I understand that you have three distinct vectors "a", "b", and "c". From your descriptions:
- "a" contains un-calibrated measurements,
- "b" contains the true values,
- "c" contains values related to the difference between "a" and "b"?
- "diff" equal to the difference between "a" and "b"?
I am not clear of the role of the vectors "c" and "diff" in your analysis. I am going to assume that you are trying to do a linear calibration of the form below:
b = K*a + Z
As you mentioned, you can use the "polyfit" and "polyval" functions to accomplish this. If you have the "Curve Fitting Toolbox", I would recommend using the "fit" function:
[myfit,gof,out] = fit(a,b,'poly1');
This produces a curve fitting object "myfit". You can find goodness-of-fit information inside the "gof" structure and residual information inside the "out" structure.
Note that you can perform more complicated fitting (multi-variate, custom equations) with "fit", as demonstrated in the "Examples" section of the documentation link below:
You can plot the fit using:
plot(myfit,a,b);
You can use the "confint" and "predint" functions to get the confidence and prediction intervals for the fit.
If the approach above does not suit your application, please provide more information about your vectors in order to clarify what you are looking to accomplish.
