How to make a linear regression coefficient algorithm

I wrote this code and I don't know how to use the formulae

function [alpha, beta] = linreg( x, y )
beta = cov( x, y ) / var( x ) ;
% ...
end

[Rik]

Only the definition for alpha is missing. What exactly is your question, and how exactly is this a Matlab question?

Answer 1

[Sugandhi]

Hi Karthik,

I understand that you want to make a linear regression coefficient algorithm by using the above formula.

function [alpha, beta] = linreg( x, y )
    beta = cov( x, y ) / var( x ) ;
    xbar=mean(x);
    ybar=mean(y);
    alpha = ybar+beta*xbar;
end

According to the formula provided, xbar and ybar are mean of x and y data respectively. Alpha is calculated using xbar,ybar and beta. Beta is ratio of covariance of x,y and variance of x data.

For more understanding, kindly go through following links-

• mean- https://www.mathworks.com/help/matlab/ref/mean.html?searchHighlight=mean&s_tid=srchtitle_mean_1
• Covariance- https://www.mathworks.com/help/matlab/ref/cov.html?searchHighlight=cov&s_tid=srchtitle_cov_1
• Variance- https://www.mathworks.com/help/matlab/ref/var.html?searchHighlight=var&s_tid=srchtitle_var_1

Answer 2

[KSSV]

x = 1:10 ;
y = rand(1,10) ; 

[a,b] = linreg(x,y) ; 
% Check
p = polyfit(x,y,1) ; 
[a b ; p(2) p(1)]

ans = 2×2

0.6914 -0.0493 0.6914 -0.0493

function [alpha, beta] = linreg( x, y )
n = length(x) ;  % get the length of x and y 

xbar = mean(x) ;  % mean of x 
ybar = mean(y) ;  % mean of y 

Sxy =  1/(n-1)*sum((x-xbar).*(y-ybar)) ;
Sx2 = 1/(n-1)*sum((x-xbar).^2) ; 

beta = Sxy/Sx2 ;
alpha = ybar-beta*xbar ; 
end

Answer 3

[John D'Errico]

Why do you want to write your own linear regression code? This is generally a bad idea. Never write code to do what a professional will have done better, and has already been written for you.

ab = polyfit(x,y,1);
Alph = ab(2);
Bet = ab(1);