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I am having a lot of trouble determining if a model is linear or not linear.

Within the computer, all models are stored as if statements ... which means they can be written as a long line of if statements. EX:

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Apparently all popular models are linear: GLM, logistic regression, polynomial regression, GAM model, splines, etc . We say that Machine Learning models like neural network, xgboost and random forest are non-linear.

If I just look at the equation of a model ... how can I tell right away if its linear model or non-linear model?

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