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Drawing conclusions about population parameters from sample data. See https://en.wikipedia.org/wiki/Inference and https://en.wikipedia.org/wiki/Statistical_inference

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Interpreting the log-likelihood in ordinary least squares linear regression

No there is nothing from that output that could have told you about the possibility of model misspecification. The formal way to see if there is misspecification (test if the model is indeed nonlinear …
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Understanding the assumptions of Linear Regression

If the errors are normal, however, $\beta s$ are also normal, so we can use the family of Normalbased distributions (t-test, F-test, Chi2, z etc), to do inference. … precision of your coefficients. from the analytical point of view you will need to at the very least correct standard errors (other methods for the estimation) if you want to make any time of statistical inference
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