Galileo data on falling bodies
Data recorded by Galileo in 1609 during his investigations of the trajectory of a falling body.
data(galileo)
A data frame with 7 observations on the following 2 variables.
Initial height of ball
Horizontal distance traveled
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.)
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.
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)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.