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Multiple regression: Difference between revisions

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Multiple regression (view source)

Revision as of 12:14, 10 September 2023

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<math>y_j = \Sigma_i \beta_i \cdot x_{ij} , j \in 1..n</math>
 
You can assume <i> y </i> is given to you as a vector (a one-dimensional array), and '''<i> X </i> is given to you as a two-dimensional array (i.e. matrix)'''.
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;Example use case:
 
Think of multiple regression as "surface fitting" rather than curve fitting. For example, you might use multiple regression to create a three-dimensional surface so you can estimate implied volatility given time to maturity and delta of an options contract. 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>{time[i], delta[i]}</code>, and Y is a matching list of <code>implied_volatility[i]</code>.
 
;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
 
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