I know you accepted @Falk’s excellent answer already, but here is my 2 cents.
- Am I correct to assume that Math Proficiency is the strongest predictor of ELA Proficiency because its slope is furthest away from zero?
No, not in general, because your predictors are not standardized. If I really wanted to know “which is the strongest” predictor here, I would do the following:
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Prior to building any models, I would visualize the relationships between predictors. Perhaps some of them are highly correlated.
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Standardize each predictor (i.e., so it has unit standard deviation). This will allow easy comparison of β values across predictors.
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I would also standardize the outcome measure so that βs are interpretable as effect sizes.
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Fit multiple models reflecting the power set of combinations of predictors (also, don’t forget about interactions).
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Evaluate the goodness of fit of all models (after ensuring convergence) using relative indices such as WAIC, LOO-CV, etc., as well as absolute goodness using PPC.
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Based on careful consideration of all of the results above, come to a conclusion about which predictors are useful and which are redundant, if any.