Sum of Squared Errors (SSE)

Definition

Sum of Squared Errors (SSE) is a measure of the total deviation of observed values from the values predicted by a regression model. It quantifies the accuracy of the model by summing the squares of the differences between observed and predicted values.

5 Must Know Facts For Your Next Test

1. SSE is used to assess the goodness-of-fit for a regression model; lower SSE indicates a better fit.
2. It is calculated as: $$SSE = \sum_{i=1}^{n} (y_i - \hat{y}_i)^2$$ where $y_i$ are observed values and $\hat{y}_i$ are predicted values.
3. SSE can never be negative because it sums squared differences.
4. In linear regression, minimizing SSE helps in finding the best-fitting line through the data points.
5. SSE is an essential component in determining other statistical measures such as Mean Squared Error (MSE) and Root Mean Squared Error (RMSE).

Review Questions

• Why is SSE important in evaluating a regression model?
• How do you calculate SSE for a given set of observed and predicted values?
• What does a low SSE value indicate about a regression model?

Related terms

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

Root Mean Squared Error (RMSE): RMSE represents the square root of MSE, providing an error measure in the same units as the observed data.

Coefficient of Determination ($R^2$): $R^2$ measures how well observed outcomes are replicated by the model, based on the proportion of total variation explained by the model.