:deps { net.mikera/core.matrix {:mvn/version "0.62.0"}
        net.mikera/vectorz-clj {:mvn/version "0.48.0"}
        org.apache.commons/commons-math3 {:mvn/version "3.5"}
}

(ns regression
  (:use clojure.core.matrix)
  (:use clojure.core.matrix.operators)
  (:import [org.apache.commons.math3.distribution
           NormalDistribution
           TDistribution
           FDistribution]))

(defn regression [xs y]
  (let [[k n] (shape xs)
        nk (- n k 1)
        tdist (TDistribution. nk)
        fdist (FDistribution. k nk)
        sig (fn [dist x] (* 2.0 (- 1.0 (.cumulativeProbability dist x))))
        X (join [(repeat n 1.0)] xs)
        XXt (mmul X (transpose X))
        beta (-> XXt inverse (mmul X y))
        yhat (mmul beta X)
        res (sub y yhat)
        ybar (/ (reduce + y) n)
        y-cen (sub y (repeat n ybar))
        yhat-cen (sub yhat (repeat n ybar))
        SSR (dot yhat-cen yhat-cen)
        SST (dot y-cen y-cen)
        SSRes (dot res res)
        se (map sqrt (scale (/ SSRes n) (diagonal XXt)))
        tscore (abs (map / beta se))
        F (/ (/ SSR k) (/ SSRes nk))
        R2 (/ SSR SST)]
    {:coeffs (seq beta)
     :se (seq se)
     :t0 (seq tscore)
     :tsig (map #(sig tdist %) tscore)
     :F F
     :Fsig (sig fdist F)
     :RSquare R2}))

#'regression/regression

(let [normal (NormalDistribution. 4.0 0.2)
      random-vector (fn [n] (take n (repeatedly rand)))
      X (array (join [(random-vector 10)]
                     [(random-vector 10)]))
      Y (add (mmul [-2 1] X)
             (seq (.sample normal 10)))]
  (regression X Y))

{:coeffs (4.0169543977679725 -1.9653087520525703 0.8539922022675653), :se (0.5189380093158233 0.30494977845244536 0.3768881235684564), :t0 (7.740721098969014 6.444696441578315 2.2659037227859207), :tsig (1.1242165296532214E-4 3.520298919033049E-4 0.05782572705551492), :F 45.39319256356398, :Fsig 1.9629026632062008E-4, :RSquare 0.9284153924812029}

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[2021-02-13] Kruskal's Algorithm Implemented in Clojure

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[2021-02-08] Binary Symmetrization

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[2021-01-27] Counting Cycle-Free Paths in a Graph

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[2020-12-18] Counting Graphs with a Prescribed Degree Sequence

[2020-12-13] Havel–Hakimi Algorithm in Clojure

[2020-12-12] Havel–Hakimi Algorithm in Common-Lisp

[2020-10-23] The Quadratic Casimir Element

[2020-07-04] Collatz Sequence in Binary

[2020-07-02] A Lazy Sequence of Primes in Clojure

[2020-06-10] Yet Another Fizz-Buzz in Common Lisp

[2020-05-12] ECB Data with Clojure and Vega-Lite

[2020-05-06] Processing ECB Data with Common Lisp

[2020-04-17] Next Permutation in the Lexicographical Ordering

[2020-04-13] Turkish Hyphenation in Common Lisp

[2020-04-01] Using JavaPlex with Clojure

[2019-11-05] Constricted Arithmetic Progressions

[2019-11-03] The Number of Arithmetic Progressions of Integers

[2019-05-06] Bron-Kerbosch Algorithm in Clojure

[2019-05-01] An Implementation of Ford-Fulkerson Algorithm in Clojure

[2019-04-22] Document Summarization via Nonnegative Matrix Factorization

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[2019-04-13] K-Nearest Neighbors Algorithm in Clojure

