# Use of ‘y-intercept’ statistic in linearity test

Dear friends,

ICH guideline Q2(R1) recommends that, linearity should be evaluated first by visual inspection of a plot of signals as a function of analyte concentration or content. If there is a linear relationship, test results should be evaluated by appropriate statistical methods, for example, by calculation of a regression line by the method of least squares. The correlation coefficient, y-intercept, slope of the regression line and residual sum of squares should be submitted. For the establishment of linearity, a minimum of 5 concentrations is recommended.

I want to raise the topic ‘y-intercept’ here as I am little bit confused how to use this statistic in the determination linearity of a developed method. It is clear from the regression analysis that, ‘y-intercept’ is supposed to be zero. ICH guideline Q2(R1) did not specify how to check whether the calculated ‘y-intercept’ is within the acceptable range or not; and what is the acceptable range (deviation from zero).

I would appreciate if you kindly let me know the recommended test procedures for the ‘y-intercept’ known to you as well as their acceptable range (deviation from zero).

Thanks,
ahma

Mr. T.Arun wrote below elsewhere:

Residual error in regression: [Y- intercept*100]/ [Response @Target conc ]

May I use this equation for the above purpose?

ahma

Hi,

Find the Calculation of y-Intercept calculation with an example.

Residual (y-intercept at concentration 0) = (y-intercept x 100)/ response at 100%

Limit: Y intercept is NMT 2% of the response corresponding to the target sample concentration of the lowest label claim.

Example Y-Intercept is about = 0.0103

Lowest strength standard absorbance at target sample concentration is = 0.856

Y-intercept * 100 / absorbance at target concentration

That is = 0.0103*100/0.856 = 1.2%

Thanks,
abr

Thank you for your kind response on the above. I identified following three important parts/ points in your reply:

1. You have supported the same calculation formula for the Residual (y-intercept at concentration 0) earlier recommended by Mr. T.Arun:
Residual (y-intercept at concentration 0) = (y-intercept x 100)/ response at 100%

2. You have proposed a Limit for the Residual (y-intercept at concentration 0):
Y intercept is NMT 2% of the response corresponding to the target sample concentration of the lowest label claim.

3. In the limit as well as in calculation, you have recommended to use “the response corresponding to the target sample concentration of the lowest label claim”. The last part of the santenses, namely “of the lowest label claim” is little bit confusing. Is this for the examples of proposed analytical methods when are to be used for the several streangths of same products?

Another conclussion can be derrived from the above that, in linearity test one of the series of concentrations should be of 100% of the concentration as proposed in the analytical method itself (same concentration which is to be measured by the method during its implementation). As I understand, this is also requirement of ICH guideline.

How to equalize/ synchronize the “100% of the concentration as proposed in the analytical method itself” and “target sample concentration of the lowest label claim”?

Thanks once again,
ahma

y- intercept means

The point at which the curve touches the y-axis is called intecept.[ extrapolate the curve ]

If the concentrations and Absorbances are exactly linear(r^2 = 1), the value of y-intercept is zero, It indicates there is no deviation of the linear curve.

if you get y-intercept other than zero, it clearly indicates there is a deviation. that deviation must be estimated by the formula as stated above.

that is expressed in % also.

(y-intercept x 100)/ response at 100%

% y -intercept conventionally acceptable.

assay :+/-2%
Impurities : +/-5%

Best regards,
Bujji Reddy Kanchi.

what is the meaning of this
The y-intercept will be < 2% of the target concentration

can anybody provide me the reference guideline for acceptance criteria for y intercept, as it is NMT 2%

Shyamal,

There is no guideline but only good scientific common sense. Typically the correlation of coefficient for an HPLC system is 0.999, that is a linear response. If so, the positive response of the analyte is due to 2 factors, the slope (m) and the y-intercept (b). The slope varies with the detector and the molecule. But, the chemist arranges the test method so the response is due to 98.0% of the m factor, and 2.0% of the b factor. Thus, a 2.0% RSD is appropriate for the y-intercept if the API label claim is 98.0-102.0%. If the API label claim is 95.0-105.0%, 5.0% is more appropriate.

Thus, the %RSD depends on your specification, label claim, molecule, sample matrix, instrument (method).