linear regresion of a set of points in 2d space

General Discussion Other

telmo.bac..

in General Discussion • Other • 7 months ago

Hi, i was wondering how can i calculate the linear regresion of a set of point in 2d space?

I need to be able to generate a line that connects all points and then calculate the angle of this line.

Which is the best way of achieving this?

cheers

Replies(1)

tfguy44

7 months ago

Directly, from the data.
Assuming you want the line that minimizes the sum of squares, if you have n data points, (x1,y1),...,(xn,yn), define:

Sx = x1 + x2 + ... + xn

Sy = y1 + y2 + ... + yn

Sxy = (x1 * y1) + ( x2 * y2 ) + ... ( xn * yn )
Sxx = ( x1 * x1 ) + ( x2 * x2 ) + ... + ( xn * xn )

Then the slope, m, is:

( ( n * Sxy ) - (Sx * Sy) ) / ( ( n * Sxx ) - ( Sx * Sx ) )

The y-intersect, b, is:

( Sy - ( m * Sx) ) / ( n )

And the line would, of course, be:

y = mx + b

A simple search online could provide you with more details...

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