In the context of Regression Analysis (specifically ANOVA for regression), SST, SSE, and SSR are used to measure the total, explained, and unexplained variations in the data, respectively. Here's the breakdown of these terms:

1. SST (Total Sum of Squares): It measures the total variation in the dependent variable (the response variable). It's the sum of the squared differences between each observed value and the mean of the observed values.

   $SST = \sum (y_i - \bar{y})^2$ Where:

   • $y_i$ is the observed value of the dependent variable.
   • $\bar{y}$ is the mean of the observed values.

2. SSE (Sum of Squares for Error): It measures the variation in the dependent variable that is unexplained by the model (the error or residual). It’s the sum of the squared differences between the observed values and the predicted values.

   $SSE = \sum (y_i - \hat{y_i})^2$ Where:

   • $y_i$ is the observed value of the dependent variable.
   • $\hat{y_i}$ is the predicted value from the regression model.

3. SSR (Sum of Squares for Regression): It measures the variation in the dependent variable that is explained by the model (the regression line). It’s the sum of the squared differences between the predicted values and the mean of the observed values.

   $SSR = \sum (\hat{y_i} - \bar{y})^2$ Where:

   • $\hat{y_i}$ is the predicted value from the regression model.
   • $\bar{y}$ is the mean of the observed values.

These quantities are related by the total variation equation: $SST = SSR + SSE$

This equation expresses that the total variation in the data (SST) is divided into two parts:

• The variation explained by the regression model (SSR)
• The variation unexplained (SSE, or error)

Summary of the Formulas:

• SST = $\sum (y_i - \bar{y})^2$
• SSE = $\sum (y_i - \hat{y_i})^2$
• SSR = $\sum (\hat{y_i} - \bar{y})^2$

Would you like to dive deeper into how these values are used in hypothesis testing or calculations of $R^2$? Or any further clarifications?

Here are some questions you might find interesting:

1. How does $R^2$ relate to SST, SSR, and SSE?
2. How can you use ANOVA to test the significance of a regression model?
3. What is the interpretation of the residual plot in regression analysis?
4. How does the least squares method minimize SSE?
5. What happens to SSE and SSR as we add more predictors to a regression model?

Tip: To calculate $R^2$ (coefficient of determination), you use the formula:
$R^2 = \frac{SSR}{SST}$ This shows the proportion of variance in the dependent variable that is explained by the independent variable(s).