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The problem tackled in this paper is the determination of sample size for agiven level and power in the context of a simple linear regression model. At atechnical level, the simple linear regression model is a five-parameter model.It is natural to base sample size calculations on the least squares' estimatorof the slope parameter of the model. Nuisance parameters such as the varianceof the predictor X and conditional variance of the response Y create problemsin the calculations. The current approaches in the literature are notilluminating. One approach is based on the conditional distribution of theestimator of the slope parameter given the data on the predictor X. Anotherapproach is based on the sample correlation coefficient. We overcome theproblems by determining the exact unconditional distribution of the teststatistic built on the estimator of the slope parameter. The exactunconditional distribution alleviates difficulties to some extent in thecomputation of sample sizes. On the other hand, the test based on the samplecorrelation coefficient of X and Y avoids the problems besetting the test basedon the slope parameter. However, we lose intuitive interpretation that comeswith the slope parameter. Surprisingly, we see that the sample size that comesfrom the correlation test works in synchronization with the one that comes fromthe test built upon the slope parameter in a broad array of settings.

Sample Size Calculations in Simple Linear Regression: Trials and Tribulations