Question

1. What is the goal of nonlinear regression fitting?
2. Why would one choose nonlinear regression over linear regression of a linearized model function?
3. Do you need to provide initial guesses for the model parameters in linear regression? In nonlinear regression? Explain the differences.

Can someone help me answer these questions? This is for a design of experiments class. I just want to make sure that I fully understand this stuff because the explanations online are slightly misleading.

Answer 1

1. What is the goal of nonlinear regression fitting?

Nonlinear least-squares fitting employs the Levenberg-Marquardt algorithm to search for the coefficients that minimize chi-square. It has become the industry standard in nonlinear regression. As the fit proceeds and better values are found, the chi-square value decreases. The fit is finished when the rate at which chi-square decreases is small enough.

Assumption of the nonlinear least-squares method:

(1) x is known precisely, all the error is in y.

(2) variation in y follows a Gaussian distribution

(3) scatter is the same all the way along the curve

2. Why would one choose nonlinear regression over linear regression of a linearized model function?

Nonlinear regression can be a powerful alternative to linear regression because it provides the most flexible curve-fitting functionality. The trick is to find the nonlinear function that best fits the specific curve in your data. that's why we would choose nonlinear regression over linear regression of a linearized model function.

3. Do you need to provide initial guesses for the model parameters in linear regression? In nonlinear regression? Explain the differences.

No need to provide initial guesses for the model parameters in linear regression. Because, The linear functions don't have any exponents higher than 1. Some of them don't have variables at all, and if they do, they have just plain x, which is equal to x to the first power. When a linear function is written in its simplest form, it looks like y = a + bx, where a and b are both constants.

Need to provide initial guesses for the model parameters in linear regression. Because, Non-linear functions all have at least one variable raised to the power of two or more. There is no formula for non-linear functions because they're all different.