9.2.6  Logarithmic regression: logarithmic_regression logarithmic_regression_plot

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.
Input:

or:

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

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.
Input:

Output: