Good morning everyone, I wondered to know when should I plot calibration curve as y=ax and when as y=ax+b ?! Is there any differences among instruments (for example, HPLC, GC, spectrometer, flame photometer, etc) in terms of their calibration curve equation? Is the difference between these two very significant?Could you please clarify it for me, I confused a little bit ...
You should use y=ax+b. The b term somehow determine/describe the error of your calib. curve, because for most detectors y=ax (with b=0) is expected.
best regards,
G
The slope is the most important part of the calibration curve. y=ax and y=ax+b have the same slope and hence the sensitivity. There are some statistical tests which tell you whether the intercept is "significant" of not.
Dear Marzieh. Concerning your issue about the linear calibration curve, y=ax or y=ax+b . Calibration curve shows a response of an analytical method to known quantities of analyte. If the analyte concentration range over which the response is proportional to concentration, i.e analytical signal proportional to the quantity of analyte, the calibration is said to be a linear response whether the plot constructed shows y=ax or y=ax+b , the only difference in the latter equation is the intercept "b". I think the following below links may help you in your issue:
https://www.mathopenref.com/linearexplorer.html
https://www.che.udel.edu/pdf/FittingData.pdf
https://www.andrews.edu/~calkins/math/edrm611/edrm06.htm
Thanks
Both equations are linear. Equation y = ax indicates the intercept is zero i.e. the graph pass through the origin. The equation y = ax + b holds when x is not equal to zero. y and b are variables on vertical and horizontal axis respectively, x is slope and b is intercept.
You should use y=ax+b. The b term somehow determine/describe the error of your calib. curve, because for most detectors y=ax (with b=0) is expected.
best regards,
G
Thank you sooo much for your valuable comment. So I will use y=ax+b to determine the error of curve, as well.
ِDear Grzegorz, so as I found, the smaller is the b, the curve is more accurate. right?
Dear Farooq , could you please let me know which statistical test should I try in this case?
Dear Marzieh Moeenfard
In fact there is a difference between,
y=ax or y=ax+b , depending on the case. But you certainly can use y=ax+b for both cases. which means if (b) representing the error only, that will be ok, such as the case with Beer's Law, where y= ax. here if the origin of your calibration is zero, then, y=ax, and y=ax+b will be the same, since (b) = zero. If not zero, then you know the value of the error.
But the case will be difference if (b) has other meaning in addition of error. For example, in the case of Ion-Selective Electrodes, Using Nernst Eq. E = K+ S(log X). which is representing y = ax +b where (b) = K .
K in this equqtion representing some other constans, in addition to error. In this case you will have Intercept K whether or not you have error.
Therefore I advise you to know the exact equation of your system. If there is no Intercept, which usually is not of a large value as it is the case if you have K value. In both cases, even if b= zero, it does not mean you dont have error in the calibration itself. Hope you understood me.
Thank and GOOD LUCK to YOU
Dear Fadhil, Thanks you so much for these great information. since my case is mainly deal with Beer's Law equation, as you suggested, y=ax+b would be appropriate, with b=0 or b=Error, depending on the conditions, right?
Dear Marzieh Moeenfard
Thank you for your response. I wish your success in your work, Good Luck to you, and thank you once agin
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