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I am testing an automated counting method. To measure its effectiveness I am doing a linear regression model comparing the manual approach to the automatic. This gives me an F statistic for the model adjustment, a coefficient of determination ($R^2$) of the model and the $a$ and $b$ parameters ($y = a + bx$).

Now I would like to determine the minimum sample size to estimate the true counting means within a given error rate of 5%, for example.

Is it possible to be determined?

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Yes, it is possible to be determined. In general I think what you want to touch upon is power analysis and accuracy in parameter estimation analysis. Please note that they are not the same notions. Kelley and Maxwell's article on "Sample Size for Multiple Regression: Obtaining Regression Coefficients That Are Accurate, Not Simply Significant" is very good place to start. Check the R package MBESS developed Kelley and Lai package to perform this kind of sample size analysis in regards to accurate parameter estimation.

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  • $\begingroup$ Thank you for the answer. I was wondering if there is a way to determine this number without the need of the power parameter, just based on the errors between the observed values and the predicted by the model. Something like sample size determination based only on the confidence interval of the mean. $\endgroup$
    – Walter
    Jan 4, 2016 at 21:41
  • $\begingroup$ Not to my immediate knowledge, sorry. $\endgroup$
    – usεr11852
    Jan 5, 2016 at 0:17

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