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Given a set of predictors which all are significantly correlated with a single outcome, how can I find the "ideal" value of each predictor to maximize the outcome?

Initially I was thinking of using the beta-coefficients, since they should minimize residuals? Or did I get something wrong there?

EDIT:

Since my data is dynamic, I do not know in advance if the regression is linear, cubic, etc. Interactions can be ignored. A rule-of-thumb approach would be enough.

kjetil b halvorsen
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Comfort Eagle
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  • Is your model linear in all your predictors? (i.e. are they all just entered 'as is'?) ... does the model describe the data well (e.g. is there no substantive curvature in residuals vs each predictor? is there no interaction?) – Glen_b Sep 12 '17 at 10:30
  • Clarified my question above. Variable are entered "as is" – Comfort Eagle Sep 12 '17 at 10:46
  • Why would OLS fail? Set up some kind of cross-validation algorithm in sklearn to find out if quadratic or cubic terms are necessary. – Dave Dec 18 '19 at 00:54
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    This is often called response-surface methods. See https://stats.stackexchange.com/questions/166690/response-surfaces-and-multiple-linear-regression, https://stats.stackexchange.com/questions/227166/what-is-the-optimal-small-sample-experimental-design-for-multiple-treatments-and, https://stats.stackexchange.com/questions/193167/finding-optimal-values-of-parameters-using-observations/368078#368078, https://stats.stackexchange.com/questions/566942/why-are-global-search-algorithms-not-used-in-doe/566960#566960 – kjetil b halvorsen Jun 25 '22 at 14:58
  • I cannot make any sense of the edit: how can you possibly perform any kind of regression without knowing what features you are using?? Could you explain what you mean by "regression is ... cubic"? – whuber Aug 04 '22 at 15:01

1 Answers1

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Based on the number of features and search space, you can either use exhaustive search (if your search space is not very large) or heuristic-based approaches (if your search space is very large).

Please note that heuristic approaches may or may not provide you with the global optima.

Checkout the following post, @Borhan Kazimipour has provided an explanation for the similar question,

https://datascience.stackexchange.com/questions/53550/what-should-i-study-to-find-optimal-value-of-best-feature-combinations-in-machin

Kanishkan
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