I would like to fit a linear model through points (x,y) with standard errors for each of them. So far I used the deming regression, but I couldn't figure out how to force the regression through the origin. Is there a simple method for this problem or do I need to perform a Monte Carlo simulation by variing each measurement point by a random error within the standard deviation and perform statistics with all possible regression lines? Thanks
From R documentation:
"A model with no intercept can be also specified as y ~ x + 0 or y ~ 0 + x"
try
mylm
Thank you Paulo. But this one lm(y~0+x) does not take into account the errors of the y and x values, right?
You could try a weighted linear regression with weights being the ratios of the standard-errors.
Thomas, would
coef( summary( mylm ) ) be suffice?
otherwise, for standard errors
sqrt( diag( vcov( mylm ) ) )
@ Paulo: lm definitely does not consider errors on X and does not correspond to the model described/needed by Thomas. lm regresses Y on X with a given order of the variables (that is, Y is explained by X, not interested in the other way: asymetrical relationship), whereas the Deming regression gives symetrical role to both variables.
@ Thomas: may be you can write down the model for the Deming regression and see what it becomes when adding the « through the origin » constraint, then implement it. Forcing regression through the origin is quite often a bad idea, already in the usual regression, I guess it's even worst in Deming regression and related techniques, so may be you should also consider if you really need it...
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