Understanding Interpolation and Extrapolation
While the data for most examples does not fall perfectly on the line, the equation is our best guess as to how the relationship will behave outside of the values for which we have data. We use a process known as interpolation when we predict a value inside the domain and range of the data. The process of extrapolation is used when we predict a value outside the domain and range of the data.
interpolation and extrapolation
Different methods of making predictions are used to analyze data.
- The method of interpolation involves predicting a value inside the domain and/or range of the data.
- The method of extrapolation involves predicting a value outside the domain and/or range of the data.
- Model breakdown occurs at the point when the model no longer applies.
The graph compares the two processes for the cricket-chirp data addressed in the previous example.
We can see that interpolation would occur if we used our model to predict temperature when the values for chirps are between [latex]18.5[/latex] and [latex]44[/latex].
Extrapolation would occur if we used our model to predict temperature when the values for chirps are less than [latex]18.5[/latex] or greater than [latex]44[/latex].
Previously, we have found that the estimated equation for the line is [latex]y = 1.12x+31.22[/latex].
Use the cricket data above to answer the following questions:
- Would predicting the temperature when crickets are chirping [latex]30[/latex] times in [latex]15[/latex] seconds be interpolation or extrapolation? Make the prediction, and discuss whether it is reasonable.
- Would predicting the number of chirps crickets will make at [latex]40[/latex] degrees be interpolation or extrapolation? Make the prediction, and discuss whether it is reasonable.