How to evaluate the "quality" of a trend?

Question

Mathematics

There is a function (in talib, in excel, anywhere) to define a trend line based on a point cloud.
Is it possible to somehow evaluate the "quality" of this trend line?
Like if all points are on the same straight line = 100%
If they are slightly spread = 70%
You can make your own bike and calculate the spread width relative to the trend line, but maybe such a method has already been implemented? If yes, what is it called to google it?

Answer 1

It sounds like you are interested in the value of the function that is minimized in linear regression. Usually this is the sum of the squared distances of each of the points to the line. It's easy to write your own implementation. As the ready-made functions in the listed products are called, I can’t tell you, alas.
If everything is clear from 100% - when all points are on a straight line and the sum = 0; what to take as a maximum, for 0% accuracy, which cannot be worse? :)

Answer 2

Ta-Lib has a stddev function ( standard deviation, standard deviation ). It seems that this is exactly the same metric that you describe in your question.
Those. to make it 100% when it matches the straight line, you need to play around with the result a little, for example, normalize the output of stddev by one, then 1 minus the answer from stddev, and multiply by 100% to convert to percentages.
And yet, you can consider the correlation coefficient between these values ​​and the projections of these values ​​on the trend line, for example.

Answer 3

Usually they consider the standard deviation (in many languages ​​\u200b\u200b- std, and in Excel somehow in Russian).