Project | Mastering Nonlinear Regression Model Estimation

Nonlinear Regression Model Estimation

Beginner

In this project, you will learn how to perform unlinear regression to find the power `p` in a nonlinear relationship between variables `x` and `y`, where `y = a * x^p + ε`. The relationship between variables in real-world examples is often nonlinear, and this project will guide you through the process of transforming the data to make it a linear relationship.

Machine Learning

Introduction

The linear regression model is simple and easy to model, but it embodies some important basic ideas in machine learning.

Given a sample $x=(x_1;x_2;\cdots;x_d)$ with $d$ attributes, the linear model can learn a function that predicts through the linear combination of attributes, that is $f(x) = w_1\cdot x_1 + w_2 \cdot x_2 + \cdots + w_d \cdot x_d + b + \epsilon$ ,

Here $b + \epsilon$ is a constant, and $\epsilon$ represents the error term. Because the attribute length is $d$ , this linear model is also called a $d$ -dimensional linear regression model.

For example, a three-dimensional linear regression model:

f_{level\_of\_a\_ML\_engineer} = 0.4 x_1 + 0.5 x_2 + 0.1 x_3 + 1.2

here:

$x_1$ means programming skills.
$x_2$ means algorithm skills.
$x_3$ means communication skills.

In this challenge, we will be working on a problem related to linear regression. The task is to find the exponent value $p$ that transforms a given nonlinear distribution into a linear one.