The collection of real-world data is crucial to science and business. Making sense of data often starts with a plot in a rectangular coordinate system.
But even in the simplest case of a known linear relationship between the measured quantities, finding the equation of a line that passes through all the data points can be impossible.
There is a line that best fits the data. This line minimizes the vertical deflections, or the residuals, between the points and the line. Similar functions can be found for data that appears to follow nonlinear relationships.
This tool allows you to experiment with fitting different curves to various sets of data.
There are lines, …
… parabolas, …
… exponentials, …
… logarithms, …
… rational expressions, …
… and power laws to fit to different sets of data.
The quality of the fit of different curves can be compared against each other for a given data set with the residuals. A smaller residual means a better fit.
Load a data set with one of the buttons on the left. There are several data sets meant to conform to different trends.
Use the checkboxes to turn off the display of the points in the data set or any of the displayed curves to see a clearer picture.
The form of each type of curve and the best-fit coefficients are displayed.
You can change the points in the data sets by editing the list …
… or by dragging the point in the graph area.
The Random button will enter a data set of 100 randomly generated ordered pairs.
You can also enter your own points to experiment. Enter at least three ordered pairs separated by commas. Use only positive numbers less than 100.
Examine all of the supplied data sets, and try some of your own. Try using the random button to predict the best fitting curve. Have fun learning!