Ordinary Least Squares - IDEA

AndreBorges

Forums

Hello everyone,
I have recently discovered some of the fantastic features and capabilities of this great software - IDEA. Now by my curiosity in studying the capabilities of the software I intend to apply to the database some statisticals. So what I intend to do now is: use the IDEA capabilities to estimate some coefficients, and for that I want to use (for now) the Ordinary Least Squares.
 
The goal will be:
Imagine that I have an equation like that:
Y = X * B + E
and: Y  -> only one column
X will be divided for example by 4 different columns: X = [X1 X2 X3 X4]
B  -> only one column
And now I want to apply to my database the following:
(((X ') * X)^(- 1)) * (X') * Y
X ' -> Matrix transpose
So my main difficulties are:
 
How can I transpose the matrix X?How can I get the inverse of the matrix: (X ') * X?
 
Is there any functionality in IDEA to perform such calculations?Has anyone tried something similar?
Thank you,
André Borges

Brian Element Thu, 07/27/2017 - 08:43

Hello André and welcome to the site.

Unfortunately my University days for math are many years away for me.  It is probably possible to do this but the math is beyond me.  Now on the positive side, when 10.3 comes out later on this year it will have Python integration and I just looked it up and this is possible to calculate in Python (http://scipy-cookbook.readthedocs.io/items/OLS.html).

If you can explain the math I might be able to create a script but no guarantees.

Thanks

Brian

AndreBorges Fri, 07/28/2017 - 12:16

Wow great news, if version 10.3 comes out then the IDEA will become a unique tool.
 
What I really wanted to calculate was the transpose of a matrix as well as its inverse.
 
remembering my last post, imagine that:
 
X = | x11 x12 x13 x14 |
| x21 x22 x23 x24 |
| x31 x32 x33 x34 |

So the transpose will be: 
X' = | x11 x21 x31 |
| x12 x22 x32 |
| x13 x23 x33 |
| x14 x24 x34 |

For the inverse X ^ (- 1) the calculation is a little more complicated, but the rule is to find a matrix in which multiplied by the matrix X is equal to the identity matrix:   x^(-1)*x= I