[2019-04-06] K-Means Implemented in Clojure

[2019-03-19] Prüfer Encoding/Decoding of a Tree in Common Lisp

[2019-03-05] Gale-Shaply Algorithm in Common Lisp

[2019-03-02] Calculating The Correct Rank of a Matrix

[2018-12-04] Feed-forward and back-propagation in neural networks as left- and right-fold

[2018-10-31] Nonnegative Matrix Decomposition in Clojure

[2018-10-30] Non-negative Matrix Decomposition in Scala

[2018-08-30] Working with European Central Bank Data in Scala

[2018-07-30] Perverse Sequences

[2018-05-28] Online Perceptron in Common Lisp

[2018-05-26] Online Perceptron

[2018-05-18] Online Regression

[2018-05-06] Knut’s Algorithm-S in Common Lisp

[2018-02-28] Irreducible Dyck Words

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[2018-02-10] Van Eck’s Sequence

[2018-02-09] Hiring networks in mathematics

[2018-02-08] Linus Sequence

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[2018-02-01] Listing all Young Tableaux

[2018-01-23] Collatz sequence (yet again)

[2018-01-15] Hofstadter's Q sequence

[2018-01-09] Farey Sequence

[2018-01-09] Catalan's Triangle

[2018-01-06] The Shoelace Formula for the Area of a Polygon

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[2017-09-27] Expected Value of the Diameter of a Tree

[2017-09-26] Using Quandl with kixi.stats on Clojure

[2017-09-22] Using Quandl with Common Lisp

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[2017-07-20] Steenrod-Milnor and Tournament Sequences

[2017-07-15] A lower bound on the radius of a graph

[2017-07-08] All partitions of an integer

[2017-07-06] Some Hasse Diagrams

[2017-07-04] Shuffles

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[2017-03-14] My First Idris Proof

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[2016-12-01] Distinguishing hash functions

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[2016-08-16] Puzzles and Group Theory

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[2016-06-01] Conjugate Partitions

[2016-04-27] Using Word2Vec from Clojure

[2016-04-24] Using Word2Vec from Common Lisp

[2016-04-18] A Migration Analysis

[2016-04-11] Basic Data Analysis with CL without Frameworks

[2016-03-25] Parallel map-reduce in Common Lisp

[2016-02-22] Text Summarization and Topic Analysis

[2016-01-27] Set Covering Problem

[2016-01-25] Kolmogorov-Smirnov Test

[2016-01-20] Eigen-values of the Laplacian and Connected Components of a Graph

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[2015-10-26] Longest Increasing Subsequence Revisited

[2015-10-16] Document Summarization via Markov Chains

[2015-10-07] Computational Literary Analysis

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[2015-09-28] Merging Association Lists in Common Lisp

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[2015-05-21] Partitions of Equal Measure Whatever the Measure May Be

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[2015-05-03] Happy Numbers

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[2015-04-05] Hamming Derivative of Hashing Functions

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[2015-02-04] Collatz-type Conjectures (Continued)

[2015-01-31] Collatz-type Conjectures (Continued)

[2015-01-30] Collatz-type Conjectures

[2015-01-28] Experiments with Infinite Recursive Sequences (continued)

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[2013-02-18] The sound of the torsion parts of homotopy groups of spheres

[2013-02-12] Monadic Units

[2013-02-07] Distribution of Collatz Lengths (continued)

[2013-02-03] Distribution of Collatz Lengths

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[2013-01-12] Path ideals

[2013-01-10] McCarthy91 Terminates

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[2013-01-04] A Simple Monte-Carlo Integration Implementation in Lisp

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[2012-11-29] Untitled

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[2012-11-19] Strictly Increasing Labellings of Directed Graphs

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[2012-11-04] Local rings, idempotents and non-invertible elements

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[2012-10-03] Source code entropy

[2012-09-28] Collisions in random walks

[2012-09-26] Transitive closure of a directed graph

[2012-09-26] Solving linear equations in ℕ

[2012-09-26] Listing partitions

[2012-09-26] Inverting formal power series

[2012-09-26] Hasse subgraph of a directed graph