• After installing the program, open it. You should see a program window similar to this:
  

  Make sure you are inside the "R Console" window.

• Enter the example code into the program:

  You can copy and paste the example below into the R Console:

  Click to copy

  # Create graph in R that plots my data points and overlays the regression curve based on my custom formula:
  
  # ----- User-defined inputs -----
  x <- c(2, 4, 8, 16, 32)
  y <- c(2.123, 3.791, 3.791, 4.516, 5.088)
  
  xlab <- "Nutrient concentration (mg/L NO3)"    # x-axis label
  ylab <- "Yield (grams of fresh weight)"        # y-axis label
  main_title <- "Rotala macrandra 'Narrow Leaf'" # plot title
  
  x_tick_by <- 2
  y_tick_by <- 1
  # y_tick_by <- 5
  
  model_name_text <- "(Model: Rational)"
  
  # Define your custom regression function here:
  regression_func <- function(x) {
  	(-27977905.393401 + 27713305.692703 * x) / (1 + 6174159.487309 * x + (-27198.019768 * x^2))
  }
  
  # Define formula text once here as an expression
  formula_text <- expression(paste(y == frac(-27977905.393401 + 27713305.692703 * x, 1 + 6174159.487309 * x + -27198.019768 * x^2)))
  # -------------------------------
  
  plot_regression <- function() {
  	y_hat <- regression_func(x)
  	SSE <- sum((y - y_hat)^2)
  	SST <- sum((y - mean(y))^2)
  	R2 <- 1 - SSE / SST
  
  	x_seq <- seq(0, max(x), length.out = 200)
  	y_pred <- regression_func(x_seq)
  
  	x_ticks <- seq(0, max(x_seq), by = x_tick_by)
  	y_ticks <- seq(0, max(c(y, y_pred)) + y_tick_by, by = y_tick_by)
  
  	# If you what to remove labels and main title (else comment this section):
  	  # Reduce plot margins (bottom, left, top, right)
  	  par(mar = c(2, 2, 1, 1))  # default is usually c(5, 4, 4, 2) + 0.1
  	  # Optionally remove outer margins too
  	  par(oma = c(0, 0, 0, 0))
  
  	# Now plot with empty axis labels and titles to maximize plot area
  	plot(x, y, pch = 19, cex = 2, 
  		# If you what to keep labels and main title:
  			# xlab = xlab, ylab = ylab, main = main_title,
  		# If you what to remove labels and main title, set them empty:
  			xlab = "", ylab = "", main = "",
  	   xaxt = "n", yaxt = "n", 
  	   ylim = c(min(y_ticks), max(y_ticks)), xlim = c(min(x_ticks), max(x_ticks)))
  
  	# Add custom axes and grids as before if needed, e.g.:
  	axis(side = 1, at = x_ticks)
  	axis(side = 2, at = y_ticks)
  
  	abline(h = y_ticks, col = "lightgray", lty = "dotted")
  	abline(v = x_ticks, col = "lightgray", lty = "dotted")
  
  	# Regression curve
  	lines(x_seq, y_pred, col = "red", lwd = 2)
  
  	# GREEN intersection (Km): x = KmConc, y = KmYield (see http://localhost/golias/abc/1_experiments/exp2.php)
  	segments(x0 = 2.284, y0 = 0, x1 = 2.284, y1 = 2.530, col = "green4")
  	segments(x0 = 0, y0 = 2.530, x1 = 2.284, y1 = 2.530, col = "green4")
  	points(2.284, 2.530, col = "green4", pch = 16, cex = 1)
  	text(2.284, 2.530, labels = "Km (50%)", pos = 4, col = "green4", font = 1, offset = 0.7, cex = 1.1)
  	
  	# BLUE intersection (Optimum): x = conc75, y = yield75 (see http://localhost/golias/abc/1_experiments/exp2.php)
  	segments(x0 = 5.741, y0 = 0, x1 = 5.741, y1 = 3.795, col = "blue", lty = "dotted")
  	segments(x0 = 0, y0 = 3.795, x1 = 5.741, y1 = 3.795, col = "blue", lty = "dotted")
  	points(5.741, 3.795, col = "blue", pch = 16, cex = 1)
  	# text(5.741, 3.795, labels = "Optimum\n(75%)", pos = 4, col = "blue", font = 2, offset = 0.7, cex = 1.1)
  	text(5.741, 3.795, labels = "Optimum (75%)", pos = 4, col = "blue", font = 1, offset = 0.7, cex = 1.1)
  	
  	r2_text <- substitute(paste("R"^2, " = ", r2_val), list(r2_val = round(R2, 4)))
  
  	usr <- par("usr")
  
  	text(x = usr[2]*0.95, y = usr[3] + (usr[4]-usr[3])*0.18, labels = formula_text, adj = c(1, 0), cex = 1.1)
  	text(x = usr[2]*0.95, y = usr[3] + (usr[4]-usr[3])*0.12, labels = model_name_text, adj = c(1, 0), cex = 1.1)
  	text(x = usr[2]*0.95, y = usr[3] + (usr[4]-usr[3])*0.05, labels = r2_text, adj = c(1, 0), cex = 1.1)
  }
  
  # Display plot in R window
  plot_regression()
  
  # Save plot as PNG file with transparent background
  png(filename = "custom_regression_plot.png", width = 1000, height = 500, units = "px", bg = "transparent")
  plot_regression()
  dev.off()
  

  You should see this now:

  

  And in R’s current working directory (usually C:/Documents) you'll find the PNG output file:

  

The example script plots measured plant yields against nitrate concentration and overlays a custom regression curve.

1. Inputs data:

   x <- c(2, 4, 8, 16, 32)  # NO3 concentration (mg/L)
   y <- c(2.123, 3.791, 3.791, 4.516, 5.088)  # Yield in grams
   

2. Defines a regression function — a mathematical formula fitted to your data.
   For example:

   regression_func <- function(x) {
     # y = (a + bx) / (1 + cx + dx^2)
     (-27977905.393401 + 27713305.692703 * x) / (1 + 6174159.487309 * x + (-27198.019768 * x^2))
   }
   

   Or:

   regression_func <- function(x) {
     # y = ax / (b + x)
     12.266 * x / (4.270 + x)
   }
   

   Note: Finding the right regression function is crucial for modeling a growth curve, but it is also the most difficult part. I use the trial version of CurveExpert Professional (curveexpert.net) for this, but it can also be done using only R, which contains several preset regression functions (like model_saturation, model_rational_zero, model_hoerl, model_modhoerl, etc.) that can be used for this purpose, although these functions do not usually provide such good results.
3. Plots:
   • Black dots = measured data points.
   • Red curve = predicted growth curve.
   • Green marker = nutrient level at 50% of max yield (Km).
   • Blue marker = nutrient level at ~75% of max yield (optimum).
4. Adds R² value (model confidence), formula, and grid lines.
5. Saves the plot as a PNG:

   png(filename = "custom_regression_plot.png", width = 1000, height = 500, bg = "transparent")
   plot_regression()
   dev.off()
   

   • 📂 Where it’s saved: In R’s current working directory → check with getwd() ← enter this command into R Console and press Enter