Practice question · Sort into groups
Sort each situation by whether the data should be interpolated or fitted.
Groups: Interpolate · Fit
- Twenty noisy points, with a degree-19 polynomial under consideration
- An exact table of physical constants; values wanted between entries
- Points computed exactly from a known formula, wanted cheaply in between
- Noisy sensor readings; the underlying trend is wanted
- Measurements each carrying about 2% error, used for prediction
Hints
- The deciding question is whether the data are exact or noisy.
- Passing exactly through a noisy point means reproducing its error.
Show the answer
Interpolate: An exact table of physical constants; values wanted between entries, Points computed exactly from a known formula, wanted cheaply in between
Fit: Noisy sensor readings; the underlying trend is wanted, Measurements each carrying about 2% error, used for prediction, Twenty noisy points, with a degree-19 polynomial under consideration
Why
Exact data deserve a curve through every point; noisy data deserve a curve near them. Insisting on passing through noisy points forces the curve to reproduce the noise, which is overfitting, the lesson's named pitfall.
Practise Interpolation and Curve Fitting
The app has 5 more questions on this lesson, and keeps your place in the course. Mathematics I is free to start.
More questions on Interpolation and Curve Fitting
- Complete the definition of least-squares fitting.
- Fitting a polynomial through all n data points guarantees passing through every one, and Runge showed the…
- A high-degree polynomial forced through many equally spaced points approximates the underlying function…
- Twenty-one exact data points are to be interpolated. Select every genuine reason to prefer a cubic spline to…
- A degree-19 polynomial through 20 noisy points passes through every one exactly, yet is a worse model than a…