# ci.reg.coef: Confidence interval for a regression coefficient In MBESS: The MBESS R Package

## Description

A function to calculate a confidence interval around the population regression coefficient of interest using the standard approach and the noncentral approach when the regression coefficients are standardized.

## Usage

 ```1 2 3 4``` ```ci.reg.coef(b.j, SE.b.j=NULL, s.Y=NULL, s.X=NULL, N, p, R2.Y_X=NULL, R2.j_X.without.j=NULL, conf.level=0.95, R2.Y_X.without.j=NULL, t.value=NULL, alpha.lower=NULL, alpha.upper=NULL, Noncentral=FALSE, Suppress.Statement=FALSE, ...) ```

## Arguments

 `b.j` value of the regression coefficient for the jth predictor variable `SE.b.j` standard error for the jth predictor variable `s.Y` standard deviation of Y, the dependent variable `s.X` standard deviation of X_j, the predictor variable of interest `N` sample size `p` the number of predictors `R2.Y_X` the squared multiple correlation coefficient predicting `Y` from the `p` predictor variables `R2.j_X.without.j` the squared multiple correlation coefficient predicting the `j`th predictor variable (i.e., the predictor of interest) from the remaining `p`-1 predictor variables `conf.level` desired level of confidence for the computed interval (i.e., 1 - the Type I error rate) `R2.Y_X.without.j` the squared multiple correlation coefficient predicting `Y` from the `p`-1 predictor variable with the `j`th predictor of interest excluded `t.value` the t-value evaluating the null hypothesis that the population regression coefficient for the `j`th predictor equals zero `alpha.lower` the Type I error rate for the lower confidence interval limit `alpha.upper` the Type I error rate for the upper confidence interval limit `Noncentral` `TRUE` or `FALSE`, specifying whether or not the noncentral approach to confidence intervals should be used `Suppress.Statement` `TRUE`/`FALSE` statement specifying whether or not a statement should be printed that identifies the type of confidence interval formed `...` optional additional specifications for nested functions

## Details

For standardized variables, do not specify the standard deviation of the variables and input the standardized regression coefficient for `b.j`.

## Value

Returns the confidence limits specified for the regression coefficient of interest from the standard approach to confidence interval formation or from the noncentral approach to confidence interval formation using the noncentral t-distribution.

## Note

Not all of the values need to be specified, only those that contain all of the necessary information in order to compute the confidence interval (options are thus given for the values that need to be specified).

The function `ci.rc` in MBESS also calculates the confidence interval for the population (unstandardized) regression coefficient. The function `ci.src` also calculates the confidence interval for the population (standardized) regression coefficient. These two functions perform the same tasks as `ci.reg.coef` does and are preferred to it because of simpler arguments.

## Author(s)

Ken Kelley (University of Notre Dame; [email protected])

## References

Kelley, K. & Maxwell, S. E. (2003). Sample size for Multiple Regression: Obtaining regression coefficients that are accurate, not simply significant. Psychological Methods, 8, 305–321.

Kelley, K. & Maxwell, S. E. (2008). Sample Size Planning with applications to multiple regression: Power and accuracy for omnibus and targeted effects. In P. Alasuuta, J. Brannen, & L. Bickman (Eds.), The Sage handbook of social research methods (pp. 166–192). Newbury Park, CA: Sage.

Smithson, M. (2003). Confidence intervals. New York, NY: Sage Publications.

`ss.aipe.reg.coef`, `conf.limits.nct`, `ci.rc`, `ci.src`