Sum of Squared Errors (SSE)

Definition

Sum of Squared Errors (SSE) measures the total deviation of observed values from the values predicted by a regression model. It is calculated by summing the squared differences between observed and predicted values.

5 Must Know Facts For Your Next Test

1. SSE is used to assess the fit of a regression model; lower SSE indicates a better fit.
2. The formula for SSE is $$ \sum_{i=1}^{n} (y_i - \hat{y}_i)^2 $$, where $y_i$ are the observed values and $\hat{y}_i$ are the predicted values.
3. SSE is always non-negative because it sums squared terms.
4. It plays a crucial role in calculating other key statistics, such as Mean Squared Error (MSE) and R-squared.
5. SSE can be compared across different models to determine which one better fits the data.

Review Questions

• What does SSE stand for and what does it measure?
• How is SSE calculated in a regression model?
• Why is SSE always non-negative?

Related terms

Mean Squared Error (MSE): Mean Squared Error (MSE) is the average of the squared differences between observed and predicted values. It is calculated as $$ MSE = \frac{SSE}{n} $$, where $n$ is the number of observations.

R-squared:

$R^2$ (R-squared) measures the proportion of variance in the dependent variable that is predictable from the independent variables. It ranges from 0 to 1, with higher values indicating better model fit.

Residuals:

Residuals are the differences between observed and predicted values in a regression model. They represent errors not explained by the model.