Power regression in R similar to excel

Question

I have a simple dataset and I am trying to use the power trend to best fit the data. The sample data is very small and is as follows:

structure(list(Discharg         


        

Answer 1

While mnel's answer is correct for a nonlinear least squares fit, note that Excel isn't actually doing anything nearly that sophisticated. It's really just log-transforming the response and predictor variables, and doing an ordinary (linear) least squares fit. To reproduce this in R, you would do:

lm(log(Age) ~ log(Discharge), data=df)

Call:
lm(formula = log(Age) ~ log(Discharge), data = df)

Coefficients:
   (Intercept)  log(Discharge)  
         5.927          -1.024  

As a check, the coefficient for log(Discharge) is identical to that from Excel while exp(5.927) ~ 375.05.

While I'm not sure how to use this as a trendline in ggplot2, you can do it in base graphics thusly:

m <- lm(log(y) ~ log(x), data=df)

newdf <- data.frame(Discharge=seq(min(df$Discharge), max(df$Discharge), len=100))
plot(Age ~ Discharge, data=df)
lines(newdf$Discharge, exp(predict(m, newdf)))

text(600, .8, substitute(b0*x^b1, list(b0=exp(coef(m)[1]), b1=coef(m)[2])))
text(600, .75, substitute(plain("R-square: ") * r2, list(r2=summary(m)$r.squared)))

Answer 2

2018 Update: The call "start" now seems to be depreciated. It is not in the stat_smooth function information either.

If you want to choose starting values, you need to use "method.args" option now.

See changes below:

ggplot(DD,aes(x = Discharge,y = Age)) +
  geom_point() + 
  stat_smooth(method = 'nls', formula = 'y~a*x^b', method.args = list(start= c(a = 1,b=1)),se=FALSE) + geom_text(x = 600, y = 1, label = power_eqn(DD), parse = TRUE)

Answer 3

Use nls (nonlinear least squares) as your smoother

eg

ggplot(DD,aes(x = Discharge,y = Age)) +
  geom_point() + 
  stat_smooth(method = 'nls', formula = 'y~a*x^b', start = list(a = 1,b=1),se=FALSE)

Noting Doug Bates comments on R-squared values and non-linear models here, you could use the ideas in Adding Regression Line Equation and R2 on graph

to append the regression line equation

# note that you have to give it sensible starting values
# and I haven't worked out why the values passed to geom_smooth work!
power_eqn = function(df, start = list(a =300,b=1)){
  m = nls(Discharge ~ a*Age^b, start = start, data = df);
  eq <- substitute(italic(y) == a  ~italic(x)^b, 
               list(a = format(coef(m)[1], digits = 2), 
                    b = format(coef(m)[2], digits = 2)))
  as.character(as.expression(eq));                 
}

ggplot(DD,aes(x = Discharge,y = Age)) +
  geom_point() + 
  stat_smooth(method = 'nls', formula = 'y~a*x^b', start = list(a = 1,b=1),se=FALSE) +  
  geom_text(x = 600, y = 1, label = power_eqn(DD), parse = TRUE)