Linear Regression [Simplest Implementation]:

https://www.mathworks.com/matlabcentral/fileexchange/64930-linear-regression-simplest-implementation

Hello, Sajad! I have worked with the Successive Projections Algorithm (SPA) which uses Multiple Linear Regression models for variable selection. I don't know if it may be viable to your problem, but I think you should try it. You shall be able to look at my profile and get some papers of mine. On the other hand, feel free to contact me directly if you have any question: [email protected]

function [ est ] = ols( y, X, varargin )

%OLS Ordinary Least Squares estimation

% Computes Ordinary Least Squares (OLS) estimation for the specified data

%

% est = OLS(y, X) computes an OLS estimation of y into X. Returns an

% estimation ouput structure, estout.

% est = OLS(y, X, Name,Value) OLS estimation with additional properties

% using one or more Name,Value pair arguments.

%

% Additional properties:

% - 'constant': 0 to ommit the constan term (intercept) in the

% estiamtion. Default 1.

% - 'vartype': compute heteroskedasticity 'robust' or 'cluster' variance

% matrix estiamtion. Default 'homo' for homoskedasticity.

% - 'clusterid': specify the cluster variable. Only if 'vartype' is set

% to 'cluster'.

% - 'dfcorrection': 0 to supress degrees-of-freedom correction of the

% variance. Default 1.

%

% Example

%

% est = ols(y, X);

%

% See also ESTOUT, IV2SLS, S2SLS, PANEL

%

% Copyright 2013-2015 Inmaculada C. Álvarez, Javier Barbero, José L. Zofío

% http://www.paneldatatoolbox.com

%

% Version: 2.0

% LAST UPDATE: 17, June, 2015

%

% Create output structure

est = estout();

% Check input

if nargin < 1

error('Dependent variable not specified');

end

if nargin < 2

error('Independent variables not specified');

end

if size(y,2) ~= 1

error('Y must be a column vector of the dependant variable');

end

if size(y,1) ~= size(X,1)

error('Number of rows in Y must be equal to number of rows in X');

end

% Parse Additional options

p = inputParser;

if verLessThan('matlab', '8.2')

addPar = @(v1,v2,v3,v4) addParamValue(v1,v2,v3,v4);

else

addPar = @(v1,v2,v3,v4) addParameter(v1,v2,v3,v4);

end

addPar(p,'constant',1,...

@(x) isnumeric(x));

addPar(p,'vartype','homo',...

@(x) any(validatestring(x,{'homo','robust','cluster'})));

addPar(p,'dfcorrection',1,@(x) isnumeric(x));

addPar(p,'clusterid',[],@(x) length(x) == length(y))

p.parse(varargin{:})

options = p.Results;

% Error if NaN's in input data

if any(isnan(y)) || any(any(isnan(X))) || any(any(isnan(options.clusterid)))

error('NaN values not allowed in input data');

end

% Extract table names and convert data to array

[y, ynames] = extracttable(y);

[X, xnames] = extracttable(X);

% Check if constant

hasConstant = options.constant;

% Check if robust

if strcmp(options.vartype,'robust') || strcmp(options.vartype,'cluster')

robust = 1;

else

robust = 0;

end

% Store original data

est.y = y;

est.X = X;

% Get number of observations

n_clus = size(y,1);

N = n_clus;

% Add constant term

if hasConstant

X = [X ones(N,1)];

end

% Number of variables

k = size(X,2);

% Compute estimates

coef = (X'*X)\X'*y;

% Fitted values

yhat = X*coef;

% Residuals

res = y - yhat;

% Residuasl degrees of freedom

resdf = N - k;

% Inverse of X'X

invXX = ((X'*X)\eye(k));

% Residual variance

resvar = (res'*res);

resvar = resvar ./ resdf;

% Covariance matrix

switch options.vartype

case 'homo'

varcoef = resvar * invXX;

case 'robust'

% White-robust standard errors

varcoef = invXX * (X' * diag(diag(res*res')) * X) * invXX;

if options.dfcorrection

varcoef = N/(N-k) * varcoef;

end

case 'cluster'

% Get unique ids

id_clus = options.clusterid;

uid_clus = unique(id_clus);

n_clus = length(uid_clus);

% Compute total sum

total_sum = 0;

for i=1:1:n_clus;

total_sum = total_sum + X(id_clus==uid_clus(i),:)'*res(id_clus==uid_clus(i))*res(id_clus==uid_clus(i))'*X(id_clus==uid_clus(i),:);

end

varcoef = invXX * total_sum * invXX;

if options.dfcorrection

varcoef = n_clus/(n_clus-1) * (N-1)/(N-k) * varcoef;

end

% Change resdf to the correct value with cluster

resdf = n_clus - 1;

end

% Standard errors

stderr = sqrt(diag(varcoef));

% Goodness of fit

M0 = eye(N) - 1/N * ones(N);

RSS = res' * res;

TSS = y' * y;

ESS = TSS - RSS;

r2 = 1 - (res' * M0 * res) ./ (y' * M0 * y);

adjr2 = 1 - (N - 1) ./ (N - k) .* (1 - r2);

% Save estimation

est.method = 'OLS';

est.options = options;

est.n = n_clus;

est.T = 1;

est.N = N;

est.k = k;

est.isMultiEq = 0;

est.isLinear = 1;

est.hasConstant = hasConstant;

est.isRobust = robust;

est.coef = coef;

est.varcoef = varcoef;

est.stderr = stderr;

est.yhat = yhat;

est.res = res;

est.resvar = resvar;

est.resdf = resdf;

est.RSS = RSS;

est.ESS = ESS;

est.TSS = TSS;

est.r2 = r2;

est.adjr2 = adjr2;

est.isAsymptotic = 0;

est.vartype = options.vartype;

% Set default var names

est.ynames = ynames;

est.xnames = xnames;

est = defaultVarNames(est);

end

function [fitresult, gof] = createFit(X, Y)

%CREATEFIT(SIGNALTIME1,RMSFEATURE1)

% Create a fit.

%

% Data for 'untitled fit 1' fit:

% X Input

% Y Output

% Output:

% fitresult : a fit object representing the fit.

% gof : structure with goodness-of fit info.

%

%% Fit: 'untitled fit 1'.

[xData, yData] = prepareCurveData( X, Y );

% Set up fittype and options.

ft = fittype( 'poly1' ); %%for linear regression

% Fit model to data.

[fitresult, gof] = fit( xData, yData, ft );

% Plot fit with data.

figure( 'Name', 'untitled fit 1' );

h = plot( fitresult, xData, yData );

legend( h, Y vs. X', 'untitled fit 1', 'Location', 'NorthEast' );

% Label axes

xlabel X

ylabel Y

grid on

Also, you can apply the linear regression on your data without any code, please follow these steps:

1. open the Matlab

2. then open the APPS option

3. and select the curve fitting tools

4. Finally, fit your data (X) and (Y) and put it in the x (data) and y (data) options that you saw it in the curve fitting tools option.

5. you will get the results of the linear regression line.

polynomial using matlab command polyfit and polyval

Linear Regression [Simplest Implementation]:

https://www.mathworks.com/matlabcentral/fileexchange/64930-linear-regression-simplest-implementation