What is the relationship between SSE, SST, and SSR?+

The relationship between SSE, SST, and SSR is fundamental in regression analysis, particularly in the context of the coefficient of determination, \( R^2 \). The relationship can be expressed as:

\[ SST = SSR + SSE \]

Here's what each term represents:
- **SST (Total Sum of Squares)**: Measures the total variation in the observed data.
- **SSR (Sum of Squares due to Regression)**: Measures the variation explained by the regression model.
- **SSE (Sum of Squared Errors)**: Measures the variation that is not explained by the regression model, also known as the residual sum of squares.

This relationship illustrates how the total variation (SST) is partitioned into the variation explained by the model (SSR) and the unexplained variation (SSE).

Additionally, the coefficient of determination, \( R^2 \), is defined as:

\[ R^2 = \frac{SSR}{SST} \]

This ratio indicates the proportion of the total variation in the dependent variable that is explained by the independent variable(s) in the model. It can also be expressed in terms of SSE:

\[ R^2 = 1 - \frac{SSE}{SST} \]

Would you like more details or have any questions?

Here are five related questions you might want to ask:
1. Can you explain how to interpret the \( R^2 \) value in regression analysis?
2. How do you calculate SSE, SST, and SSR from a given dataset?
3. What are some limitations of using \( R^2 \) as a measure of model fit?
4. How does adding more predictors to a regression model affect SSE, SST, and SSR?
5. Can you provide a step-by-step example of partitioning SST into SSR and SSE?

**Tip:** Always check the assumptions of your regression model (linearity, independence, homoscedasticity, and normality of residuals) to ensure the validity of your results.

Explore the essential relationship between SSE, SST, and SSR in regression analysis. This page provides key formulas, explanations of each term, and related questions to enhance your understanding of the coefficient of determination (R^2). Suitable for high school and college students.

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