Correlation

Hello who i can do the correlation between two numbers? thank you

[EDIT SCd - moved answer to question]

i've seen that there is the function corrcoef(x,y) but i want to know if i have an x and an y vector of the same size does this function correlate each x(i) element with the y(i) at the same position? to be clear i need the correlation of x(1) with y(1), x(2) with y(2)..x(n) with y(n).

Answer 1

[Sean de Wolski]

Yes. It does.

A good example:

corrcoef(1:10,10:-1:1)

More:

corrcoef when called with two scalars or vectors produces a 2x2 matrix. The diagonal of the matrix is the correlation of the two vectors to themselves. These should always be 1 (unless there is a nan or an inf).

The antidiagonal is each vector's correlation to each other.

so corrcoef(x,y) will be: [x2x, x2y; y2x y2y]

These are the values you are most likely after. Scalars will always be perfectly correlated to each other. If I give pi and 42 to corrcoef for the data provided they are perfectly correlated (as is pi and -42 or any other number out there!). The same is true for 2 element vectors except there is an addition of sign, e.g:

corrcoef([1,2],[1,1000])

versus

corrcoef([1,2],[1,-1000])

[Salvatore Turino]

uhm if i do corrcoef(1,1) i expect 1 instead i got NaN, instead if i do corrcoef([1,2],[1,5]) i got a matrix...that is also strange since i have as result:

1.0000 1.0000

1.0000 1.0000

can you explain me how to interpretate this result?i mean what is the element 11, 12, 21 and 22 of this matrix?

Answer 2

[Salvatore Turino]

ok but if i need the correlation of two scalar how can i do it?what i need is the simple correlation index of Pearson.

http://it.wikipedia.org/wiki/Indice_di_correlazione_di_Pearson

so a value that is around 0 or 1.

doing

corrcoef(1:10,10:-1:1)

at the end i obtain always a matrix 2x2 and i can't watch the correlation of the single values.

[Sean de Wolski]

Unless there is a nan,inf or two zeros, the correlation between two scalars will always b1. You could also, always exctract the component of the 2x2 matrix that you need. I explained what each was above.

[Salvatore Turino]

mmm doesn't exist any other function for the correlation? i mean i need to know how different is a number from another and not the whole vector.

[Tom Lane]

I'm not sure what you want. How different is 1 from 3?

Normally correlation requires a sequence of numbers. But even then, you're measuring how much they vary in tandem, not how their specific values differ.

[Salvatore Turino]

well from what my teacher told me i need to know how different is 1 from 3 or 1 from 2, and he told me to use the correlation.

[Sean de Wolski]

oh. I would use a difference (minus).

3 - 1