Interpolation

Definition

Interpolation is the process of estimating unknown values that fall within the range of known data points. It is commonly used to predict values in a linear model based on existing data.

5 Must Know Facts For Your Next Test

1. Linear interpolation assumes that the change between two known values is linear and uses this assumption to estimate intermediate values.
2. The formula for linear interpolation between two points $(x_1, y_1)$ and $(x_2, y_2)$ is: $y = y_1 + \frac{(x - x_1)(y_2 - y_1)}{(x_2 - x_1)}$.
3. Interpolation can only be used within the range of the given data points; it cannot be applied to estimate values outside this range (extrapolation).
4. In linear models, interpolation helps in constructing piecewise linear functions that approximate more complex datasets.
5. Accuracy of interpolation depends on how well the data fits a linear pattern and how closely spaced the data points are.

Review Questions

Related terms

Extrapolation:

The process of estimating values outside the range of known data points using assumptions based on trends in the data.

Linear Model: A mathematical model that assumes a linear relationship between input variables (independent) and output variables (dependent).

Piecewise Linear Function: A function composed of multiple linear segments, each defined over a specific interval.