+--------+-------------------+
| cars   | R Documentation   |
+--------+-------------------+

Speed and Stopping Distances of Cars
------------------------------------

Description
~~~~~~~~~~~

The data give the speed of cars and the distances taken to stop. Note
that the data were recorded in the 1920s.

Usage
~~~~~

::

    cars

Format
~~~~~~

A data frame with 50 observations on 2 variables.

+--------+---------+-----------+--------------------------+
| [,1]   | speed   | numeric   | Speed (mph)              |
+--------+---------+-----------+--------------------------+
| [,2]   | dist    | numeric   | Stopping distance (ft)   |
+--------+---------+-----------+--------------------------+

Source
~~~~~~

Ezekiel, M. (1930) *Methods of Correlation Analysis*. Wiley.

References
~~~~~~~~~~

McNeil, D. R. (1977) *Interactive Data Analysis*. Wiley.

Examples
~~~~~~~~

::

    require(stats); require(graphics)
    plot(cars, xlab = "Speed (mph)", ylab = "Stopping distance (ft)",
         las = 1)
    lines(lowess(cars$speed, cars$dist, f = 2/3, iter = 3), col = "red")
    title(main = "cars data")
    plot(cars, xlab = "Speed (mph)", ylab = "Stopping distance (ft)",
         las = 1, log = "xy")
    title(main = "cars data (logarithmic scales)")
    lines(lowess(cars$speed, cars$dist, f = 2/3, iter = 3), col = "red")
    summary(fm1 <- lm(log(dist) ~ log(speed), data = cars))
    opar <- par(mfrow = c(2, 2), oma = c(0, 0, 1.1, 0),
                mar = c(4.1, 4.1, 2.1, 1.1))
    plot(fm1)
    par(opar)

    ## An example of polynomial regression
    plot(cars, xlab = "Speed (mph)", ylab = "Stopping distance (ft)",
        las = 1, xlim = c(0, 25))
    d <- seq(0, 25, length.out = 200)
    for(degree in 1:4) {
      fm <- lm(dist ~ poly(speed, degree), data = cars)
      assign(paste("cars", degree, sep="."), fm)
      lines(d, predict(fm, data.frame(speed=d)), col = degree)
    }
    anova(cars.1, cars.2, cars.3, cars.4)

