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.
- 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.
r programming non linear least square
Syntax
- 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.
Example
- 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.
plot(xvalues,yvalues)
# 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.
new.data <- data.frame(xvalues = seq(min(xvalues),max(xvalues),len = 100))
lines(new.data$xvalues,predict(model,newdata = new.data))
# Save the file.
dev.off()
# Get the sum of the squared residuals.
print(sum(resid(model)^2))
# Get the confidence intervals on the chosen values of the coefficients.
print(confint(model))
- 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
- 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.