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For example, we have a dataset, and we want to find best representative hyperplane for this dataset. In other words, we aim to perform regression operation.

This hyperplane can be in linear, sinusoidal or logistic format.

How can I determine this ?

How can we understand which model is the best one for our dataset ?

This is very important because if the data samples are distributed nonlinearly, we cannot choose a linear model.

The first answer to this question which comes to my mind is plotting the samples. In this way, I can see the distribution pattern of our data samples, and I can decide my learner function

(f = sin(x) or f = sigmoid(x))

However, if we have more than 2 features, we cannot plot our data samples. This means that plotting is not a good solution for model selection and understanding the data.

Is there any other solution for understanding the samples distribution and determining model function (learner function f) ?

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closed as too broad by Nick Cox, Michael Chernick, Sycorax, Peter Flom Apr 3 at 11:44

Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

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    $\begingroup$ This is, in a strong sense, a if not the central problem of applied statistics, how to find a good model for a dataset, and you've touched upon some fine ideas, but this is too broad to be a good question. $\endgroup$ – Nick Cox Apr 2 at 13:00
  • $\begingroup$ @NickCox There is no such thing as a bad question $\endgroup$ – David Apr 2 at 14:08
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    $\begingroup$ I did not use the word bad; not good is not the quite the same. But either way: Not so; there are questions not good for CV and some are closed or put hold every day. They are defined as precisely as we can define them in the advice for CV. Naturally, the definition is social, especially that a question is deemed not good if and only if a moderator or sufficiently high-rep users vote a certain way. And individuals might disagree. $\endgroup$ – Nick Cox Apr 2 at 14:21
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    $\begingroup$ @asdf There certainly are bad questions. I'm not saying this is one, but there are some. But Nick's point is that this is not a good question for CV. $\endgroup$ – Peter Flom Apr 3 at 11:44
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That's the magic of data science. There is no way to know a priori!

It is true that you cannot see everything in one simple visualization with more than 2 variables, but you can find some workaround. For example, represent each of the interest variables separately in different plots (or maybe, use color for some of them insted of position on an axis!!)

If the data is still way too high-dimensional, split your data into training and testing sets, fit each model and look for significant differences in predictive performance for the test set.

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