power for testing if $\lambda=0$ for the simple linear regression
$y_i=\gamma+\lambda x_i + \epsilon_i, \epsilon_i\sim N(0, \sigma_{e}^2).$
lambda.a
regression coefficient in the simple linear regression
$y_i=\gamma+\lambda x_i + \epsilon_i, \epsilon_i\sim N(0, \sigma_{e}^2).$
sigma.x
standard deviation of the predictor.
sigma.y
standard deviation of the outcome.
n.lower
lower bound for the sample size.
n.upper
upper bound for the sample size.
alpha
type I error rate.
verbose
logical. TRUE means printing sample size; FALSE means not printing sample size.
Value
n
sample size.
res.uniroot
results of optimization to find the optimal sample size.
Details
The test is for testing the null hypothesis $\lambda=0$
versus the alternative hypothesis $\lambda\neq 0$
for the simple linear regressions:
$$y_i=\gamma+\lambda x_i + \epsilon_i, \epsilon_i\sim N(0, \sigma^2_{e})$$
References
Dupont, W.D. and Plummer, W.D..
Power and Sample Size Calculations for Studies Involving Linear Regression.
Controlled Clinical Trials. 1998;19:589-601.