options(show.signif.stars=FALSE)
### Several models fit to the Formaldehyde data
lm1 <- lm(optden ~ 1 + carb, Formaldehyde)

## This formula can also be written optden ~ carb because the
## intercept term is implicit.  Some people prefer to include it and
## some don't.

lm0 <- lm(optden ~ 0 + carb, Formaldehyde)
## To suppress the intercept term you must include 0 + or - 1, as in
## optden ~ carb - 1, in the formula

## Residual sums of squares for the two models
(RSS <- c(lm0 = deviance(lm0), lm1 = deviance(lm1)))

## Comparative anova
anova(lm0, lm1)

## Corresponding t-statistic from coefficient table for lm1
coef(summary(lm1))

## Compare to F statistic in the comparative anova
coef(summary(lm1))["(Intercept)", "t value"]^2

### Testing for non-zero values of coefficients by using an offset

## Suppose we wish to test
##   H_0: beta_0 = 0.001 versus H_a: beta_0 != 0.001
## within the full model lm1

## We can fit
lm2 <- lm(optden ~ 0 + carb + offset(rep(0.001, 6)), Formaldehyde)

## and compare
anova(lm2, lm1)

## It may be more obvious to fit the full model as
lm3 <- lm(optden ~ 1 + carb + offset(rep(0.001, 6)), Formaldehyde)

## which is equivalent to model lm1
all.equal(fitted(lm1), fitted(lm3))
all.equal(coef(lm1), coef(lm3) + c(0.001, 0))

## but more obvious about the comparison
anova(lm2, lm3)
## and
coef(summary(lm3))
coef(summary(lm3))["(Intercept)", "t value"]^2

## In general, the sequential sums of squares for different terms come
## from the "effects" vector
effects(lm1)
effects(lm1)[2]^2                       # sum of squares due to carb
sum(effects(lm1)[-(1:2)]^2)             # residual sum of squares
anova(lm1)                              # arranged in an anova table