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I have measured 2 parameters, r and p. Each parameter was measured in three technical replicates (n=3) per sample. r is measured directly. p is measured indirectly; the data obtained is output voltages of a measurement instrument. To correlate these with p, I produced a calibration curve by measuring samples of known p. I then calculated a linear regression and obtained a formula
$p(V) = m*V +b$ in which V is the measured voltage. But this regression was calculated using the mean of the three measurements.

1) How do I calculate a linear regression that takes into account the error of each measurement?

To obtain values of p for my samples I entered the measured voltages in the formula.

2) How do I calculate the error of a value predicted by linear regression?

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I'm not sure about your first question, but the second one has many answers to it. I'll describe main statistical techniques for measuring error rate.

  • residuals. The most simple approach is to find the difference between the predicted value and real value.
  • variance of the errors. The bigger variance is, the worse model works.
  • standart errors for intercept and beta values. I think that no explanation is needed.
  • residuals standart errors. Better way to measure residuals.
  • t-statistics of beta values and resulting probability of beta values to be 0. The bigger probability is, the higher possibility that there's no correlation between variables.
  • amount of variance explained by the model.
  • correlation between model and output.

Not all the measurements described here are error rates, but they help us to evaluate how well model works and may be useful for you.

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