Nonlinear regression


Nonlinear regression NPS
Table of Contents

What is nonlinear regression?

Linear regression is used when the independent and dependent variables have a linear relationship with each other. Meaning, when one variable increases, the other increases too. This gives a straight line on the graph as a line of best fit. But when it comes to nonlinear regression, as the name suggests, the relationship between the independent and the dependent variable is not linear. Meaning, when one variable increases, the other variable may increase or decrease. This gives us a curve as the line of best fit on a graph.

Nonlinear regression NPS

Hence, the nonlinear regression is a curved function of the X variable (independent variable) that is used to predict the Y variable (dependent variable).

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Nonlinear regression model

A simple nonlinear regression model is stated as follows:

Nonlinear regression NPS


Y is vector of predictors P

β is a vector of parameters k

f is the regression function

ϵ is error

Nonlinear regression model can also be written as:

Nonlinear regression NPS


Yi is a response variable

x is input

h is function

Ѳ is the estimated parameter 

The model is focused on reducing the sum of squares as minimum as possible using the iterative numeric procedure. The least-square method is the best fit for the same which tells us how many observations are different from the dataset mean.

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Example of nonlinear regression

An example of nonlinear regression can be studying the share price of a certain company. Any booking app uses graphs to state the development of the company’s stock market performance. You can see no graph have a straight line upwards or downwards. You will get to see a nonlinear relationship between prices and time. A regime-switch model can be used to see the past performance of the share and how it can grow in the future. 

The important thing to observe here is that both the independent and dependent variables are quantitative. Meaning, they are measured in numbers. All the qualitative or categorical data should be measured in binary or other quantitative variables.

What are the applications of nonlinear regression?

  • Nonlinear can be the best fit for financial forecasting.
  • Nonlinear regression can define the changes in financial prices over time using scatterplots.
  • The logistic price change model is used to estimate the prices in the market that were not touched before. It can also help you predict future prices in the market. 
  • Nonlinear regression is the best fit when it comes to predicting the stock market. It can use models like regime-switching, smooth and threshold.
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