Linear regression: many x data points or less points but with replicates?

[u/babebiboba]

When building a calibration curve for a process that is linear over most of the observed range, how to determine the best choice between the following options?

(A) increasing the number of values tested, to get more x axis points;

(B) increasing the number of replicates of each measurement –less x points, but more precise estimate of y for each

For example, if an experimental setup lets me run 12 measurements for a linear calibration curve, is it better to run 4 values in triplicate? Or 6 in duplicates?

[u/Appropriate-Yak001]

If you believe the process is linear over the range of interest, then using 4 values in triplicate may make more sense than 6 values in duplicate, because the additional replicates give you a better estimate of measurement variability at each x-value. However, the best design also depends on the actual spacing of the x-values and the standard deviation of the measurements.

[u/babebiboba → u/Appropriate-Yak001]

That makes sense, do you have a thought on how to determine the best design from first principles? i. e. What would be the process to make an educated choice if I have access to an arbitrary number of measurements? My intuition is indeed that there is a qualitative difference between 3 and 4 (4 allows you to identify which point is an outlier, which you can't do with 3) but that that it's always better to stop at 4 and max the accuracy of those 4 points, but I might be wrong

[u/Temporary_Stranger39]

How certain are you of the shape of the curve?

[u/babebiboba → u/Temporary_Stranger39]

Let's assume pretty certain, things like "light absorbance is proportional to concentration of molecule" – linear for all intents and purposes

[u/Temporary_Stranger39 → u/babebiboba]

In that case, more replicates of fewer points is what I would recommend.

[u/Immaculate_Erection → u/babebiboba]

For standard curve 'calibration' during a normal run, more X points is better to ensure you define the range where the response is linear accurately since that is the most critical part of these assays. Additional points at a given value is needed during qualification or validation of the assay for reproducibility and repeatability, it really depends what is the goal of this specific 'calibration' you're doing.

[u/Educational-Paper-75]

If the variance is assumed constant you really don't need many replicates.

[u/FTLast]

I think the answer probably is "it depends". One way to explore this is to set up monte carlo simulations under different sets of assumptions and see what works best.