# power.SLR.rho: Power for testing slope for simple linear regression In powerMediation: Power/Sample Size Calculation for Mediation Analysis

## Description

Calculate power for testing slope for simple linear regression.

## Usage

 ```1 2 3 4``` ```power.SLR.rho(n, rho2, alpha = 0.05, verbose = TRUE) ```

## Arguments

 `n` sample size. `rho2` square of the correlation between the outcome and the predictor. `alpha` type I error rate. `verbose` logical. `TRUE` means printing power; `FALSE` means not printing power.

## Details

The power is for testing the null hypothesis λ=0 versus the alternative hypothesis λ\neq 0 for the simple linear regressions:

y_i=γ+λ x_i + ε_i, ε_i\sim N(0, σ^2_{e})

## Value

 `power ` power for testing if b_2=0. `delta ` √{n}/√{1/ρ^2-1}.

## Note

The test is a two-sided test. For one-sided tests, please double the significance level. For example, you can set `alpha=0.10` to obtain one-sided test at 5% significance level.

## Author(s)

Weiliang Qiu stwxq@channing.harvard.edu

## 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.

`minEffect.SLR`, `power.SLR`, `ss.SLR.rho`, `ss.SLR`.
 `1` ``` power.SLR.rho(n=100, rho2=0.6, alpha = 0.05, verbose = TRUE) ```