Nonlinear Least Squares r | R Nonlinear Least Square - r - learn r - r programming

  • When displaying real world data for regression analysis, we observe that it is rarely the case that the equation of the model is a linear equation giving a linear graph.
  • Most of the time, the calculation of the model of real world data involves mathematical functions of higher degree like an exponent of 3 or a sin function.
  • In such a situation, the plot of the model gives a curve rather than a line.
  • The goal of both linear and non-linear regression is to adjust the values of the model's constraints to find the line or curve that comes closest to your data.
  • On finding these values we will be able to estimate the response variable with good accuracy.
  • In Least Square regression, we establish a regression model in which the sum of the squares of the vertical distances of different points from the regression curve is minimized.
  • r programming non linear least square

    r programming non linear least square

  • We generally start with a defined model and assume some values for the coefficients.
  • We then apply the nls() function of R to get the more accurate values along with the confidence intervals.


  • The basic syntax for creating a nonlinear least square test in R is
nls(formula, data, start)
  • formula is a nonlinear model formula including variables and parameters.
  • data is a data frame used to evaluate the variables in the formula.
  • start is a named list or named numeric vector of starting estimates.


  • We will consider a nonlinear model with assumption of initial values of its coefficients.
  • Let's consider the below equation for this purpose
a = b1*x^2+b2
  • Let's assume the initial coefficients to be 1 and 3 and fit these values into nls() function.
xvalues <- c(1.6,2.1,2,2.23,3.71,3.25,3.4,3.86,1.19,2.21)
yvalues <- c(5.19,7.43,6.94,8.11,18.75,14.88,16.06,19.12,3.21,7.58)

# Give the chart file a name.
png(file = "nls.png")

# Plot these values.

# Take the assumed values and fit into the model.
model <- nls(yvalues ~ b1*xvalues^2+b2,start = list(b1 = 1,b2 = 3))

# Plot the chart with new data by fitting it to a prediction from 100 data points. <- data.frame(xvalues = seq(min(xvalues),max(xvalues),len = 100))
lines($xvalues,predict(model,newdata =

# Save the file.

# Get the sum of the squared residuals.

# Get the confidence intervals on the chosen values of the coefficients.
  • When we execute the above code, it produces the following result
[1] 1.081935
Waiting for profiling to be done...
   2.5%    97.5%
b1 1.137708 1.253135
b2 1.497364 2.496484
The trend in the above graph helps us predicting the probability of survival at the end of a certain number of days.
We can conclude that the value of b1 is more close to 1 while the value of b2 is more close to 2 and not 3.
  • We can conclude that the value of b1 is more close to 1 while the value of b2 is more close to 2 and not 3.

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