Okay, I need to write a professional Wikipedia-style document in about the topic of "잔차곱합" (Sum Squared Residuals under the categories of Science, Statistics, and Regression Analysis. Let me start by understanding the user's requirements.

First, the should have a clear H1 title, an/introduction section, several sections using H2 and H3 headings, and possibly a references or related documents section. The content must be accurate, objective, and have sufficient depth but be easy to understand. Technical terms should be explained, and the markdown format needs proper structure with lists, tables, code blocks if necessary. The length should be over 800 characters, which I think translates to about a few paragraphs.

Starting with the title: "잔차 제곱합" is correct. Then the introduction should define what it is. Maybe start by explaining residuals in regression analysis. Residuals are the differences between observed and predicted values. The sum of squared residuals (SSR) is a measure of the discrepancy between the data and the regression model. It's important in evaluating the model's performance.

Next, structure the sections. The overview should give a basic definition. Then, maybe a section on its mathematical expression. Then, importance in regression analysis, how it's used in model evaluation, its relationship with other statistical measures like R-squared, and maybe examples or applications. Also, potential issues, like overfitting, and related concepts like MSE or adjusted R-squared.

I need to ensure that each section flows logically. Use H2 for main sections and H3 for subsections. For example, under "수학적 표현", I can have H3 for formula and example. In "회귀 분석에서의 중요성", maybe break into model evaluation and parameter estimation.

I should explain technical terms. For instance, when mentioning OLS (Ordinary Least Squares), clarify that it's a method where the goal is to minimize SSR. Also, mention how SSR relates to total sum of squares (SST) and explained sum of squares (SSE) since R-squared is derived from these.

Including an example would help. Maybe a simple linear regression case where observed values are given, predicted values calculated, residuals squared, and summed. A small table could illustrate this.

Potential pitfalls: Overfitting can lead to low SSR but poor generalization. Mention that SSR alone isn't sufficient for model selection and should be used with other metrics like AIC, BIC, or cross-validation.

Also, connect SSR to other loss functions and metrics like MSE (Mean Squared Error), which is SSR divided by the number of observations. This helps in understanding scale differences.

Need to check accuracy: SSR is the sum of squared residuals, which is the same as the residual sum of squares (RSS) in some contexts. Make sure there's no confusion with other terms like SSE (sometimes used for Error Sum of Squares). In ANOVA, SSE might be the sum of squared errors, which is similar. Clarify if necessary.

Make sure to mention that minimizing SSR is the basis for OLS estimation. When estimating regression coefficients, the goal is to find the line (or hyperplane) that minimizes SSR.

Also, in the related concepts section, link SSR to other evaluation metrics. For instance, R-squared = 1 - (SSR/SST), so explaining SST (total sum of squares) and SSE (explained sum of squares) would be helpful.

I should structure the document as follows:

1. 제목 (H1)
2. 개요 (Introduction)
3. 수학적 표현 (Mathematical Expression)
4. 공식
5. 예시 (table)
6. 회귀 분석에서의 중요성 (Importance in Regression)
7. 모델 평가
8. 매개변수 추정
9. 다른 통계 지표와의 관계 (Relationship with other metrics)
10. R-제곱
11. MSE
12. 한계 및 주의사항 (Limitations)
13. 과적합
14. 다른 지표와의 비교
15. 참고 자료 및 관련 문서

Wait, the user mentioned "잔차 제곱합" which is the sum of squared residuals. But sometimes in statistics, the residual sum of squares (RSS) or sum of squared errors (SSE) might be used. Need to clarify that SSR here refers to the same as RSS or SSE in some literature, but in ANOVA, SSE can be different. So maybe in the mathematical section, clarify the different terms.

Also, ensure that the example is correct. Let's say we have observed y and predicted ŷ values. Compute residuals, square them, sum up.

For the markdown format, use tables for examples, code blocks for formulas if needed, but since it's mathematical expressions, using LaTeX in markdown is appropriate. For example, the formula for SSR would be written as:

$$ \text{SSR} = \sum_{i=1}^{n} (y_i - \hat{y}_i)^2 $$

But since the user wants Korean text, the formula should be in italics or using LaTeX notation.

