Extrapolation

Definition

Extrapolation is the process of estimating unknown values by extending or projecting from known data points. It applies linear models to predict values outside the range of existing data.

5 Must Know Facts For Your Next Test

1. Extrapolation relies on the assumption that the established trend continues beyond the known data.
2. It is often less reliable than interpolation because it extends beyond the available data range.
3. Mathematically, extrapolation uses the equation of the fitted linear model: $y = mx + b$.
4. Over-extrapolation can lead to significant errors if trends change outside the observed data range.
5. Graphical representation includes extending a line beyond plotted points on a scatter plot.

Review Questions

• What are the risks associated with using extrapolation in predictions?
• How do you mathematically perform extrapolation using a linear equation?
• Why might extrapolated results be less accurate than interpolated ones?

Related terms

Interpolation: The process of estimating unknown values within the range of known data points.

Linear Regression: A statistical method for modeling the relationship between a dependent variable and one or more independent variables using a linear equation.

$R^2$ (Coefficient of Determination): $R^2$ measures how well a linear model explains the variability of the dependent variable around its mean.