MATLAB: How to set slope in linear regression

Question

I want to run a linear regression where I set the slope of the regression line to 1 and the intercept to 0. In other words, I want to see how well a set of points fits along the line y = x and I am not concerned about finding the line of best fit. I know how to use the fitlm to remove the intercept term, but I don't yet know how to set the slope. This is what I have so far:

    vec1 = (0:10)+rand(1,11);
    vec2 = (0:10)+rand(1,11);
    scatter(vec1, vec2)
    hold on
    plot(0:11, 0:11)
    
    mdl = fitlm(vec1, vec2, 'Intercept', false); 

.Are there any other arguments that I can add to this function to set the slope, or is it necessary to calculate terms like R^2 and the p-value manually?

Answer 1

Determing the statistic you want to use to determine how well the regression explains the points is not difficult. It is relatively striaghtforward to calculate the Coefficient of determination, .

vec1 = (0:10)+rand(1,11);
vec2 = (0:10)+rand(1,11);
scatter(vec1, vec2)
hold on
plot(0:10, 0:10)
hold off
SStot = sum((vec2-mean(vec2)).^2);
SSres = sum((vec2-vec1).^2);
Rsq = 1-SSres/SStot;
pval = ttest(resd);
text(min(xlim)+0.2*diff(xlim), min(ylim)+0.7*diff(ylim), sprintf('R^2 = %.3f\n\\itp\\rm = %.3f', Rsq,pval))

A one-sample t-test on the residuials is probably adequate to provide a p-value.