### 20.2.7 Power regression

The power_regression command finds the graph y=bxm which best fits a set of data points.

- power_regression takes two arguments:
  - xcoords, a list of x-coordinates.
  - ycoords, a list of y-coordinates.
  You can combine two arguments into a matrix with two columns (each list becomes a column of the matrix).
- power_regression(xcoords,ycoords) returns a sequence m,b of the numbers in the best fit power equation y=b xm.

#### Example

power_regression([[1,1],[2,4],[3,9],[4,16]])

or:

power_regression([1,2,3,4],[1,4,9,16])

2.0,1.0 |  |  |  |  |  |  |  |  |  |

so the best fit (in this case, exact fit) power curve will be y=1.0 x2.

The power_regression_plot command draws the best fit power function.

- power_regression_plot takes two arguments:
  - xcoords, a list of x-coordinates.
  - ycoords, a list of y-coordinates.
  You can combine two arguments into a matrix with two columns (each list becomes a column of the matrix).
- power_regression_plot(xcoords,ycoords) draws the best fit power function, and puts the equation and R2 value above the graph.

#### Example

power_regression_plot([1,2,3,4],[1,4,9,16])

Note that in this case the R2 value is 1, indicating that data points fall directly on the curve.