galileo {UsingR}

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)