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

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)