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By using a model with three variables instead of one, we get to a model with a mean squared error of 19.12 and an R² score of 0.72. That’s definitely a nice improvement!
"to" could be used as preposition, so "get to a model" seems to be grammatical.
why do people say "get to a model" instead of "get a model"?
Using "to" emphasizes that a new model with a lower error and higher R² score was reached, a sort of accomplishment has occurred. The sentence works fine if the "to" was deleted, it slightly changes the meaning to mean "the result of the modification"
Using to emphasises that this is a refinement of a previous model.
We have come from a model with one variable and we go to a model with three. It adds the sense that we have reached the improved model.
It would be possible to say "we get a model with three variables", and if the idea of "refining from a previous model" was not needed, this would be the normal way of saying it.
We get a model uses a metaphor of "get" = "acquire", and says nothing about the circumstances of the acquisition.
We get to a model uses a different metaphor of "get to" = "reach, attain a destination", and implies that acquiring the model is the end-point of a journey.
As mentioned by Colin Fine, "get to" implies motion towards some goal, but the first clause doesn't provide any action; it assumes we are already using the model we are supposedly moving towards. I would write one of the following to be consistent:
"By adding two variables to our model, we get to a model ..." That is, we started with a one-variable model, and the act of adding two variables moved us to a model with the new properties.
"By using a model with three variables instead of one, we have a model with ..." That is, we don't dwell on "how" we arrived a three-variable model; we have one, and we state what its desirable properties are.
