Analyst Regression Equations


日付: 12/04/2017
カテゴリー: Analyst Software

0 投票
   印刷する    記事を評価する:

For research use only. Not for use in diagnostic procedures.
Quant Regression Equations

This document summarises the equations used by Analyst to calculate the regression curves used for Quantitation.

 

In the equations given below, “x” represents the analyte concentration for standards and “y” represents the corresponding peak area or height. More precise definitions are given in the following table where:

 

Ca = actual analyte concentration

Cis = internal standard concentration

DF = dilution factor

Aa = analyte peak area

Ais = internal standard peak area

Ha = analyte peak height

His = internal standard peak height

 

IS Used?

Area Used?

x

y

yes

yes

Ca / Cis / DF

Aa / Ais

 

no

 

Ha / His

no

yes

Ca / DF

Aa

 

no

 

Ha

 

Weighting Factors

The following table shows how the weighting factor (w in the equations below) is calculated for each of the seven weighting types.

 

Weighting Type

Weight (w)

None

Always 1.0.

1 / x

If |x| < 10-5 then w = 105, otherwise w = 1 / |x|.

1 / x2

If |x| < 10-5 then w = 1010, otherwise w = 1 / x2.

1 / y

If |y| < 10-8 then w = 108, otherwise w = 1 / |y|.

1 / y2

If |y| < 10-8 then w = 1016, otherwise w = 1 / y2.

ln x

If x < 0 an error is generated, otherwise if x < 10-5 then w = ln 105, otherwise w = |ln x|.

ln y

If y < 0 an error is generated, otherwise if y < 10-8 then w = ln 108, otherwise w = |ln y|.

 

Regressions

This section gives the equations for each of the regression types. In the equations below x, y and w are as defined above. All sums are calculated over all standards (with the exception of those standards which are marked as “not used”).Linear

 

The linear calibration equation is:

y = m x + b

 

The slope and intercept are calculated as:

m = ( w wxy - wx wy ) / Dx

b = ( wx2 wy - wx wxy ) / Dx

 

and the correlation co-efficient is calculated as:

r = ( w wxy - wx wy ) / ( Dx Dy)

 

where:

 

Dx = w wx2 - ( wx )2

Dy = w wy2 - ( wy )2

Linear Through Zero

The liner through zero calibration equation is:

y = m x

 

The slope is calculated as:

m = wxy / wx2

 

and the correlation co-efficient as:

r = wxy / ( wx2 wy2 )

 

Mean Response Factor

The mean response factor calibration is:

y = m x

 

This is the same equation as for the linear though zero case. However the slope is calculated differently as:

m = wy/x / wand the standard deviation as:

= ( nD / ( n - 1 ) ) / w

 

where:

D = w * wy2/x2 - ( wy/x )2

Note that points whose x value is zero are excluded from the sums.

 

RUO-IDV-0888-A