Okay, I to write a professional Korean wiki-style document the Least Squares Method under the of Regression Analysis in Statistics Let me start by breaking down the requirements.

First, the document structure needs a clear H1 title, an overview/introduction section, detailed sections with H2 and H3 headings, and possibly references or related documents. The content must be accurate, objective, have sufficient depth, be easy to read, and explain technical terms.

Starting with the title: "최소 제곱법" as specified. The overview should introduce the method, its purpose, and where it's used. Maybe mention that it's a standard approach in regression analysis for minimizing the sum of squared residuals.

Next, the detailed sections. Let me think about the key aspects. There's the basic concept, mathematical formulation, types (like linear vs. nonlinear), applications, advantages/disadvantages, and maybe examples. Also, historical context or related methods could be useful.

For the mathematical formulation, I should explain the equation for minimizing the sum of squared residuals. Maybe include the normal equation for linear regression. Use LaTeX formatting for equations, but since it's markdown, I'll need to use appropriate syntax.

In the linear least squares section, discuss ordinary least squares, assumptions like linearity and homoscedasticity. Then in nonlinear, mention iterative methods. Applications in various fields like economics, engineering, etc., would show its usefulness.

Advantages: simplicity, efficiency, unbiased under certain conditions. Disadvantages: sensitivity to outliers, assumes errors are normally distributed. Maybe mention robust regression as an alternative.

Examples: Simple linear regression example with data points, fitting a line. Maybe a small dataset and show calculations. Or refer to real-world applications like trend analysis.

References could include textbooks like "Applied Linear Regression Models" by Kutner et al., or online resources like university lectures.

Wait, the user mentioned to use markdown with proper heading hierarchy. So H1 is the title, H2 for main sections, H3 for subsections. Use bullet points, tables where necessary. For equations, use code blocks with LaTeX.

Need to ensure the document is over 800 characters. Let me check each section's length.

I should also avoid markdown errors. Make sure equations are correctly formatted. For example, the normal equation is β = (X^T X)^{-1} X^T y.

Make sure to explain terms like residuals, homoscedasticity, normal distribution in the context. Maybe add a subsection under overview explaining key terms.

Also, include a section on the history—Gauss and Legendre's contributions. That adds context.

Applications section can list different fields where it's used, like economics for OLS in econometrics, engineering for system identification, biology for data modeling.

In examples, maybe a simple numerical example with two variables, show how the line is calculated. Or at least describe the process.

Potential pitfalls: overfitting when using higher-order polynomials, the necessity of checking assumptions.

I need to structure all this into sections:

1. 개요
2. 수학적 정의
3. 종류 (선형, 비선형)
4. 응용 분야
5. 장단점
6. 예제
7. 참고 자료

Wait, the user example might not need a separate example section if the explanation includes examples. Maybe integrate examples into the linear/nonlinear sections.

Also, ensure that each section flows logically. Check for any missing key points. Maybe mention the Gauss-Markov theorem in the linear section regarding BLUE.

Need to write in Korean, so all terms should be properly translated. For example, "residuals" are 잔차, "regression coefficients" are 회귀 계수.

I should also verify the accuracy of historical facts. Gauss used it in 1795 but published later, Legendre in 1805. Priority dispute maybe mentioned briefly.

Alright, putting it all together step by step, making sure each part meets the requirements and connects smoothly.