/sci/ - Science & Math » Thread #14207263

169KiB, 750x750, 1606147377097.png

View Same Google iqdb SauceNAO

Anonymous Wed 09 Feb 20:22:47 2022 No.14207263 View Reply Original Report

Quoted By: >>14207383 >>14207464 >>14207505

Why is the "sum of squares" significant enough to get its own name? To me it just seems like an arbitrary step on the way to calculating standard deviation, but I'm a math noob so I could be wrong.
Is it ever relevant on its own? Would there ever be a research paper that mentions "sum of squares" without mentioning standard deviation or variance?

Anonymous

Anonymous Wed 09 Feb 2022 20:38:05 No.14207354 Report

Quoted By:

Probably convenience. As in, its the core of the computation and the annoyingly nonlinear portion so most of the analysis will go there. No need to carry the 1/N or be bothered by square roots.

Anonymous

Anonymous Wed 09 Feb 2022 20:43:14 No.14207379 Report

Quoted By: >>14207486

What is a hypotenuse.

Also, since you're smart and know its not significant.... given a domain of positive integers, is there a sum of cubes which add to another cube? hmmmmm.....

Anonymous

Anonymous Wed 09 Feb 2022 20:43:59 No.14207383 Report

Quoted By:

>>14207263
sum of squares sounds like an inner product, which would be important in more advanced treatments of statistics phrased in terms of linear algebra

Anonymous

Anonymous Wed 09 Feb 2022 20:44:47 No.14207385 Report

Quoted By:

theres two hanyuus in the /sci/ catalog rn, thats gotta be a record.

Anonymous

Anonymous Wed 09 Feb 2022 21:00:58 No.14207464 Report

Quoted By: >>14207501

>>14207263
>To me it just seems like an arbitrary step on the way to calculating standard deviation, but I'm a math noob so I could be wrong.
It's usually (but not always) wrong. Sum of squares the way it's generally mentioned is "sum of x-x'" where x is either a data point or some function (such as mean) applied to the data point, and x' is the output of some model. Whereas variance would be something you compute on the points in a dataset themselves.

It's typically used as a loss function for optimization algorithms. Basically, you iterate on your model parameters in a way that drives this down.

Basically, sum of square(d distance)s is a common loss function for optimizers.

Anonymous

Anonymous Wed 09 Feb 2022 21:08:00 No.14207486 Report

Quoted By: >>14207501

>>14207379
>What is a hypotenuse.
I'm talking about statistics, not geometry. If there's a relationship that makes a hypotenuse relevant, I'm all ears

Anonymous

Anonymous Wed 09 Feb 2022 21:11:50 No.14207501 Report

Quoted By:

>>14207486
See >>14207464. It's the distance between dataset points and regression model output, but you don't bother taking the root. You can just minimize the sum of squares directly.

Anonymous

Anonymous Wed 09 Feb 2022 21:12:23 No.14207505 Report

Quoted By:

>>14207263
>Why is the "sum of squares" significant enough to get its own name?
The squares in question are squares of differences. Sometimes you want a differentiable measure of how far off one set of values is from another one, so you square the differences instead of using the absolute value function. This comes up a lot.

Capcode	All Only User Posts Only Moderator Posts Only Admin Posts Only Developer Posts
Show Posts	All Only With Images Only Without Images
Deleted Posts	All Only Deleted Posts Only Non-Deleted Posts
Ghost Posts	All Only Ghost Posts Only Non-Ghost Posts
Post Type	All Only Sticky Threads Only Opening Posts Only Reply Posts
Results	All Grouped By Threads
Order	Latest Posts First Oldest Posts First

Your latest searches