boot.slope.bca: BCa Bootstrap Test and CI for the Slope of a Population...
In wBoot: Bootstrap Methods

Description Usage Arguments Details Value Author(s) Examples

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.

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

`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 is "greater".
`R`	the number of bootstrap replications; default is 9999.

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.

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.

Neil A. Weiss

# 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

Loading required package: boot
Loading required package: simpleboot
Simple Bootstrap Routines (1.1-7)
'data.frame':	44 obs. of  3 variables:
 $ HOUSE.SIZE: num  2311 2968 3773 1934 5466 ...
 $ LOT.SIZE  : num  2.37 2.09 2.21 2.21 2.1 2.06 2.03 2.44 2.14 2.63 ...
 $ VALUE     : num  396 355 586 254 646 278 279 748 546 338 ...


 RESULTS OF BCa BOOTSTRAP FOR SLOPE 

    SUMMARY Predictor Response  n Statistic Observed
 STATISTICS  LOT.SIZE    VALUE 44     slope 67.11283

 BOOTSTRAP Replications     Mean       SE Bias Percent.bias
   SUMMARY          999 76.01825 65.69974 8.91         13.3

 HYPOTHESIS Null  Alternative P.value
       TEST    0 greater-than  0.0943

 CONFIDENCE Level        Type Confidence.interval
   INTERVAL   95% lower-bound         -14.3 (LCB)




 RESULTS OF BCa BOOTSTRAP FOR SLOPE 

    SUMMARY  Predictor Response  n Statistic  Observed
 STATISTICS HOUSE.SIZE    VALUE 44     slope 0.1115874

 BOOTSTRAP Replications      Mean         SE     Bias Percent.bias
   SUMMARY          999 0.1125549 0.01493498 0.000968        0.867

 HYPOTHESIS Null  Alternative P.value
       TEST    0 greater-than 0.00119

 CONFIDENCE Level      Type Confidence.interval
   INTERVAL   90% two-sided   (0.08943, 0.1367)