CODEWITHSUNDEEP
pythonscipystatisticsregressiongaussian
DK.
DK.

Reputation: 53

Getting a series of Normal Distributions from a Least Squares regression

I am not particularly good at math. I would like to get some breadcrumbs about how to solve the following formula using python code.

As per this question, any vector of solutions like a in a regression is basically a series of single points each taken from a normal distribution that describes the error of every point on the regression. In effect, every single digit in the solution vector a is the mean of a normal distribution of errors centred on zero.

I would like to find those normal distributions rather than the scalar value for every single point in the solution. Apologies for the poor description of the mathy bits, I was never trained in math in Uni.

Upvotes: 0

Views: 151

Answers (2)

JeeyCi
JeeyCi

Reputation: 579

you do NOT need find those normal distributions, Least Squares Linear (or non-linear) Regression algorithm is fitting the line (or curve) to means you're interested in... and, as pointed by Kaposci, your residuals have to be normally distributed,

Upvotes: 0

Kapocsi
Kapocsi

Reputation: 1022

Here is a hint. Let me know if you want more.

scipy.linalg.lstsq(M, y) returns four things:

x : (N,) or (N, K) ndarray
  Least-squares solution.

residues : (K,) ndarray or float
  Square of the 2-norm for each column in b - a x, if M > N and ndim(A) == n
  (returns a scalar if b is 1-D). Otherwise a (0,)-shaped array is returned.

rank : int
  Effective rank of a.

s : (min(M, N),) ndarray or None
  Singular values of a. The condition number of a is s[0] / s[-1].

residues is going to be of interest to you!

https://docs.scipy.org/doc/scipy/reference/generated/scipy.linalg.lstsq.html

Upvotes: 2

Related Questions