Nenne mir alle formeln zur berechnung von SSE, SST, SSR auf englisch.

Sure, here are the formulas for calculating SSE (Sum of Squared Errors), SST (Total Sum of Squares), and SSR (Sum of Squares due to Regression) in English:

1. **Sum of Squared Errors (SSE):**
   \[
   SSE = \sum_{i=1}^{n} (y_i - \hat{y}_i)^2
   \]
   where \( y_i \) is the observed value and \( \hat{y}_i \) is the predicted value.

2. **Total Sum of Squares (SST):**
   \[
   SST = \sum_{i=1}^{n} (y_i - \bar{y})^2
   \]
   where \( y_i \) is the observed value and \( \bar{y} \) is the mean of the observed values.

3. **Sum of Squares due to Regression (SSR):**
   \[
   SSR = \sum_{i=1}^{n} (\hat{y}_i - \bar{y})^2
   \]
   where \( \hat{y}_i \) is the predicted value and \( \bar{y} \) is the mean of the observed values.

Would you like more details or have any questions? 

Here are five related questions you might want to ask:
1. How are these formulas used in regression analysis?
2. Can you show an example calculation for SSE, SST, and SSR?
3. What is the relationship between SSE, SST, and SSR?
4. How do these sums of squares relate to the coefficient of determination (R²)?
5. What assumptions are necessary for these sums of squares to be valid in linear regression?

**Tip:** Always verify your observed and predicted values are correctly paired when calculating SSE, SST, and SSR to ensure accuracy in your regression analysis.

Explore the formulas for SSE (Sum of Squared Errors), SST (Total Sum of Squares), and SSR (Sum of Squares due to Regression) used in regression analysis. Understand how these calculations are crucial in evaluating the goodness of fit and understanding the variance in data. Suitable for advanced learners and practitioners in statistics and data analysis.

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