MyRegressionINV

Resolve a calibration problem that is: to estimate mean value and confidence interval of x since y

Description

MYREGRINV: Resolve a calibration problem (inverse regression problem) that is: to estimate mean value and confidence interval of x since y.
This function computes a least-square linear regression using the supplied calibration points and then computes the X values for a supplied y observed vector. This routine use MYREGR function. If it is not present on the computer, MyregrINV will try to download it from FEX.

References:
Sokal R.R. and Rohlf F.J. 2003 BIOMETRY. The Principles and Practice of Statistics in Biological Research (3rd ed., 8th printing, Freeman and Company, New York, XIX + 887 p.) pag. 491 - 493.

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• Required Products: Statistics Toolbox
• MATLAB release: MATLAB 7.3 (R2006b)

[Dimitri Shvorob]

What is the 'calibration problem'? Can you provide a reference? I am especially interested in how you construct CIs.

[Giuseppe Cardillo]

A calibration problem (inverse regression problem) is: to estimate mean value and confidence interval of x since y.
I used university lessons issues and the indicated reference is:
Sokal R.R. and Rohlf F.J. 2003 BIOMETRY. The Principles and Practice of Statistics in Biological Research (3rd ed., 8th printing, Freeman and Company, New York, XIX + 887 p.) pag. 491 - 493.

For the confidence intervals (CIs) first of all you must check if these CIs exist (in the new upload version this is implemented). Then you must calculate a parameter K. K is a value depending from alpha and degrees of freedom of error variance; it can be estimated by tinv(alpha/2,n-2), the same used in MYREGR function to test slope and intercept.