9.2.5  Exponential regression: exponential_regression exponential_regression_plot

You might expect a set of points to lie on an exponential curve y=b a^x. The exponential_regression command finds the values of a and b which give you the best fit exponential.

• exponential_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).
• exponential_regression(xcoords,ycoords) returns a sequence a,b of the numbers in the best fit exponential y=ba^x.

Example.
Input:

or:

(where the evalf is used to get a numeric approximation to an exact expression, see Section 6.8.1).
Output:

so the best fit exponential curve will be y = 0.5*(2.49146187923)^x.

The exponential_regression_plot command draws the best fit exponential.

• exponential_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).
• exponential_regression_plot(xcoords,ycoords) draws the best fit exponential, and puts the equation and R² value above the graph.

Example.
Input:

Output: