# How to remove outliers from a linear fit?

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Thar on 28 Jan 2017
Commented: Star Strider on 31 Jan 2017
Hi all!
I have points P(xi,yi)and the linear fit y=ax+b. I want to remove the maximum outlier from the linear fit and I will do a new linear fit. Then to remove the maximum outlier and a new linear fit and so on, until I have the 50% of points P(xi,yi). Any ideas?
Thank you!

Star Strider on 28 Jan 2017
My idea:
x = 1:100; % Create Data
y = randi(99, 1, 100); % Create Data
nr_pts_to_remove = fix(length(x)/2);
for k1 = 1:nr_pts_to_remove
dm = [ones(size(x(:))) x(:)]; % Design Matrix
b = dm\y(:); % Estimate Parameters
yfit = dm*b; % Fit Data
[~,idx] = max(abs(y(:) - yfit)); % Index Of Maximum Residual
x(idx) = []; % Remove Maximum ‘x’
y(idx) = []; % Remove Maximum ‘y’
end
xv = linspace(min(x), max(x)); % Create Vectors For Plot
yv = [ones(size(xv(:))) xv(:)]*b; % Create Vectors For Plot
figure(1)
plot(x, y, 'pg', 'MarkerFaceColor','g')
hold on
plot(xv, yv, '-r')
hold off
grid
The ‘(:)’ creates column vectors for all data and other variables.

Star Strider on 30 Jan 2017
If you plot them with subplot, it should save all of them as the same figure. It would be crowded to look at, but all the information would be available.
Thar on 31 Jan 2017
I want to save them in different figures. I wrote savefig('graphk1.fig'),but save the first graph only.
Star Strider on 31 Jan 2017
You have two options, to save them all in the same file:
H(1) = figure(1)
plot( . . . )
. . .
H(22) = figure(22)
plot( . . . )
savefig(H,'graphk.fig')
or to save every figure individually:
savefig('graphk01.fig')
savefig('graphk02.fig')
. . .
savefig('graphk22.fig')
I would save them all in the same file (the first option). See the documentation for savefig for details. The documentation says it was ‘Introduced in R2013b’, so if you have that or a later version, you should be able to do this.