Standard error of the estimate

Definition

The standard error of the estimate measures the accuracy of predictions made with a regression line. It quantifies the average distance that observed values fall from the regression line.

5 Must Know Facts For Your Next Test

1. It represents the standard deviation of the residuals (prediction errors).
2. A smaller standard error indicates a better fit of the regression model to the data.
3. It is calculated using the formula: $$SE = \sqrt{\frac{\sum (Y - \hat{Y})^2}{n-2}}$$ where $Y$ is an observed value, $\hat{Y}$ is a predicted value, and $n$ is the number of observations.
4. The degrees of freedom used in its calculation are $(n-2)$ due to estimating two parameters (intercept and slope) in simple linear regression.
5. It helps in constructing confidence intervals for predictions made using a regression model.

Review Questions

• What does a smaller standard error of the estimate indicate about your regression model?
• How do you calculate the standard error of the estimate?
• Why are $(n-2)$ degrees of freedom used when calculating the standard error of the estimate?

Related terms

Residuals: The differences between observed values and predicted values in a regression model.

$R^2$ (Coefficient of Determination): A measure that assesses how well a regression model explains and predicts future outcomes; it ranges from 0 to 1.

Regression Line: A straight line that best fits the data points on a scatter plot, showing the relationship between two variables.