Which model is the best model based on significance for summary outputs regardin

Question

Which model is the best model based on significance for summary outputs regarding images 1-4??

I get confused on how to interpret the significant F.

And if none of the conbinations from images 1-4 are significant, would any of the ones below be the best model? (X1, X2, X3)

1.

2.

3.

4.

Which model is the best model based on significance for summary outputs regarding images 1-4??

I get confused on how to interpret the significant F.

And if none of the conbinations above from images 1-4 are significant, would any of the ones below be the best model? (X1, X2, X3)

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X1:

X2:

X3.

SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations 0.605450551 0.36657037 0.325259742 11326.58083 50 ANOVA df MS Significance F Regression Residual Total 3 3415186868 11383956238.87351239 9.46941E-05 46 5901405932 128291433.3 49 9316592800 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 96 Admit rate (X1) College ranking (X2) %4Yea r graduation rate (X3) 80172.357 34929.69472 2.29524929 0.026328839 9862.528234 150482.2 9862.528234150482.1858 -484.3018915 105.1768931-4.604641543 3.26869E-05 -696.0119968-272.592 -696.0119968 -272.5917862 15.10955437 113.7684485 -0.1328097080.894923156 -244.1135636213.8945 -244.1135636 213.8944549 725.4337403 -76.1040078 398.2013516-0.191119411 0.849273109-877.6417559 725.4337-877.6417559

Explanation / Answer

To begin with Significance F = FDIST(Regression F, Regression df, Residual df) = Probability that the regression equation does NOT explain the variation in y, i.e. that any fit is purely by chance.  This is based on the F probability distribution.  If the Significance F is not less than 0.1 (10%) you do not have a meaningful correlation.

The R^2 value explains how much of the variation in the dependent variable is explained by the independent variable, Higher the value of R^2 and the closer it is to 1, the better the fit, R^2 =1 will therfore be a perfect fit.

So based on significance of summary outputs, model 4 is the best as it has the least significant F which it has the most meaningful correlation between the dependent and the independent variables and also it has the best R^2 and among X1, X2 and X3,

X1 will be the best model for the same reason outlined above i.e. lowest significant F and highest R^2

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