```
# NOT RUN {
require(graphics)
## Analysis of the life-cycle savings data
## given in Belsley, Kuh and Welsch.
lm.SR <- lm(sr ~ pop15 + pop75 + dpi + ddpi, data = LifeCycleSavings)
inflm.SR <- influence.measures(lm.SR)
which(apply(inflm.SR$is.inf, 1, any))
# which observations 'are' influential
summary(inflm.SR) # only these
# }
# NOT RUN {
inflm.SR # all
# }
# NOT RUN {
plot(rstudent(lm.SR) ~ hatvalues(lm.SR)) # recommended by some
plot(lm.SR, which = 5) # an enhanced version of that via plot(<lm>)
## The 'infl' argument is not needed, but avoids recomputation:
rs <- rstandard(lm.SR)
iflSR <- influence(lm.SR)
identical(rs, rstandard(lm.SR, infl = iflSR))
## to "see" the larger values:
1000 * round(dfbetas(lm.SR, infl = iflSR), 3)
cat("PRESS :"); (PRESS <- sum( rstandard(lm.SR, type = "predictive")^2 ))
stopifnot(all.equal(PRESS, sum( (residuals(lm.SR) / (1 - iflSR$hat))^2)))
## Show that "PRE-residuals" == L.O.O. Crossvalidation (CV) errors:
X <- model.matrix(lm.SR)
y <- model.response(model.frame(lm.SR))
## Leave-one-out CV least-squares prediction errors (relatively fast)
rCV <- vapply(seq_len(nrow(X)), function(i)
y[i] - X[i,] %*% .lm.fit(X[-i,], y[-i])$coef,
numeric(1))
## are the same as the *faster* rstandard(*, "pred") :
stopifnot(all.equal(rCV, unname(rstandard(lm.SR, type = "predictive"))))
## Huber's data [Atkinson 1985]
xh <- c(-4:0, 10)
yh <- c(2.48, .73, -.04, -1.44, -1.32, 0)
lmH <- lm(yh ~ xh)
# }
# NOT RUN {
summary(lmH)
# }
# NOT RUN {
im <- influence.measures(lmH)
# }
# NOT RUN {
im
# }
# NOT RUN {
plot(xh,yh, main = "Huber's data: L.S. line and influential obs.")
abline(lmH); points(xh[im$is.inf], yh[im$is.inf], pch = 20, col = 2)
## Irwin's data [Williams 1987]
xi <- 1:5
yi <- c(0,2,14,19,30) # number of mice responding to dose xi
mi <- rep(40, 5) # number of mice exposed
glmI <- glm(cbind(yi, mi -yi) ~ xi, family = binomial)
# }
# NOT RUN {
summary(glmI)
# }
# NOT RUN {
signif(cooks.distance(glmI), 3) # ~= Ci in Table 3, p.184
imI <- influence.measures(glmI)
# }
# NOT RUN {
imI
# }
# NOT RUN {
stopifnot(all.equal(imI$infmat[,"cook.d"],
cooks.distance(glmI)))
# }
```

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