[R] Bootstrap CI of Slope in a Weighted Simple Linear Regression

[Tom La Bone]

Greetings,

I would like to use the "boot" function to generate a bootstrap confidence
interval for the slope in a SLR that has a zero intercept. My attempt to do
this is shown below. Is this the correct implementation of the boot function
to solve this problem? In particular, should I be doing anything with the
residuals in the "bs" function (e.g., using weighted residuals)? Thanks for
the help.

X <- c(0.875691867,0.871198003,0.814833892,0.788439976,0.738949275,
0.662589259,0.625487458,0.596570413,0.573693499,0.541569432,0.490628528,
0.440835275,0.397729163,0.358838088,0.323749892,0.24980067,0.213632079,
0.159989195,0.127709133,0.109218152,0.104276109,0.086467125,0.075718558,
0.059271067,0.05441905,0.049097803,0.044388138,0.014282204,0.004744354)

Y <-
c(1.710091172,1.719901584,1.677683515,1.586374357,1.492977191,1.327498848,
1.301327304,1.25174086,1.149220115,1.130543366,0.974774745,0.912550499,0.752369319,
0.745150543,0.639280298,0.478799628,0.433639966,0.346051447,0.280818024,0.230285038,
0.201046915,0.179974417,0.163766453,0.102048289,0.111175621,0.100711353,0.072401066,
0.023761328,0.013927331)

W <- 1/X

fit <- lm(Y ~ X - 1,weights=W)
Y.hat <- predict(fit)
r <- resid(fit)
data.df <- as.data.frame(cbind(X,Y,W))
bs <- function(data, indices) {
  Y.b <- Y.hat + r[indices]
  fit.b <- lm(Y.b ~ X - 1,weights=W)
  return(coef(fit.b))}
results <- boot(data=data.df, statistic=bs,R=1000)

boot.ci(results, type="perc", index=1)

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