Multiple regressions in a scatter plot

I have several scatter plots that look like a hockey stick, or even more crooked, and I want to fit a linear trend in each of the segments. Is there a way to get this? Thanks

Answer 1

[bym]

one way: [edit: added pp]

pp = mkpp([0 5 10],[[.5,0];[4,2.5]]);
x = (0:.1:10)';
y = ppval(pp,x);
y = y+rand(101,1);     % make hockey stick example data
plot(x,y,'b.')         % plot data
hold on

x1 = x(1:50);    x1 = [ones(size(x1)),x1];
x2 = x(51:101);  x2 = [ones(size(x2)),x2];
y1 = y(1:50);    y2 = y(51:101);

c1 = x1\y1;      c2 = x2\y2;        % least squares coefficients

yhat1 = x1*c1;  yhat2 = x2*c2;      % fits

plot(x(1:50),yhat1,'--',...
    x(51:101),yhat2,'--','LineWidth',2)

[edit]

%  R^2 calculation
res1 = y1-yhat1; res2 = y2-yhat2;
r_sq1 = 1-(sum(res1.^2)/sum((y1-mean(y1)).^2));
r_sq2 = 1-(sum(res2.^2)/sum((y2-mean(y2)).^2));

[the cyclist]

What is "pp" in your second line?

[Walter Roberson]

Looks like a pp = polyfit() call went missing, but I don't know what parameters were intended.

[bym]

sorry about that, sloppy cut and paste. Thanks for pointing that out

Answer 2

[the cyclist]

One way to do this would be with the nlinfit() function of the Statistics Toolbox. You could define a function that is parameterized to be a series of line segments, and then nlinfit() will find the parameters that give the best fit to the data.

[Julio]

The problem is I don't have the statistics toolbar in my university's Matlab

Answer 3

[Julio]

Thanks a million! it works nice. Although I will have to look manually for the breaks of all the plot, but at least I can do it now. But how can I get now the R^2 of the fits?

[bym]

see my edit above for R^2