MATLAB: Regress(x,y) for least square regression of two variables x,y

regressionStatistics and Machine Learning Toolbox

when i use regress(x,y),I obtain only one answer :shouldn't i get two answers which are the slope and y-intercept ?

Best Answer

You don't show us your code, but I am guessing you neglected to add a column of ones to your x input, as described in the documentation:

doc regress

This code will give you the two-parameter output you expect:

x = [ones(3,1),rand(3,1)];
y = rand(3,1);
b = regress(y,x)

Related Solutions

MATLAB: Linear regression

% Define sample data.
X = [1,2,3,4,5,6,7,8,9];
Y = [4 5 6 9 8 7 4 1 2];
% Do the plotting:

plot(X, Y, 'bo', 'LineWidth', 3, 'MarkerSize', 15);
grid on;
% Maximize the figure window.
set(gcf, 'units','normalized','outerposition',[0 0 1 1]);
% Label the various parts of the plot.
fontSize = 20;
title('lowcalorie Plot', 'FontSize', fontSize);
xlabel('X', 'FontSize', fontSize);
ylabel('Y', 'FontSize', fontSize);
coefficients = polyfit(X, Y, 1);
fittedY = polyval(coefficients, X);
hold on;
% Do the plotting:
plot(X, fittedY, 'rs-', 'LineWidth', 3, 'MarkerSize', 15);
legend('Y', 'Fitted Y');

MATLAB: How does MATLAB calculate standard error in ‘fitlm’

The following code can be used to calculate the standard error on mock data both in the case that the intercept is set to 'false' and when an intercept is present:

%%Sample Data Definition
X = [1 2 3 4 5 6 7 8 9 10];
Y = [1 1.5 2.1 4 5 6.3 7.3 7.8 9 9.9];
%%Calculation of Standard Error Without Intercept
n = length(X);                                       %  Number of observations

Slope = sum(X.*Y)/sum(X.^2);                         %  Calculates slope
yfit=X*Slope;                                        %  Fitted response values based on the slope

r = Y - yfit;                                        %  r is the residuals, which is the observed minus fitted values

SSE = sum(r.^2);                                     %  SSE is the sum of squared errors

MSE=SSE/(n-1);                                       %  Mean Squared Error 

Code_NoIntercept_SE=sqrt(MSE/sum(X.^2))              %  Standard error of the slope
model1 = fitlm(X,Y,'Intercept',false);               %  Calls 'fitlm'

MATLAB_NoIntercept_SE=model1.Coefficients.SE         %  Queries the standard error of MATLAB's model

%%Clear Variables then Redefine Data
clear all
X = [1 2 3 4 5 6 7 8 9 10];
Y = [1 1.5 2.1 4 5 6.3 7.3 7.8 9 9.9];
%%Calculation of Standard Error With Intercept
n = length(X);                                      %  Number of observations
XBar=mean(X);                                       %  Calculates mean of X
YBar=mean(Y);                                       %  Calculates mean of Y
Sxx=sum((X-XBar).^2);  
Sxy=sum((X-XBar).*(Y-YBar));
Slope = Sxy/Sxx;                                    %  Calculates Slope
Intercept= YBar-Slope*XBar;                         %  Calculates Intercept
yfit=Intercept + X*Slope;                           %  Fitted response values based on the slope
r = Y - yfit;                                       %  r is the residuals, which is the observed minus fitted values
SSE = sum(r.^2);                                    %  SSE is the sum of squared errors
MSE=SSE/(n-2);                                      %  Mean Squared Error 
Code_Intercept_SE=[                                 %  Standard Error of the regression coefficients
    sqrt(MSE*sum(X.^2)/(n*Sxx));                    %  Standard Error of the intercept coefficient
    sqrt(MSE/Sxx)]                                  %  Standard Error of the slope coefficient
model2 = fitlm(X,Y,'Intercept',true);               %  Calls 'fitlm'
MATLAB_Intercept_SE=model2.Coefficients.SE          %  Queries the standard error of MATLAB's model

Best Answer

Related Solutions

MATLAB: Linear regression

MATLAB: How does MATLAB calculate standard error in ‘fitlm’

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