Question

# Based on this study, what is the final model you would recommend to the Head of...

Based on this study, what is the final model you would recommend to the Head of the Science Department?

Comment on the overall adequacy of the final model.

DATA 1:

 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

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