Initial data commit

Task/Multiple-regression/J/multiple-regression-1.j

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+   NB. Wikipedia data
+   x=: 1.47 1.50 1.52 1.55 1.57 1.60 1.63 1.65 1.68 1.70 1.73 1.75 1.78 1.80 1.83
+   y=: 52.21 53.12 54.48 55.84 57.20 58.57 59.93 61.29 63.11 64.47 66.28 68.10 69.92 72.19 74.46
+
+   y %. x ^/ i.3   NB. calculate coefficients b1, b2 and b3 for 2nd degree polynomial
+128.813 _143.162 61.9603

Task/Multiple-regression/J/multiple-regression-2.j

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+   X=: x ^/ i.3                  NB. form Design matrix
+   X=: (x^0) ,. (x^1) ,. (x^2)   NB. equivalent of previous line
+   4{.X                          NB. show first 4 rows of X
+1 1.47 2.1609
+1  1.5   2.25
+1 1.52 2.3104
+1 1.55 2.4025
+
+   NB. Where y is a set of observations and X is the design matrix
+   NB. y %. X does matrix division and gives the regression coefficients
+   y %. X
+128.813 _143.162 61.9603

Task/Multiple-regression/J/multiple-regression-3.j

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+   mp=: +/ .*                    NB. matrix product
+                                 NB. %.X is matrix inverse of X
+                                 NB. |:X is transpose of X
+
+   (%.(|:X) mp X) mp (|:X) mp y
+128.814 _143.163 61.9606
+   xpy=: mp~ |:                  NB. Or factoring out "X prime y" (monadically "X prime X")
+   X (%.@:xpy@[ mp xpy) y
+128.814 _143.163 61.9606

Task/Multiple-regression/J/multiple-regression-4.j

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+   load 'math/lapack'
+   load 'math/lapack/gels'
+   gels_jlapack_ X;y
+128.813 _143.162 61.9603