# 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

• 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.

## Syntax

• The basic syntax for creating a nonlinear least square test in R is
• 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
• Let's assume the initial coefficients to be 1 and 3 and fit these values into nls() function.
• When we execute the above code, it produces the following result
• 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.