I am doing my project work in snowmelt runoff modelling. I have collected a Matlab code which I found very difficult to understand due to its complexity.
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.
Linear Regression [Simplest Implementation]:
https://www.mathworks.com/matlabcentral/fileexchange/64930-linear-regression-simplest-implementation
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