Adding a 3rd order polynomial and its equation to a ggplot in r

Question

I have plotted the following data and added a loess smoother. I would like to add a 3rd order polynomial and its equation (incl. the residual) to the plot. Any advice?

set.seed(1410) dsmall<-diamonds[sample(nrow(diamonds), 100), ] df<-data.frame("x"=dsmall$carat, "y"=dsmall$price)  p <-ggplot(df, aes(x, y))  p <- p + geom_point(alpha=2/10, shape=21, fill="blue", colour="black", size=5)  #Add a loess smoother p<- p + geom_smooth(method="loess",se=TRUE) 

How can I add a 3rd order polynomial? I have tried:

p<- p + geom_smooth(method="lm", se=TRUE, fill=NA,formula=lm(y ~ poly(x, 3, raw=TRUE)),colour="red") 

Finally how can I add the 3rd order polynomial equation and the residual to the graph? I have tried:

 lm_eqn = function(df){     m=lm(y ~ poly(x, 3, df))#3rd degree polynomial     eq <- substitute(italic(y) == a + b %.% italic(x)*","~~italic(r)^2~"="~r2,     list(a = format(coef(m)[1], digits = 2),     b = format(coef(m)[2], digits = 2),     r2 = format(summary(m)$r.squared, digits = 3)))     as.character(as.expression(eq)) }   data.label <- data.frame(x = 1.5,y = 10000,label = c(lm_eqn(df)))   p<- p + geom_text(data=data.label,aes(x = x, y = y,label =label), size=8,family="Times",face="italic",parse = TRUE) 

Answer 1

Part 1: to fit a polynomial, use the arguments:

• method=lm - you did this correctly
• formula=y ~ poly(x, 3, raw=TRUE) - i.e. don't wrap this in a call to lm

The code:

p + stat_smooth(method="lm", se=TRUE, fill=NA,                 formula=y ~ poly(x, 3, raw=TRUE),colour="red") 

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Part 2: To add the equation:

• Modify your functionlm_eqn() to correctly specify the data source to lm - you had a closing parentheses in the wrong place
• Use annotate() to position the label, rather than geom_text

The code:

lm_eqn = function(df){   m=lm(y ~ poly(x, 3), df)#3rd degree polynomial   eq <- substitute(italic(y) == a + b %.% italic(x)*","~~italic(r)^2~"="~r2,                    list(a = format(coef(m)[1], digits = 2),                         b = format(coef(m)[2], digits = 2),                         r2 = format(summary(m)$r.squared, digits = 3)))   as.character(as.expression(eq)) }   p + annotate("text", x=0.5, y=15000, label=lm_eqn(df), hjust=0, size=8,               family="Times", face="italic", parse=TRUE) 

Answer 2

Answer 1, is a good start but it is not for a 3rd degree polynomial as asked, and can not properly deal with negative values for parameter estimates. Easiest is to use package polynom. I will show a version without defining a function, because really one should use a ggplot stat_ in a case like this.

Below I show how to generate the text to be used as the parsed label for polynomials of any degree. I use signif() instead of format() as this is more useful for parameter estimates. Also note that face is no longer needed. Using family = "Times" is not portable, and the same effect can be achieved with "serif". All the hard work is done by as.character.polynomial()!

library(polynom) library(ggplot2)  set.seed(1410) dsmall <- diamonds[sample(nrow(diamonds), 100), ] df <- data.frame("x"=dsmall$carat, "y"=dsmall$price)  my.formula <- y ~ poly(x, 3, raw = TRUE) p <- ggplot(df, aes(x, y))  p <- p + geom_point(alpha=2/10, shape=21, fill="blue", colour="black", size=5) p <- p + geom_smooth(method = "lm", se = FALSE,                       formula = my.formula,                       colour = "red")  m <- lm(my.formula, df) my.eq <- as.character(signif(as.polynomial(coef(m)), 3)) label.text <- paste(gsub("x", "~italic(x)", my.eq, fixed = TRUE),               paste("italic(R)^2",                       format(summary(m)$r.squared, digits = 2),                      sep = "~`=`~"),                     sep = "~~~~")  p + annotate(geom = "text", x = 0.2, y = 15000, label = label.text,               family = "serif", hjust = 0, parse = TRUE, size = 4) 

A final note: variance increases with the mean, so using lm() and a 3rd degree polynomial model is probably not the best approach for the analysis of these data.