Confidence and prediction intervals for regression.

lmInt contructs confidence and prediction intervals for linear regression. It computes confidence intervals around the regression line (i.e. the point-wise confidence bands of \(E(Y | X = x)\) for each individual \(x\)), confidence intervals for the regression line (i.e. the simultaneous confidence bands of \(E(Y)\) for all \(x\)), and prediction intervals (i.e. point-wise confidence bands for new observations \(Y\) for each individual \(x\)).

lmInt(m, newdata = NULL, level = 0.95)

Arguments

m

a fitted linear model
newdata

a data frame to look for predictors. If omitted, fitted values will be used. If a single numeric and if the model specifies a single predictor only, a new data frame will get generated by taking newdata values to uniformly span the range of the predictor.
level

confidence level

Details

The confidence intervals around the regression line and the prediction intervals are computed using the predict.lm function. The confidence intervals for the regression line are computed according to eq. (4.15) in Zvara2008.

Value

An object of class lmInt - a data frame consisting of the model matrix followed by columns of the: fit holding the mean value fitted by the regression model, ciaLwr and ciaUpr holding confidence intervals around the regression line, cifLwr and cifUpr holding confidence intervals for the regression line, and piLwr and piUpr holding predictions intervals.

References

Karel Zv\'ara: Regrese, Matfyzpress Praha 2008

See also

plot.lmInt, predict.lm, lm

Examples

iris.setosa<-iris[iris$Species=='setosa',]
attach(iris.setosa)

# simple line fitting (one predictor only)
m <- lm(Sepal.Width ~ Sepal.Length)
lmi <- lmInt(m)
#> Warning: predictions on current data refer to _future_ responses
plot(Sepal.Length, Sepal.Width)
plot(lmi, fit = TRUE, lty = 1, col='red')
plot(lmi, cia = TRUE, lty = 1)
plot(lmi, cif = TRUE, lty = 2)
plot(lmi, pi = TRUE, lty = 3)
legend('bottomright', bg='white',
  c('fitted regression line',
  'confidence interval around the regression line',
  'confidence interval for the regression line',
  'prediction int.'),
  col = c('red', 'black', 'black', 'black'), lty = c(1, 1, 2, 3))

# using more predictors
m2 <- lm(Sepal.Width ~ Sepal.Length + Petal.Length + offset(Petal.Width))
lmi2 <- lmInt(m2, newdata = data.frame(
  Sepal.Length = Sepal.Length,
  Petal.Length = mean(Petal.Length),
  Petal.Width = mean(Petal.Width)))
plot(Sepal.Length, Sepal.Width)
plot(lmi2, fit = TRUE, lty = 1, col='red')
plot(lmi2, cia = TRUE, band = TRUE, border = NA, col = scales::alpha('red',.3))
plot(lmi2, cif = TRUE, band = TRUE, border = NA, col = scales::alpha('blue',.2))
plot(lmi2, pi = TRUE, band = TRUE, border = NA, col = scales::alpha('black',.2))
legend('bottomright', bg='white',
  c('fitted regression line',
  'confidence interval around the regression line',
  'confidence interval for the regression line',
  'prediction int.'),
  col = c('red', scales::alpha('red',.3), scales::alpha('blue',.2), scales::alpha('black',.1)),
  lty = 1, lwd = c(1, 15, 15, 15))

detach(iris.setosa)