How to set slope in linear regression

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Colin Lynch
Colin Lynch 2020-1-11
评论： dpb 2020-1-12
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?
  1 个评论
dpb
dpb 2020-1-11
If the intercept is zero and the slope is one; you've already determined the regression expression uniquely--there's nothing left to solve for.
I've at least temporarily lost access to ML license so can't test; but I don't think any of the regression toolsets are coded such as to just allow for the statistics to be computed from a given regression for a data set.
Not such a bad idea to ask for a tool enhancement to do so...

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Star Strider
Star Strider 2020-1-11
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.
  1 个评论
dpb
dpb 2020-1-12
It would be kinda' convenient to have a prepared function that output a clean table, though...the presentation of results in the statistics area is still pretty far from ideal altho has certainly gotten better.

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