# Julia for linear regression

The similarity of the Julia programming language to Matlab and its syntax makes it very easy to translate simple Matlab programs into Julia code. The following code shows simulating linear regression parameter and standard error estimation in Julia and Matlab. The superficial similarity of the code is remarkable.

First, here is the Matlab code:

clc; clear; vY = randn(100, 1); % outcome variable mX = randn(100, 4); % design matrix iN = size(vY, 1); % sample size vBeta = (vY\mX)'; % estimated coefficients vE = vY - mX*vBeta; % residuals dSigmaSq = vE'*vE/iN; % residual variance mV = dSigmaSq.*(inv(mX'*mX)); % covariance matrix vStdErr = diag(mV); % std. err. vT = (sqrt(iN)*vBeta)./vStdErr; % t-statistics [vBeta, vStdErr, vT]

and here is the Julia code

vY = randn(100, 1); # outcome variable mX = randn(100, 4); # design matrix iN = size(vY, 1); # sample size vBeta = (vY\mX)'; # estimated coefficients vE = vY - mX*vBeta; # residuals dSigmaSq = vE'*vE/iN; # residual variance mV = dSigmaSq[1,1].*(inv(mX'*mX)); # covariance matrix; dSigmaSq.* vStdErr = diag(mV) # std. err. vT = (sqrt(iN).*vBeta)./vStdErr # t-statistics println([vBeta'; vStdErr'; vT']')

Note that Matlab knows how to print matrices without a call to the `println`

function. The main difference here is that Julia does not know that a 1×1 matrix is a scalar and issues a matrix multiplication conformability error, whereas Matlab simply switches to elementwise multiplication which is the mathematically justifiable default.

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