How can I maximize the range of included data to built my robust regression model?

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Riyadh Muttaleb 2017-9-13

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I would like to use "robustfit" function with including maximum points that I have in the regression,

[b,stats] = robustfit(X,y,wfun,tune,const)

the example below is from matlab help:

x = (1:10)';
rng default; % For reproducibility
y = 10 - 2*x + randn(10,1);
y(10) = 0;
bls = regress(y,[ones(10,1) x])
[brob,stats] = robustfit(x,y,'andrews',1.339,'on')
ac=sum(stats.resid)
scatter(x,y,'filled'); grid on; hold on
plot(x,bls(1)+bls(2)*x,'r','LineWidth',2);
plot(x,brob(1)+brob(2)*x,'g','LineWidth',2)
legend('Data','Ordinary Least Squares','Robust Regression')