how to compute maximum of fitted polynomial?
Hello, As for the first question, you can use ?optim to compute the maximum of a function. Note that by default optim minimizes, to maximize you must set the parameter control$fnscale to a negative value. fit <- lm(y ~ poly(x, 3)) fn <- function(x, coefs) as.numeric(c(1, x, x^2, x^3) %*% coefs) sol <- optim(0, fn, gr = NULL, coef(fit), control = list(fnscale = -1), method = "L-BFGS-B", lower = 0, upper = 1) As for the second question, I believe you can do something like dfdx <- D( expression(a + b*x + c*x^2 + d*x^3), "x") a <- coef(fit)[1] b <- coef(fit)[2] c <- coef(fit)[3] d <- coef(fit)[4] x <- sol$par eval(dfdx) See the help page for ?D Hope this helps, Rui Barradas Em 04-06-2013 21:32, Joseph Clark escreveu:
My script fits a third-order polynomial to my data with something like this: model <- lm( y ~ poly(x, 3) ) What I'd like to do is find the theoretical maximum of the polynomial (i.e. the x at which "model" predicts the highest y). Specifically, I'd like to predict the maximum between 0 <= x <= 1. What's the best way to accomplish that in R? Bonus question: can R give me the derivative or 2nd derivative of the polynomial? I'd like to be able to compute these at that maximum point. Thanks in advance! // joseph w. clark , phd , visiting research associate \\ university of nebraska at omaha - college of IS&T
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