wBoot (version 1.0.3)

boot.slope.per: Percentile 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 percentile bootstrap method.

Usage

boot.slope.per(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.

Warning

This routine should be used only when bias is small and the sampling distribution is roughly symmetric, as indicated by the output of the bootstrap. Otherwise, use the BCa version.

concept

• Bootstrap
• Percentile 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.per(LOT.SIZE, VALUE, null.hyp = 0, alternative = "greater", R = 999)
# See the preceding warning!

# 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.per(HOUSE.SIZE, VALUE, null.hyp = 0, alternative = "greater",
conf.level = 0.90, type = "two-sided", R = 999)

detach(homes) # clean up