A curve of best fit is a curve that approximates the relationship between two variables in a scatter plot.
NoteThe curve of best fitis not a perfect representation of the data, but it provides a general trendthat can be used to make predictions.
Parabolas of Best Fit
A parabola of best fit is a quadratic curve that approximates the relationship between two variables in a scatter plot.
| Time (s) | Height (m) |
|---|---|
| 0 | 1 |
| 1 | 5 |
| 2 | 7 |
| 3 | 7 |
| 4 | 5 |
| 5 | 1 |
When using technology to find a parabola of best fit, make sure to checkthe fitof the curve by plottingit on the scatter plot.
Exponential Curves of Best Fit
An exponential curve of best fit is an exponential curve that approximates the relationship between two variables in a scatter plot.
| Year | Population |
|---|---|
| 0 | 1000 |
| 1 | 1200 |
| 2 | 1440 |
| 3 | 1728 |
| 4 | 2073.6 |
When using technology to find an exponential curve of best fit, make sure to checkthe fitof the curve by plottingit on the scatter plot.
| x | y |
|---|---|
| 1 | 2 |
| 2 | 4 |
| 3 | 6 |
| 4 | 8 |
| 5 | 10 |
| x | y |
|---|---|
| 1 | 2 |
| 2 | 4 |
| 3 | 8 |
| 4 | 16 |
| 5 | 32 |
How do we decide which type of curve (linear, quadratic, exponential) best fits a given set of data? What are the implications of choosing one model over another?
