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.
1 2 3 4 
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 
R2.j_X.without.j 
the squared multiple correlation coefficient predicting the 
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 
t.value 
the tvalue evaluating the null hypothesis that the population regression coefficient for the 
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 

Suppress.Statement 

... 
optional additional specifications for nested functions 
For standardized variables, do not specify the standard deviation of the variables and input the standardized
regression coefficient for b.j
.
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 tdistribution.
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.
Ken Kelley (University of Notre Dame; KKelley@ND.Edu)
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
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