Today I ran into the problem, that I had a graph full of data points, which obviously did not form a straight line.
There is a method called
Linear least squares to calculate the straight line with least difference to the original data points.
Since I needed the method in javascript, here is what I came up with in the end.
function findLineByLeastSquares(values_x, values_y) {
var sum_x = 0;
var sum_y = 0;
var sum_xy = 0;
var sum_xx = 0;
var count = 0;
/*
* We'll use those variables for faster read/write access.
*/
var x = 0;
var y = 0;
var values_length = values_x.length;
if (values_length != values_y.length) {
throw new Error('The parameters values_x and values_y need to have same size!');
}
/*
* Nothing to do.
*/
if (values_length === 0) {
return [ [], [] ];
}
/*
* Calculate the sum for each of the parts necessary.
*/
for (var v = 0; v < values_length; v++) {
x = values_x[v];
y = values_y[v];
sum_x += x;
sum_y += y;
sum_xx += x*x;
sum_xy += x*y;
count++;
}
/*
* Calculate m and b for the formular:
* y = x * m + b
*/
var m = (count*sum_xy - sum_x*sum_y) / (count*sum_xx - sum_x*sum_x);
var b = (sum_y/count) - (m*sum_x)/count;
/*
* We will make the x and y result line now
*/
var result_values_x = [];
var result_values_y = [];
for (var v = 0; v < values_length; v++) {
x = values_x[v];
y = x * m + b;
result_values_x.push(x);
result_values_y.push(y);
}
return [result_values_x, result_values_y];
}
