Nonlinear Regression Model Estimation

# 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.