Initial data commit

Task/Multiple-regression/Tcl/multiple-regression-1.tcl

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+package require math::linearalgebra
+namespace eval multipleRegression {
+    namespace export regressionCoefficients
+    namespace import ::math::linearalgebra::*
+
+    # Matrix inversion is defined in terms of Gaussian elimination
+    # Note that we assume (correctly) that we have a square matrix
+    proc invert {matrix} {
+	solveGauss $matrix [mkIdentity [lindex [shape $matrix] 0]]
+    }
+    # Implement the Ordinary Least Squares method
+    proc regressionCoefficients {y x} {
+	matmul [matmul [invert [matmul $x [transpose $x]]] $x] $y
+    }
+}
+namespace import multipleRegression::regressionCoefficients

Task/Multiple-regression/Tcl/multiple-regression-2.tcl

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+# Simple helper just for this example
+proc map {n exp list} {
+    upvar 1 $n v
+    set r {}; foreach v $list {lappend r [uplevel 1 $exp]}; return $r
+}
+
+# Data from wikipedia
+set 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
+}
+set 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
+}
+# Wikipedia states that fitting up to the square of x[i] is worth it
+puts [regressionCoefficients $y [map n {map v {expr {$v**$n}} $x} {0 1 2}]]