I have some data,
calvarbyruno.1<-structure(list(Nominal = c(1, 3, 6, 10, 30, 50, 150, 250), Run = structure(c(1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L), .Label =
The easiest option is to use geom_smooth() and let ggplot2 fit the model for you.
ggplot(calvarbyruno.1, aes(y = PAR, x = Nominal, weight=Nominal^calweight)) +
geom_smooth(method = "lm") +
geom_smooth(method = "lm", formula = y ~ poly(x, 2), colour = "red") +
geom_point() +
coord_flip()

Or you can create a new dataset with the predicted values.
newdata <- data.frame(Nominal = pretty(calvarbyruno.1$Nominal, 100))
newdata$Linear <- predict(callin.1, newdata = newdata)
newdata$Quadratic <- predict(calquad.1, newdata = newdata)
require(reshape2)
newdata <- melt(newdata, id.vars = "Nominal", variable.name = "Model")
ggplot(calvarbyruno.1, aes(x = PAR, y = Nominal, weight=Nominal^calweight)) +
geom_line(data = newdata, aes(x = value, colour = Model)) +
geom_point()