Correlation between two vectors

Question

I have two vectors   A 1           10       200       7       150  A 2          0 001       0 450       0 0007       0 200   I would like to know if there is correlation between these two vectors   I could subtract to each value the mean of the vector and than do     A 1    A 2   Are there any better ways

User · Answer

For correlations you can just use the corr function (statistics toolbox)

corr(A_1(:), A_2(:))

Note that you can also just use

corr(A_1, A_2)

But the linear indexing guarantees that your vectors don't need to be transposed.

User · Answer

Try xcorr  it s a built-in function in MATLAB for cross-correlation   c   xcorr A 1  A 2     However  note that it requires the Signal Processing Toolbox installed  If not  you can look into the corrcoef command instead

User · Answer

Given   A 1    10 200 7 150    A 2    0 001 0 450 0 007 0 200       As others have already pointed out  There are tools to simply compute correlation  most obviously corr   corr A 1  A 2     Returns 0 956766573975184   Requires stats toolbox    You can also use base Matlab s corrcoef function  like this   M   corrcoef  A 1 A 2      Returns  1 0 956766573975185  0 956766573975185 1   M 2 1     Returns 0 956766573975184    Which is closely related to the cov function   cov  condition A 1  condition A 2         As you almost get to in your original question  you can scale and adjust the vectors yourself if you want  which gives a slightly better understanding of what is going on   First create a condition function which subtracts the mean  and divides by the standard deviation   condition     x   x-mean x    std x     Function to subtract mean AND normalize standard deviation   Then the correlation appears to be  A 1   A 2   A 1 2   like this    condition A 1     condition A 2     sum condition A 1   2     Returns 0 956766573975185   By symmetry  this should also work   condition A 1     condition A 2     sum condition A 2   2    Returns 0 956766573975185   And it does   I believe  but don t have the energy to confirm right now  that the same math can be used to compute correlation and cross correlation terms when dealing with multi-dimensiotnal inputs  so long as care is taken when handling the dimensions and orientations of the input arrays

User · Answer

To perform a linear regression between two vectors x and y follow these steps    p err    polyfit x y 1       First order polynomial y fit   polyval p x err       Values on a line y dif   y - y fit             y value difference  residuals  SSdif   sum y dif  2          Sum square of difference SStot    length y -1  var y       Sum square of y taken from variance rsq   1-SSdif SStot           Correlation  r  value  If 1 0 the correlelation is perfect   For x  10 200 7 150  and y  0 001 0 45 0 0007 0 2  I get rsq   0 9181   Reference URL  http   www mathworks com help matlab data analysis linear-regression html

[matlab] Correlation between two vectors?

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