Question

Based on this study, what is the final model you would recommend to the Head of the Science Department? And Comment on the overall adequacy of the final model.

DATA 1

HS_SCI	HS_ENG	HS_MATH	U	Gender	ATAR
SUMMARY OUTPUT
Multiple R	0.48301716
R Square	0.23330558
Adjusted R Square	0.21210666
	1.18199152
	224
ANOVA
	df	SS	MS	F	Significance F
	6	92.2552908	15.3758818	11.0055388	1.0596E-10
	217	303.171559	1.39710396
	223	395.42685
	Coefficients		t Stat	P-value	Lower 95%	Upper 95%
Intercept	1.81105553	0.64338389	2.81489099	0.00532825	0.54297399	3.07913706	0.54297399	3.07913706
HS_SCI	0.09600825	0.10389727	0.92406901	0.35647679	-0.1087687	0.30078523	-0.1087687	0.30078523
HS_ENG	0.05585575	0.10411875	0.53646199	0.59218883	-0.1493577	0.26106925	-0.1493577	0.26106925
HS_MATH	0.26024847	0.10209913	2.54897824	0.01149448	0.05901554	0.46148139	0.05901554	0.46148139
U	-0.3967997	0.18116867	-2.1902223	0.02957342	-0.7538752	-0.0397241	-0.7538752	-0.0397241
Gender	-0.0978474	0.17959186	-0.5448323	0.58642836	-0.4518151	0.25612026	-0.4518151	0.25612026
ATAR	-0.0049033	0.02658113	-0.1844651	0.85382087	-0.0572935	0.04748696	-0.0572935	0.04748696

Answer 1

From the above result, we can conclude, that as the multiple R-sq is 0.48, the full model can explain the 48% of total variability.

BEST MODEL:

we will use the p-value concepts for selecting the best model. we know that the if the associated p-value is less than 0.05 then the variable is a significant predictor.

Here the variable HS_MATH & U, these two variables are significant. our final model will be:

Predicted= 1.81105553+0.26024847*HS_MATH - 0.3967997*U

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