  The problem tackled in this paper is the determination of sample size for a
given level and power in the context of a simple linear regression model. At a
technical level, the simple linear regression model is a five-parameter model.
It is natural to base sample size calculations on the least squares' estimator
of the slope parameter of the model. Nuisance parameters such as the variance
of the predictor X and conditional variance of the response Y create problems
in the calculations. The current approaches in the literature are not
illuminating. One approach is based on the conditional distribution of the
estimator of the slope parameter given the data on the predictor X. Another
approach is based on the sample correlation coefficient. We overcome the
problems by determining the exact unconditional distribution of the test
statistic built on the estimator of the slope parameter. The exact
unconditional distribution alleviates difficulties to some extent in the
computation of sample sizes. On the other hand, the test based on the sample
correlation coefficient of X and Y avoids the problems besetting the test based
on the slope parameter. However, we lose intuitive interpretation that comes
with the slope parameter. Surprisingly, we see that the sample size that comes
from the correlation test works in synchronization with the one that comes from
the test built upon the slope parameter in a broad array of settings.
