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On pg. 130 of "An Introduction to Statistical Learning with Applications in R" by Hastie et al. [http://www-bcf.usc.edu/~gareth/ISL] they are talking about using linear regression for predicting a binary response and say:

"Curiously, it turns out that the classifications that we get if we use linear regression to predict a binary response will be the same as for the linear discriminant analysis (LDA) procedure we discuss in Section 4.4."

Can you please show me how these 2 methods turn out to produce the same classification?

sambajetson
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    It is indeed so that LDA with 2 classes (aka "Fisher's LDA") is equivalent to linear regression with binary variable. Not only as "classifier:" but also as a "dimensionality reducer". More generally, LDA with g classes (aka canonical LDA) is equivalent (= a particular case of) canonical correlation analysis or multivariate regression/MANOVA. Please see my answers in [1](https://stats.stackexchange.com/q/31459/3277), [2](https://stats.stackexchange.com/q/169436/3277), [3](https://stats.stackexchange.com/q/190806/3277), – ttnphns Aug 29 '17 at 02:45
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    (cont.) with links to other answers found is that latter answer, especially check some amoeba's answers. – ttnphns Aug 29 '17 at 02:45
  • In a footnote behind my link [2] (in the comment above) it is said how exactly to recalculate LDA's and canonical correlation's (CCA) coefficients one into another. But in g=2 case, we know, CCA turns just into linear regression with one binary response variable. – ttnphns Aug 29 '17 at 02:50

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