Using the linear regression method outlined in the following https://www.easycalculation.com/statistics/learn-regression.php I wrote some javascript to find the outliers of a given set. However I would like the method to work with curves and in 3d. Not sure of the forumlae in 3d.

 

<script>
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;
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!');
}

if (values_length === 0) {
return [ [], [] ];
}

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 formula:
* 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;

return [m, b];
}

function outliers(values_x,values_y,m,b,outlierdistance){
var outlier = [];
for (var v = 0; v < values_x.length; v++) {
x = values_x[v];
y = values_y[v];
distance = (m*x - y + b)/(Math.sqrt(Math.pow(x,2)+Math.pow(y,2)));
if(distance<0){
distance = distance * -1;
}

if(distance>outlierdistance){
outlier.push(x,y);
}

}
return outlier;
}
values_x = [10,2330,9,44,20,30,40,50];
values_y = [10,20,900,44,20,30,40,50];
slope = findLineByLeastSquares(values_x, values_y);
document.write(outliers(values_x,values_y,slope[0],slope[1],1));
</script>

 

Outlier detection is as much art as it is science.

 

Can't help with the code but this paper gives the formulas for several types of outlier detection in multivariate regression.

 

But when you say curves you mean you want to use non-linear regression?

 

 

But when you say curves you mean you want to use non-linear regression?​

 

 

Exactly the above only works for linear regression in 2D.