9.2.4  Linear regression: linear_regression linear_regression_plot

Given a set of points (x₀,y₀),…,(x_n−1,y_n−1), linear regression finds the line y=mx+b that comes closest to passing through all of the points; i.e., that makes

as small as possible. The linear_regression command finds the linear regression of a set of points.

• linear_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).
• linear_regression(xcoords,ycoords) returns a sequence m,b of the slope and y-intercept of the regression line.

Example.
Input:

or:

Output:

which means that the line y = 4x − 2 is the best fit line.

The linear_regression_plot command draws the best fit line.

• linear_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).
• linear_regression_plot(xcoords,ycoords) draws the line of best fit through the points. It will also give you the equation at the top, as well as the R² value, which is

  R2 =	n−1 ∑ j=0  (m xj + b − ȳ)2 n−1 ∑ j=0  (yj − ȳ)2

  (The R² value will be between 0 and 1 and is one measure of how good the line fits the data; a value close to 1 indicates a good fit, a value close to 0 indicates a bad fit.)

Example.
Input:

Output: