| Abstract: | This paper develops an explicit relationship between sample size, sampling error, and related costs for the application of multiple regression models in observational studies. Graphs and formulas for determining optimal sample sizes and related factors are provided to facilitate the application of the derived models. These graphs reveal that, in most cases, the imprecision of estimates and minimum total cost are relatively insensitive to increases in sample size beyond n=20. Because of the intrinsic variation of the regression model, even if larger samples are optimal, the relative change in the total cost function is small when the cost of imprecision is a quadratic function. A model-utility approach, however, may impose a lower bound on sample size that requires the sample size be larger than indicated by the estimation or cost-minimization approaches. Graphs are provided to illustrate lower-bound conditions on sample size. Optimal sample size in view of all considerations is obtained by the maximin criterion, the maximum of the minimum sample size for all approaches. |
