Dear colleagues,
I need to perform a regression. The input data is shown in Figure 1 and is also attached as an MS Excel file.
Figure 1 (Figures are shown in the end of the letter.
The equation is z = a*x^m/(y+c)^n.
The parameters of the fit are shown in Figure 2 and are also attached.
Figure 2

The output data is shown in Figure 3.
Figure 3
The individual differences in percentage are shown in Figure 4.
Figure 4
I know that by using a weighted matrix, it is possible to decrease some differences (priority zones) at the expense of increasing others. However, in this case, my goal is to estimate the minimal possible error (one border value) for all of the values. For example, in the first fit, the maximum difference is 93%. It is easy to decrease it by applying individual weight coefficients, but of course, somewhere, the difference will increase. Therefore, the question is: what method can be used to find the minimal possible difference? If this for example is 18%, it means that everywhere the difference will be smaller, and it is likely that there is no 0 % anymore. Example by hand (not real) is given in Figure 5.
Figure 5
And if we try to decrease the difference at the point with an 18% difference, this will lead to an increase in the difference somewhere above 18%. Also, if in the first fit I have a 0% or 1% difference at a given point, in the second fit, the difference at this point is likely to be close (but smaller) to 18%. And one more thing – if there is a way for doing the whole procedure, is it possible to use curve fitter app or need to use a code?Dear colleagues,
I need to perform a regression. The input data is shown in Figure 1 and is also attached as an MS Excel file.
Figure 1 (Figures are shown in the end of the letter.
The equation is z = a*x^m/(y+c)^n.
The parameters of the fit are shown in Figure 2 and are also attached.
Figure 2

The output data is shown in Figure 3.
Figure 3
The individual differences in percentage are shown in Figure 4.
Figure 4
I know that by using a weighted matrix, it is possible to decrease some differences (priority zones) at the expense of increasing others. However, in this case, my goal is to estimate the minimal possible error (one border value) for all of the values. For example, in the first fit, the maximum difference is 93%. It is easy to decrease it by applying individual weight coefficients, but of course, somewhere, the difference will increase. Therefore, the question is: what method can be used to find the minimal possible difference? If this for example is 18%, it means that everywhere the difference will be smaller, and it is likely that there is no 0 % anymore. Example by hand (not real) is given in Figure 5.
Figure 5
And if we try to decrease the difference at the point with an 18% difference, this will lead to an increase in the difference somewhere above 18%. Also, if in the first fit I have a 0% or 1% difference at a given point, in the second fit, the difference at this point is likely to be close (but smaller) to 18%. And one more thing – if there is a way for doing the whole procedure, is it possible to use curve fitter app or need to use a code? Dear colleagues,
I need to perform a regression. The input data is shown in Figure 1 and is also attached as an MS Excel file.
Figure 1 (Figures are shown in the end of the letter.
The equation is z = a*x^m/(y+c)^n.
The parameters of the fit are shown in Figure 2 and are also attached.
Figure 2

The output data is shown in Figure 3.
Figure 3
The individual differences in percentage are shown in Figure 4.
Figure 4
I know that by using a weighted matrix, it is possible to decrease some differences (priority zones) at the expense of increasing others. However, in this case, my goal is to estimate the minimal possible error (one border value) for all of the values. For example, in the first fit, the maximum difference is 93%. It is easy to decrease it by applying individual weight coefficients, but of course, somewhere, the difference will increase. Therefore, the question is: what method can be used to find the minimal possible difference? If this for example is 18%, it means that everywhere the difference will be smaller, and it is likely that there is no 0 % anymore. Example by hand (not real) is given in Figure 5.
Figure 5
And if we try to decrease the difference at the point with an 18% difference, this will lead to an increase in the difference somewhere above 18%. Also, if in the first fit I have a 0% or 1% difference at a given point, in the second fit, the difference at this point is likely to be close (but smaller) to 18%. And one more thing – if there is a way for doing the whole procedure, is it possible to use curve fitter app or need to use a code? curve fitter toolbox, weighted regression MATLAB Answers — New Questions

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