)?

2. State the multiple regression model for this problem.

3. What % of the variation in GPA are we explaining by the multiple regression?

4. Specify the prediction equation (Include all the regressors)

5. Determine if this is a significant model, i.e. check ANOVA table. (If significant, then p-value < α.) Here significant level α is 0.05.

6. Determine if each predictor variable is significant to the model, give the reason, based on the JMP output (i.e. compare the test statistics or p-value)

Answer 1

a.

Source	DF	Sum of Squares	Mean Squares	F ratio
Model(Reg)	5	135.46-105.65=29.81	29.81/5=5.962	5.962/0.4846433=12.30183
Error(Residual)	223-5=218	105.65	0.4846433	Prob>F
Total	224-1=223	135.46		<0.001

(A)=5, (B)=218, (C)=223, (D)=29.81, (E)=5.962, (F)=12.30183 and (G)=(0.1464842907) / (0.03900487) =3.76

b.

c.

d.

e. Since p-value of F test <0.05 so there is sufficient evidence that this is a significant mode .

f. HSM is only significant predictor since its p-value= 0.0002 <0.05 and other predictor are not significant at 5% level of significance. Though HSE is significant at 10% level of significant (since its p-value=0.0511<0.1).