Data :- concentration vs response at 5 levels; and in triplicate measurements for each level. ( i.e., 5_concentrations & 3 measurements at each level, 5-levels of 3 sets each)

Requirement :- required to demonstrate goodness of regression equation., and test for homoscadasticity is recommended.

F-Value and Normal plot for residuals is considered qualitative / not-objective and are deemed generally not-acceptable/adequate. and

certain alternatives of ‘White’s’ test and ‘Breusch pagan’ test were tried; but the simulation of results were counter-intuitive. viz., despite highly variable residuals, decreasing residuals leads to still failing of the criteria; and seemingly the tests anticipate certain bias in the residuals. ( viz., higher conc have higher residuals)

For linear ranges, the deviations should be equally distributed between positive and negative values. Another approach is to divide signal data by their respective concentrations, yielding the relative responses. A graph is plotted with the relative responses on the y-axis and the corresponding concentrations on the x-axis, on a log scale.The obtained line should be horizontal over the full linear range. At higher concentrations, there will typically be a negative deviation from linearity. Parallel horizontal lines are drawn on the graph corresponding, for example, 95 percent and 105 percent of the horizontal line. The method is linear up to the point where the plotted relative response line intersects the 95 percent line.

(Araujo_LinearitY-sdarticle%20(2).pdf)

Analytical Method Committee suggests using the F-test as a reliable approach to check the linearity of any calibration function.

• The value of F(I–2)/(IJ–I) calculated experimentally is compared against the critical value of F found in statistical tables, generally at the 95% confidence level for I − 2 and IJ − J degrees of freedom in the numerator and denominator respectively. If the experimental data set describes a genuine linear calibration of the form given by Eq.(1)then the condition Ftabulated > F(I–2)/(IJ–I) must be fulfilled. Otherwise there are grounds to suspect that a different model to the described by Eq. (1) must be proposed.

• The estimation of the various error sum squares and the Fisher ratio for testing the acceptability of a linear model proposed in the literature is discussed in Appendix A.

Paragraph 1. Data

Paragraph 2. In statistical tests, a significance level of five per cent (5%) shall be used.

Paragraph 3. Correlation coefficient shall be above 0.990.

Paragraph 4. Angular coefficient shall be significantly different from zero.

2.2.2. If there is apparent linear relation after visual examination of the graph, the results of the tests must be handled with appropriate statistical methods for determination of the correlation coefficient, intersection with the Y axis, angular coefficient, residual addition of the minimum squares of the linear regression and relative standard deviation. If there is no linear relation, undertake mathematical transformation.

2.2.3. The acceptable minimum criterion of the correlation coefficient (r) must be = 0.99.

2.2.4. The curves obtained must be presented (from the experiment and from the result of the mathematical treatment).

Requirement :- required to demonstrate goodness of regression equation., and test for homoscadasticity is recommended.

**problem**:-F-Value and Normal plot for residuals is considered qualitative / not-objective and are deemed generally not-acceptable/adequate. and

certain alternatives of ‘White’s’ test and ‘Breusch pagan’ test were tried; but the simulation of results were counter-intuitive. viz., despite highly variable residuals, decreasing residuals leads to still failing of the criteria; and seemingly the tests anticipate certain bias in the residuals. ( viz., higher conc have higher residuals)

**references**looked up on net are as follows :-**(1)JP xiv :- validation of analytical****(1`)Development and validation of an analytical method using High Performance Liquid Chromatography (HPLC) to determine ethyl butylacetylaminopropionate in topical repellent formulations****Brazilian Journal of Pharmaceutical Sciences***On-line version*ISSN 2175-9790For linear ranges, the deviations should be equally distributed between positive and negative values. Another approach is to divide signal data by their respective concentrations, yielding the relative responses. A graph is plotted with the relative responses on the y-axis and the corresponding concentrations on the x-axis, on a log scale.The obtained line should be horizontal over the full linear range. At higher concentrations, there will typically be a negative deviation from linearity. Parallel horizontal lines are drawn on the graph corresponding, for example, 95 percent and 105 percent of the horizontal line. The method is linear up to the point where the plotted relative response line intersects the 95 percent line.

**(2)A Practical Guide to Analytical Method Validation**(Araujo_LinearitY-sdarticle%20(2).pdf)

Analytical Method Committee suggests using the F-test as a reliable approach to check the linearity of any calibration function.

• The value of F(I–2)/(IJ–I) calculated experimentally is compared against the critical value of F found in statistical tables, generally at the 95% confidence level for I − 2 and IJ − J degrees of freedom in the numerator and denominator respectively. If the experimental data set describes a genuine linear calibration of the form given by Eq.(1)then the condition Ftabulated > F(I–2)/(IJ–I) must be fulfilled. Otherwise there are grounds to suspect that a different model to the described by Eq. (1) must be proposed.

• The estimation of the various error sum squares and the Fisher ratio for testing the acceptability of a linear model proposed in the literature is discussed in Appendix A.

**(4)Establishing Acceptance Criteria for Analytical Methods****(3)ANVISA :- RESOLUTION OF THE COLLEGIATE BOARD - RDC Nº. 166, DATED JULY 24th, 2017 Providing for the validation of analytical methods and other provisions.**Paragraph 1. Data

**homocedasticity**shall be investigated for the use of a proper model.Paragraph 2. In statistical tests, a significance level of five per cent (5%) shall be used.

Paragraph 3. Correlation coefficient shall be above 0.990.

Paragraph 4. Angular coefficient shall be significantly different from zero.

**ANVISA :-****(3)Resolution - RE n. 899, of May 29, 2003 D.O.U. 02/06/2003 - Original link is dead.****GUIDE FOR VALIDATION OF ANALYTICAL AND BIOANALYTICAL METHODS - Original ink is dead (http ://www .anvisa.gov. br/hotsite/ genericos/ legis/ resolucoes/ 2003/899_03re_e.pdf) Available on Scribd (pay site) - 899_03re_e.pdf | Coefficient Of Variation | Detection Limit - 2003**2.2.2. If there is apparent linear relation after visual examination of the graph, the results of the tests must be handled with appropriate statistical methods for determination of the correlation coefficient, intersection with the Y axis, angular coefficient, residual addition of the minimum squares of the linear regression and relative standard deviation. If there is no linear relation, undertake mathematical transformation.

2.2.3. The acceptable minimum criterion of the correlation coefficient (r) must be = 0.99.

2.2.4. The curves obtained must be presented (from the experiment and from the result of the mathematical treatment).

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