Also, in the related documents section, link to regression analysis, R-squared, OLS, ANOVA if applicable.

Now, checking for 800 characters. The example section with a table might help reach the length requirement. Also, detailed explanations in each section.

Potential mistakes to avoid: Confusing SSR with SSE in different contexts. In some references, SSR is the regression sum of squares (explained), and SSE is the error. Need to confirm. For example, in ANOVA and regression, sometimes:

Total Sum of Squares (SST) = Regression Sum of Squares (SSR) + Error Sum of Squares (SSE)

But in other contexts, SSR might stand for residual sum of squares. So this is a possible confusion point. The user's topic is "잔차 제곱합", which translates to Sum of Squared Residuals, so it's the error part. So in the document, clarify that there can be different notations in literature to avoid confusion.

Therefore, in the mathematical expression section, mention that SSR is sometimes called Residual Sum of Squares (RSS) or Error Sum of Squares (SSE) in different sources. But in this document, we'll use SSR as Sum of Squared Residuals.

This is important for accuracy. So the user might be following a specific convention where SSR is the residual sum, but others might use RSS or SSE. Clarifying this helps the reader not get confused when they encounter different terms elsewhere.

Also, in the relationship with R-squared, SST is total, SSR (regression) + SSE (error). Wait, if SSR here is regression sum of squares, then R-squared is SSR/SST. But if SSR is the residual sum, then it's 1 - (SSR/SST). So the terminology is critical.

This is a key point. Therefore, in the document, I need to make sure that the definition aligns with the common usage in regression. Typically:

• Total Sum of Squares (SST) = Σ(y_i - ȳ)^2
• Regression Sum of Squares (SSR) = Σ(ŷ_i - ȳ)^2
• Error Sum of Squares (SSE) = Σ(y_i - ŷ_i)^2

And SST = SSR + SSE

Then R-squared = SSR/SST = 1 - SSE/SST

But some sources use different notations. For example, some might call SSE as the sum of squared residuals. So the confusion comes from whether SSR is the regression sum or the residual sum.

Since the topic here is "잔차 제곱합", which is the sum of squared residuals, that corresponds to SSE in the above notation. But if the user refers to it as SSR, then there's inconsistency. Therefore, in the document, I must clarify this discrepancy.

Alternatively, maybe in some sources, the terminology is different. For example, in Wikipedia, the "sum of squared residuals" can be called residual sum of squares (RSS) or sum of squared errors (SSE). The Ordinary Least Squares method minimizes RSS/SSE.

Therefore, in the document, I should define SSR (잔차 제곱합) as the sum of squared residuals, which is equivalent to SSE in some contexts. Also, explain that notation can vary, but the concept is the same.

This is crucial to prevent confusion. So in the mathematical expression section, clarify that the term may be called differently (RSS, SSE) in various references, but here it's referred to as SSR.

So the formula would be:

$$ \text{SSR} = \sum_{i=1}^{n} (y_i - \hat{y}_i)^2 $$

And note that this is sometimes called residual sum of squares (RSS) or sum of squared errors (SSE) in other literature.

Then, in the relationship with R-squared, explain that R-squared = 1 - (SSR/SST), which aligns with SSR being the residual sum.

Yes, this makes sense. So the document should make it clear that terminology can vary, but the focus is on the sum of squared residuals as SSR here.

Including this clarification will make the document more accurate and helpful, preventing potential misunderstandings.

Now, putting it all together in Korean. Ensure that the explanations are clear, even for those new to the topic. Use examples and tables where necessary.

For the example, create a small dataset with observed y, predicted ŷ, residuals, squared residuals, then sum them up. A table would look like:

This shows that SSR is 0.58 in this case.

Also, mention that lower SSR indicates a better fit, but caution against overfitting.

In the limitations section, discuss how SSR can be misleading if the model is too complex, leading to very low SSR on training data but poor performance on new data. Therefore, other metrics like adjusted R-squared or cross-validation are needed.

Finally, in related concepts, link to MSE (Mean Squared Error), which is SSR divided by n-p (n observations, p parameters), and RMSE (root MSE).

Make sure all these points are covered in the document with proper structure and markdown formatting.