How to fit logarithmic curve over the points in r?

Question

I want to fit my points with logarithmic curve. Here is my data which contains x and y. I desire to plot x and y and the add a logarithmic fitting curve.

    x<-structure(list(X2.y = c(39.99724745, 29.55541525, 23.39578201, 
15.46797044, 10.52063652, 7.296161198, 6.232038434, 4.811851132, 
4.641281547, 4.198523289, 3.325515839, 2.596563723, 1.894902523, 
1.556380314), X5.y = c(62.76037622, 48.54726084, 37.71302646, 
24.93942365, 17.71060023, 13.31130267, 10.36341862, 7.706914722, 
7.170517624, 6.294292013, 4.917428837, 3.767836298, 2.891519878, 
2.280974128), X10.y = c(77.83154815, 61.12151516, 47.19228808, 
31.21034981, 22.47098182, 17.29384973, 13.09875178, 9.623698726, 
8.845091983, 7.681873268, 5.971413758, 4.543320659, 3.551367285, 
2.760718282), X25.y = c(96.87401383, 77.00911883, 59.16936025, 
39.13368164, 28.48573658, 22.32580849, 16.55485248, 12.0455604, 
10.96092113, 9.435085861, 7.303126501, 5.523147205, 4.385086234, 
3.366876291), X50.y = c(111.0008027, 88.79545082, 68.05463659, 
45.01166182, 32.94782526, 26.05880295, 19.11878542, 13.84223574, 
12.53056405, 10.73571912, 8.291067088, 6.25003851, 5.003586577, 
3.81655893), X100.y = c(125.0232816, 100.4947544, 76.87430545, 
50.84623991, 37.37696657, 29.76423356, 21.66378667, 15.6256447, 
14.08861698, 12.0267487, 9.271712877, 6.971562563, 5.61752001, 
4.262921183)), class = "data.frame", row.names = c(NA, -14L))
    

I tried this:

      single_idf<-function(x) {
 idf<-x
  durations = c(5/60, 10/60, 15/60, 30/60, 1, 2, 3, 4, 5, 6, 8, 12, 18, 24)
  nd = length(durations)                                                      
  Tp = c(2, 5, 10, 25, 50, 100)
  nTp = length(Tp)
  psym = seq(1, nTp)
  
  
  # open new window for this graph, set plotting parameters for a single graph panel 
  windows()          
  par(mfrow = c(1,1), mar = c(5, 5, 5, 5), cex = 1)
  
  
  # set up custom axis labels and grid line locations
  ytick = c(1,2,3,4,5,6,7,8,9,10,20,30,40,50,60,70,80,90,100,
            200,300,400,500,600,700,800,900,1000,1100,1200,1300,1400)
  yticklab = as.character(ytick)
  
  xgrid = c(5,6,7,8,9,10,15,20,30,40,50,60,120,180,240,300,360,
            420,480,540,600,660,720,840,960,1080,1200,1320,1440)
  
  xtick = c(5,10,15,20,30,60,120,180,240,300,360,480,720,1080,1440)
  xticklab = c("5","10","15","20","30","60","2","3","4","5","6","8","12","18","24")
  
  ymax1 = max(idf)
 
  durations = durations*60 
  plot(durations, col=c("#FF00FF") ,lwd=c(1), idf[, 1], 
          xaxt="n",yaxt="n",
          pch = psym[1], log = "xy",
          xlim = c(4, 24*60), ylim = range(c(1,idf+150)),
          xlab = "(min)          Duration          (hr)",
          ylab = "Intensity (mm/hr)"
  )
  
  
  for (iT in 2:nTp) {
    points(durations, idf[, iT], pch = psym[iT], col="#FF00FF",lwd=1)
  }
  
  for (iT in 1:nTp) {
    mod.lm = lm(log10(idf[, iT]) ~ log10(durations))
    b0 = mod.lm$coef[1]
    b1 = mod.lm$coef[2]
    yfit = log(10^(b0 + b1*log10(durations)))
    lines(durations,col=c("#FF00FF"),yfit, lty = psym[iT],lwd=1)
  }


}

But when I run this, the curves stands far away from the points. I want to see curves over the points. How can I arrange this?

single_idf(x)

Answer 1

Consider this as an option for you using ggplot2 and dplyr . Also added method='lm' to match OP expected output (Many thanks and credits to @AllanCameron for his magnificent advice):

library(ggplot2)
library(dplyr)
#Data
df <- data.frame(x,y)
#Plot
df %>%
  pivot_longer(-y) %>%
  ggplot(aes(x=log(y),y=log(value),color=name,group=name))+
  geom_point()+
  stat_smooth(geom = 'line',method = 'lm')

Output:

Answer 2

The main problem is that you were plotting the natural log of the fit rather than the fit itself.

If you change the line

yfit = log(10^(b0 + b1*log10(durations)))

To

yfit = 10^(b0 + b1*log10(durations))

And rerun your code, you get