# Find coefficients from linear regression in R (really fast)

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[This is the first part of a three part series that demonstrates how to create an R package that includes RcppArmadillo source code; follow these links for parts two and three]

Every journey needs motivation … so let’s say you want to run a **LOT** of regressions. Additionally, let’s say you are really **only** interested in the coefficients.

In that case, `lm.fit`

in R does way too much work and we can speed it up with a few relatively simple tricks (TL;DR RcppArmadillo is fastest!)

First of all, it should be noted that it might not be worth the effort. You can get a long way without linking to C++ code. In the present slightly contrived case, the `lm.fit`

and `.lm.fit`

functions are much faster than `lm`

.

set.seed(1) ROWS <- 1e5 Y <- 1:ROWS + runif(ROWS, -1, 1) X <- 1:ROWS + rnorm(ROWS, 0, 3) # get coefs coef_1st <- function() lm(Y ~ X)$coefficients coef_2nd <- function() lm.fit(cbind(rep(1, length(X)), X), Y)$coefficients coef_3rd microbenchmark(coef_1st(), coef_2nd(), coef_3rd(), times = 1e4) # benchmark microbenchmark(coef_1st(), coef_2nd(), coef_3rd(), times = 1e4) Unit: milliseconds expr min lq mean median uq max neval coef_1st() 25.453486 34.005381 49.059493 45.734325 60.332143 1476.2446 10000 coef_2nd() 3.976818 5.264472 9.967156 7.899375 11.087321 177.8020 10000 coef_3rd() 2.868874 3.476643 7.131980 5.091950 7.207663 114.3153 10000

Using medians, `lm.fit`

is ~6x faster than `lm`

, and `.lm.fit`

is a little over 9x faster! These are big improvements for little effort. So if this is your exact problem, you can now stop reading.

HOWEVER if you have REAL work to do, you might still be interested in C++. And if you want to do regressions, you need linear algebra. Enter RcppArmadillo!

You could of course use the `fastLmPure`

function in the RcppArmadillo package. I have done that below.

require(RcppArmadillo) coef_4th <- function() { # note to make XX to get intercept from fastLmPure; # this behavior is the default for the other functions XX <- cbind(rep(1L, length(X)), X) fastLmPure(XX, Y)$coefficients }

Note that we need to prepare the data differently, by adding the column of 1s to the matrix (this is the intercept). This isn't free so i included that step in the benchmarking function.

Right away you should be thinking that we can do better … we could move the code that adds the column of 1s (creating `XX`

) into C++, and also do only the calculations we need.

This C++ code does just that:

#include // [[Rcpp::depends(RcppArmadillo)]] //[[Rcpp::export]] arma::colvec getCoef(const arma::vec & X, const arma::vec & Y) { // this function takes two numeric vectors // checks to make sure the dimensions match // returns the coefficients from a bivariate regression // TODO: add an intercept switch ... noInt int Xlen = X.size(); int Ylen = Y.size(); if( Xlen != Ylen ) Rcpp::stop("X and Y must have the same length"); arma::mat XX(Xlen, 2); for( int i = 0; i < Xlen; i++) { XX(i, 0) = 1; // constant XX(i, 1) = X(i); } // find coefficients arma::colvec coef = arma::solve(XX, Y); return coef; }

Now we source the C++ function using `Rcpp::sourceCpp`

, loading `getCoef`

as a function in the global environment.

R> `Rcpp::sourceCpp("~/Dropbox/Cpp/R/fastLMCo.cpp")`

As you would expect, our custom getCoef function is fastest, besting RcppArmadillo’s fastLmPure by ~25%

coef_5th <- function() getCoef(X, Y) microbenchmark(coef_1st(), coef_2nd(), coef_3rd(), coef_4th(), coef_5th(), times = 1e4) Unit: milliseconds expr min lq mean median uq max neval coef_1st() 24.688233 28.716522 33.826753 32.054957 35.927653 187.17681 10000 coef_2nd() 3.672581 4.328348 7.166927 4.916639 8.739248 87.31223 10000 coef_3rd() 2.508058 3.079421 5.142339 3.409392 4.531942 101.43583 10000 coef_4th() 2.242320 2.614726 3.578321 2.834551 3.240812 106.49090 10000 coef_5th() 1.986783 2.169972 2.467147 2.260406 2.530783 44.72023 10000

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