Is this statement correct for formal usage?
This model is a good approximation to the data.
Or, should I use
This model is a good approximation of the data.
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3On Google, "approximation to" gives 224 million results and "approximation of" gives 339 million results. But which one is correct in what context?– vinc17Commented Jun 1, 2018 at 12:45
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2 Answers
X to Y makes Y a target or destination that X wants to reach.
X of Y makes Y relate to X such that you can say "X belongs to Y".
This model is a good approximation to the data.
This sounds like you are trying to make the model fit the data. You had an idea of what the model should be before making it.
This model is a good approximation of the data.
This sounds like you made the model, then compared with the data, and found that it "belongs". You didn't necessarily have an idea of what the model should be before making.
It appears "approximation of" would be best suited for numbers (mathematical approximation) and "approximation to" best for conceptual approximations.
https://dictionary.cambridge.org/dictionary/english/approximation
approximation noun [ C, usually singular ] UK /əˌprɒksɪˈmeɪʃən/ US
a figure that is close to a particular number or time but not exactly that number or time:
Sales-tax receipts provide **an approximation of** retail sales.
something that is similar to another thing but not exactly the same:
**approximation to sth** A closer **approximation to** the truth is that he started out as a genuine entrepreneur.
