galileo {UsingR} | R Documentation

## Galileo data on falling bodies

### Description

Data recorded by Galileo in 1609 during his investigations of the trajectory of a falling body.

### Usage

    data(galileo)

### Format

A data frame with 7 observations on the following 2 variables.

init.h
  Initial height of ball
h.d
  Horizontal distance traveled

### Details

A simple ramp 500 punti above the ground was constructed. A ball was placed on the ramp at an indicated height from the ground and released. The horizontal distance traveled is recorded (in punti). (One punto is 169/180 millimeter, not a car by FIAT.)

### Source

This data and example come from the Statistical Sleuth by Ramsay and Schafer, Duxbury (2001), section 10.1.1. They attribute an article in Scientific American by Drake and MacLachlan.

### Examples

    data(galileo)
    polynomial = function(x,coefs) {
      sum = 0
      for(i in 0:(length(coefs)-1)) {
        sum = sum + coefs[i+1]*x^i
      }
      sum
    }
    res.lm = lm(h.d ~ init.h, data = galileo)
    res.lm2 = update(res.lm, . ~ . + I(init.h^2), data=galileo)
    res.lm3 = update(res.lm2, . ~ . + I(init.h^3), data=galileo)
    plot(h.d ~ init.h, data = galileo)
    curve(polynomial(x,coef(res.lm)),add=TRUE)
    curve(polynomial(x,coef(res.lm2)),add=TRUE)
    curve(polynomial(x,coef(res.lm3)),add=TRUE)

[Package UsingR version 0.1-4 Index]