Logarithmic regression

### 20.2.6 Logarithmic regression

You might expect a set of points to lie on a logarithmic curve y=m ln(x)+b. The logarithmic_regression command finds the logarithmic curve of best fit.

- logarithmic_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).
- logarithmic_regression(xcoords,ycoords) returns a sequence m,b of the numbers in the best fit logarithmic curve y=m ln(x)+b.

#### Example

evalf(logarithmic_regression([[1,1],[2,4],[3,9],[4,16]]))

or:

evalf(logarithmic_regression([1,2,3,4],[1,4,9,16]))

(where the evalf is used to get a numeric approximation to an exact expression):

10.1506450002,−0.564824055818 |  |  |  |  |  |  |  |  |  |

so the best fit logarithmic curve will be y=10.1506450002 ln(x) −0.564824055818.

The logarithmic_regression_plot command draws the best fit logarithmic curve.

- logarithmic_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).
- logarithmic_regression_plot(xcoords,ycoords) draws the best fit logarithmic curve, and puts the equation and R2 value above the graph.

#### Example

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