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I am currently working a lot with R and Python. I am not able to access the C code the the R function lm_fit. I am wondering how is the linear regression optimize in R and python ?

I am pretty sure in R it is optimize with the Normal equation (since R is good with matrix multiplication) and I would think it is optimize with Gradient descent in Python ?

Am I right ?

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By default lm uses QR decomposition, but there are other options available -- see the documentation. Using the normal equations is a pretty bad way to solve this problem because of problems related to numerical precision; this point is covered extensively on Stats.SE. See this thread for an example.

There are several OLS and GLM implementations in Python so there's no single answer to that question.

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R uses QR decomposition. My answer here has some useful links on how to solve a least square problem.

Also, check this awesome answer for the details of lm. Least Squares Regression Step-By-Step Linear Algebra Computation.

Finally, I do not think you can find the C code, since it uses basic linear algebra package such as BLAS / LAPACK, many of them are compiled and the source is in FORTRAN. Check slide 4 in this link.

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