How to fit a smooth curve to my data in R?

Question

I\'m trying to draw a smooth curve in R. I have the following simple toy data:

> x
 [1]  1  2  3  4  5  6  7  8  9 10
> y
 [1]  2  4  6  8         


        

Answer 1

In order to get it REALLY smoooth...

x <- 1:10
y <- c(2,4,6,8,7,8,14,16,18,20)
lo <- loess(y~x)
plot(x,y)
xl <- seq(min(x),max(x), (max(x) - min(x))/1000)
lines(xl, predict(lo,xl), col='red', lwd=2)

This style interpolates lots of extra points and gets you a curve that is very smooth. It also appears to be the the approach that ggplot takes. If the standard level of smoothness is fine you can just use.

scatter.smooth(x, y)

Answer 2

I didn't see this method shown, so if someone else is looking to do this I found that ggplot documentation suggested a technique for using the gam method that produced similar results to loess when working with small data sets.

library(ggplot2)
x <- 1:10
y <- c(2,4,6,8,7,8,14,16,18,20)

df <- data.frame(x,y)
r <- ggplot(df, aes(x = x, y = y)) + geom_smooth(method = "gam", formula = y ~ s(x, bs = "cs"))+geom_point()
r

First with the loess method and auto formula Second with the gam method with suggested formula

Answer 3

I like loess() a lot for smoothing:

x <- 1:10
y <- c(2,4,6,8,7,12,14,16,18,20)
lo <- loess(y~x)
plot(x,y)
lines(predict(lo), col='red', lwd=2)

Venables and Ripley's MASS book has an entire section on smoothing that also covers splines and polynomials -- but loess() is just about everybody's favourite.

Answer 4

LOESS is a very good approach, as Dirk said.

Another option is using Bezier splines, which may in some cases work better than LOESS if you don't have many data points.

Here you'll find an example: http://rosettacode.org/wiki/Cubic_bezier_curves#R

# x, y: the x and y coordinates of the hull points
# n: the number of points in the curve.
bezierCurve <- function(x, y, n=10)
    {
    outx <- NULL
    outy <- NULL

    i <- 1
    for (t in seq(0, 1, length.out=n))
        {
        b <- bez(x, y, t)
        outx[i] <- b$x
        outy[i] <- b$y

        i <- i+1
        }

    return (list(x=outx, y=outy))
    }

bez <- function(x, y, t)
    {
    outx <- 0
    outy <- 0
    n <- length(x)-1
    for (i in 0:n)
        {
        outx <- outx + choose(n, i)*((1-t)^(n-i))*t^i*x[i+1]
        outy <- outy + choose(n, i)*((1-t)^(n-i))*t^i*y[i+1]
        }

    return (list(x=outx, y=outy))
    }

# Example usage
x <- c(4,6,4,5,6,7)
y <- 1:6
plot(x, y, "o", pch=20)
points(bezierCurve(x,y,20), type="l", col="red")

Answer 5

the qplot() function in the ggplot2 package is very simple to use and provides an elegant solution that includes confidence bands. For instance,

qplot(x,y, geom='smooth', span =0.5)

produces

Answer 6

Maybe smooth.spline is an option, You can set a smoothing parameter (typically between 0 and 1) here

smoothingSpline = smooth.spline(x, y, spar=0.35)
plot(x,y)
lines(smoothingSpline)

you can also use predict on smooth.spline objects. The function comes with base R, see ?smooth.spline for details.