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Perform an ordinary least-squares regression on a set of predictors, and calculate the goodness-of-fit of the regression.

The returned pair consists of:

• A vector of regression coefficients. This vector has one more element than the list of predictors; the last element is the y-intercept value.
• R², the coefficient of determination (see rSquare for details).

>>> import qualified Data.Vector.Unboxed as VU
>>> :{
 olsRegress [ VU.fromList [0,1,2,3]
            ] (VU.fromList [1000, 1001, 1002, 1003])
:}
([1.0000000000000218,999.9999999999999],1.0)

Compute the ordinary least-squares solution to overdetermined linear system \(Ax = b\). In other words it finds

\[ \operatorname{argmin}|Ax-b|^2 \].

All columns of \(A\) must be linearly independent. It's not checked function will return nonsensical result if resulting linear system is poorly conditioned.

>>> import qualified Data.Vector.Unboxed as VU
>>> :{
 ols (fromColumns [ VU.fromList [0,1,2,3]
                  , VU.fromList [1,1,1,1]
                  ]) (VU.fromList [1000, 1001, 1002, 1003])
:}
[1.0000000000000218,999.9999999999999]

>>> :{
 ols (fromColumns [ VU.fromList [0,1,2,3]
                  , VU.fromList [4,2,1,1]
                  , VU.fromList [1,1,1,1]
                  ]) (VU.fromList [1000, 1001, 1002, 1003])
:}
[1.0000000000005393,4.2290644612446807e-13,999.9999999999983]

Compute R², the coefficient of determination that indicates goodness-of-fit of a regression.

This value will be 1 if the predictors fit perfectly, dropping to 0 if they have no explanatory power.

Bootstrap a regression function. Returns both the results of the regression and the requested confidence interval values.