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.
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, ...)value of the regression coefficient for the jth predictor variable
standard error for the jth predictor variable
standard deviation of Y, the dependent variable
standard deviation of \(X_j\), the predictor variable of interest
sample size
the number of predictors
the squared multiple correlation coefficient predicting Y from the p predictor variables
the squared multiple correlation coefficient predicting the jth predictor variable (i.e., the predictor of interest) from the remaining p-1 predictor variables
desired level of confidence for the computed interval (i.e., 1 - the Type I error rate)
the squared multiple correlation coefficient predicting Y from the p-1 predictor variable with the jth predictor of interest excluded
the t-value evaluating the null hypothesis that the population regression coefficient for the jth predictor equals zero
the Type I error rate for the lower confidence interval limit
the Type I error rate for the upper confidence interval limit
TRUE or FALSE, specifying whether or not the noncentral approach to confidence intervals should be used
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
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.
For standardized variables, do not specify the standard deviation of the variables and input the standardized
regression coefficient for b.j.
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