wBoot (version 1.0.3)

boot.slope.bca: BCa Bootstrap Test and CI for the Slope of a Population Regression Line in Simple Linear Regression

Description

Obtains a confidence interval and (optionally) performs a hypothesis test for the slope of a population regression line in simple linear regression, using the BCa bootstrap method.

Usage

boot.slope.bca(x, y, null.hyp = NULL,
               alternative = c("two.sided", "less", "greater"),
               conf.level = 0.95, type = NULL, R = 9999)

Arguments

x

a (non-empty) numeric vector of predictor-variable data values.

y

the corresponding numeric vector of response-variable data values.

null.hyp

the null-hypothesis value; if omitted, no hypothesis test is performed.

alternative

a character string specifying the alternative hypothesis; must be one of "two.sided" (default), "greater", or "less".

conf.level

the confidence level (between 0 and 1); default is 0.95.

type

character string specifying the type of CI; if user-supplied, must be one of "two-sided", "upper-bound", or "lower-bound"; defaults to "two-sided" if alternative is "two.sided", "upper-bound" if alternative is "less", and "lower-bound" if alternative i

R

the number of bootstrap replications; default is 9999.

Value

• A list with class "boot.regcor" containing the following components:
• Boot.values
  the point estimates for the slope obtained from the bootstrap.
• Confidence.limits
  the confidence limit(s) for the confidence interval.
• Header
  the main title for the output.
• Variable.1
  the predictor variable.
• Variable.2
  the response variable.
• n
  the sample size.
• Statistic
  the name of the statistic, here slope.
• Observed
  the observed point estimate for the slope.
• Replications
  the number of bootstrap replications.
• Mean
  the mean of the bootstrap values.
• SE
  the standard deviation of the bootstrap values.
• Bias
  the difference between the mean of the bootstrap values and the observed value.
• Percent.bias
  the percentage bias: 100*|Bias/Observed|.
• Null
  the null-hypothesis value or NULL.
• Alternative
  the alternative hypothesis or NULL.
• P.value
  the P-value or a statement like P < 0.001 or NULL.
• p.value
  the P-value or NULL.
• Level
  the confidence level.
• Type
  the type of confidence interval.
• Confidence.interval
  the confidence interval.
• cor.ana
  a logical; always FALSE for this function.

concept

• Bootstrap
• BCa bootstrap
• Simple linear regression
• Confidence interval
• Hypothesis test
• Inferences for the slope of a population regression line

Details

If null.hyp = 0 and alternative = "two.sided", then the hypothesis test is equivalent to testing whether the predictor variable is useful for making predictions.

Examples

# Lot size, house size, and value for a sample of homes in a particular area.
data("homes")
str(homes)
attach(homes)

# 95% (default) lower confidence bound for the slope of the population regression
# line relating lot size and value, a right-tailed test with null hypothesis 0,
# and 999 bootstrap replications.
boot.slope.bca(LOT.SIZE, VALUE, null.hyp = 0, alternative = "greater", R = 999)

# 90% two-sided confidence interval for the slope of the population regression line
# relating house size and value, a right-tailed test with null hypothesis 0, and
# 999 bootstrap replications.
boot.slope.bca(HOUSE.SIZE, VALUE, null.hyp = 0, alternative = "greater",
conf.level = 0.90, type = "two-sided", R = 999)

detach(homes) # clean up