require("tidyverse")
data("davenant")
# Plot values (dots) and Jevon's fitted line
ggplot(davenant, aes(x = quantity)) +
geom_point(mapping = aes(y = price)) +
geom_line(mapping = aes(y = fitted))
# Jevon's values of a = 0.824, b = 0.12
# is close to the Nonlinear least squares solution
price <- function(par) {
est <- par[1] / (par[2] - davenant$quantity) ^ 2
sum((davenant$price - est) ^ 2)
}
nlpar <- optim(c(0, 0), price)
nlpar$par
# The third difference is constant
base::diff(davenant$price, differences = 3)
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