how to create a linear regression in least squares method and Least absolute value method, and find the correlation coefficients.

I would like to create a linear regression in a scatter plot which are created by following code in two methods, least squares method and Least absolute value method, and I find the correlation coefficients. I want to create a linear regression from all of the plot, not for each data set. If you have good idea, please give me advice.

following my code;

for i = 1:12
    hold on
    if i==1 || i==3 || i==5 || i==7 || i==8 || i==10 || i==12
        for j = 1:31
            xfilename = sprintf('TA2004%02d%02d.txt',i,j);
            yfilename = sprintf('TS2004%02d%02d.txt',i,j);
            x = load(xfilename);
            y = load(yfilename);
            if i==1 && j == 1
            scatter(x,y);
            else
            scatter(x,y);
            end
        end
    elseif i==2
        for j = 1:29
            xfilename = sprintf('TA2004%02d%02d.txt',i,j);
            yfilename = sprintf('TS2004%02d%02d.txt',i,j);
            x = load(xfilename);
            y = load(yfilename);
            scatter(x,y);
        end
    else
        for j = 1:30
            xfilename = sprintf('TA2004%02d%02d.txt',i,j);
            yfilename = sprintf('TS2004%02d%02d.txt',i,j);
            x = load(xfilename);
            y = load(yfilename);
            scatter(x,y);
        end        
    end
    hold off
end
xlabel('surface temperature');
ylabel('near-surface air temperature');

Answer 1

[michio]

As far as I know, MATLAB does not have least absolute value method implemented. Related answers are

1. Is there a routine to perform quantile regression or LAD (Least Absolute Deviations) in MATLAB?
2. Least Absolute Value based regression

It seems that you have two text files for each day in 2004 (366x2=732 files). If you are looking at getting some statistics from data, instead of just visualizing them (eg. scatter, histogram), I'd suggest you import all of the data (if RAM allows, it seems it does) then use functions like polyfit and corrcoef.

There are multiple ways to achieve this, but if you are using R2014b or later, I strongly recommend using datastore functionality. See Getting started with datastore.

If the data format allows, your data import becomes as simple as the following four lines.

dsX = datastore('TA2004*.txt');
x = readall(dsX);
dsY = datastore('TS2004*.txt');
y = readall(dsY);