A solution to minimum sample size for regressions

Regressions and meta-regressions are widely used to estimate patterns and effect sizes in various disciplines. However, many biological and medical analyses use relatively low sample size (N), contributing to concerns on reproducibility. What is the minimum N to identify the most plausible data pattern using regressions? Statistical power analysis is often used to answer that question, but it has its own problems and logically should follow model selection to first identify the most plausible model. Here we make null, simple linear and quadratic data with different variances and effect sizes. We then sample and use information theoretic model selection to evaluate minimum N for regression models. We also evaluate the use of coefficient of determination (R2) for this purpose; it is widely used but not recommended. With very low variance, both false positives and false negatives occurred at N