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Talk:Multiple regression: Difference between revisions
Clarify the difference between multiple and single regression -- most examples on the page were cargo-culted and incorrect.
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imported>Stevegt (Clarify the difference between multiple and single regression -- most examples on the page were cargo-culted and incorrect.) |
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= Examples are not multiple regression =
Many if not most of the examples on this page were apparently translated blindly from a single incorrect example that had height as X and weight as Y -- a single-axis regression. Regression of a single X axis is not multiple regression -- see References below. Those height/weight examples do not belong on this page. Much of the confusion in this discussion, and many of the suggestions for merging with [[Polynomial Fitting]], stem from that error.
Multiple regression, as mentioned in the description, is where the X input is a N-dimensional array; a matrix of two or more dimensions, not a list.
Think of multiple regression as "surface fitting" rather than curve fitting. Some examples:
* You want to use multiple regression to create a three-dimensional surface so you can estimate option contract price given spot price and implied volatility. For pretty pictures of this, see [https://www.google.com/search?q=+volatility+surface&tbm=isch volatility surface] graphs. In this case, X is a two-dimensional matrix of <code>{spot_price[i], implied_volatility[i]}</code>, and Y is a matching list of <code>option_contract_price[i]</code>.
* As a possible modification to the existing height/weight examples: You want to use height and body-mass index (BMI) to create a three-dimensional surface so you can estimate weight: X is a two-dimensional matrix <code>{height[i], bmi[i]}</code>, Y is <code>weight[i]</code>.
== Summary for clarification: ==
* '''Examples on this page must support a matrix of at least two dimensions as the X input''', as mentioned in the page description. (Any reasonable, non-hackish implementation will support any number of dimensions, due to the way the math works.)
* Do not merge this page with [[Polynomial Fitting]] -- the [[Polynomial Fitting]] page is about single regression. This page is about multiple regression.
* Do remove or replace the single-regression examples, specifically those that predict a weight from a height. They do not belong on a page about multiple regression.
== References: ==
* [https://en.wikiversity.org/wiki/Multiple_linear_regression Multiple Regression] page on Wikiversity
* [https://en.wikipedia.org/wiki/Linear_regression#Simple_and_multiple_linear_regression Multiple Regression] description in Wikipedia
--[[User:Stevegt|Stevegt]] ([[User talk:Stevegt|talk]]) 03:04, 9 September 2023 (UTC)
= Older discussion showing confusion due to proliferation of single-regression examples =
== Clarification needed ==
This task needs more clarification, like a link to a suitable wikipedia page. —[[User:Dkf|Donal Fellows]] 17:04, 29 June 2009 (UTC)
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The task doesn't ask for an example computation, and the wikipedia page on OLS is impenetrable to the good programmer/lesser mathematician. --[[User:Paddy3118|Paddy3118]] 07:13, 2 April 2011 (UTC)
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The main page of this task is one of a number of Rosetta task pages which simply show a set of framed blank panels (not even a fallback image) in lieu of equations, when viewed on OS X with Safari or Chrome (FWIW the MathML on this Talk page is displaying without problem in the same browsers).
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