From a52ef2d3f4c1bc92b74eb1fb4ce4a2c408cc07ac Mon Sep 17 00:00:00 2001
From: Dorai Sitaram <ds26gte@gmail.com>
Date: Fri, 12 Apr 2024 16:48:28 -0400
Subject: [PATCH 01/14] statistics.arr: added variance, variance-sample,
 t-test-paired, t-test-pooled, t-test-independent, chi-square #1732

---
 src/arr/trove/statistics.arr | 80 +++++++++++++++++++++++++++++++-----
 1 file changed, 70 insertions(+), 10 deletions(-)

diff --git a/src/arr/trove/statistics.arr b/src/arr/trove/statistics.arr
index 2532a39401..01db5d7abe 100644
--- a/src/arr/trove/statistics.arr
+++ b/src/arr/trove/statistics.arr
@@ -8,10 +8,16 @@ provide {
     mode-smallest: mode-smallest,
     mode-largest: mode-largest,
     mode-any: mode-any,
+    variance: variance,
     stdev: stdev,
+    variance-sample: variance-sample,
     stdev-sample: stdev-sample,
     linear-regression: linear-regression,
-    r-squared: r-squared
+    r-squared: r-squared,
+    t-test-paired: t-test-paired,
+    t-test-pooled: t-test-pooled,
+    t-test-independent: t-test-independent,
+    chi-square: chi-square
 } end
 provide-types *
 import global as _
@@ -143,24 +149,36 @@ fun mode-any(l :: List<Number>) -> Number:
     ms.get(num-random(ms.length()))
   end
 end
-  
-fun stdev(l :: List) -> Number:
-  doc: ```returns the standard deviation of the list 
+
+fun variance(l :: List) -> Number:
+  doc: ```returns the variance of the list
        of numbers, or raises an error if the list is empty```
   reg-mean = mean(l)
   sq-diff = l.map(lam(k): num-expt((k - reg-mean), 2) end)
   sq-mean = mean(sq-diff)
-  num-sqrt(sq-mean)
+  sq-mean
 end
 
-fun stdev-sample(l :: List) -> Number:
-  doc: ```returns the standard deviation of the list 
+fun stdev(l :: List) -> Number:
+  doc: ```returns the standard deviation of the list
+       of numbers, or raises an error if the list is empty```
+  num-sqrt(variance(l))
+end
+
+fun variance-sample(l :: List) -> Number:
+  doc: ```returns the variance of the list
        of numbers, or raises an error if the list is empty```
   len = l.length()
   reg-mean = mean(l)
   sq-diff = l.map(lam(k): num-expt((k - reg-mean), 2) end)
   sq-mean = math.sum(sq-diff) / (len - 1)
-  num-sqrt(sq-mean)
+  sq-mean
+end
+
+fun stdev-sample(l :: List) -> Number:
+  doc: ```returns the standard deviation of the list
+       of numbers, or raises an error if the list is empty```
+  num-sqrt(variance-sample(l))
 end
 
 fun linear-regression(x :: List<Number>, y :: List<Number>) -> (Number -> Number):
@@ -177,8 +195,8 @@ fun linear-regression(x :: List<Number>, y :: List<Number>) -> (Number -> Number
     covariance = xpt-xy - xpt-x-xpt-y
     v1 = math.sum(map(lam(n): n * n end, x))
     v2 = (math.sum(x) * math.sum(x)) / x.length()
-    variance = v1 - v2
-    beta = covariance / variance
+    variance1 = v1 - v2
+    beta = covariance / variance1
     alpha = mean(y) - (beta * mean(x))
 
     fun predictor(in :: Number) -> Number:
@@ -204,3 +222,45 @@ fun r-squared(x :: List<Number>, y :: List<Number>, f :: (Number -> Number)) ->
   end
 end
 
+fun t-test-paired(l1 :: List, l2 :: List) -> Number:
+  doc: "t-test-paired"
+  n1 = l1.length()
+  n2 = l2.length()
+  if n1 <> n2:
+    raise(E.message-exception("t-test-paired: input lists must have equal lengths"))
+  else if n1 == 0:
+    raise(E.message-exception("t-test-paired: input lists should have at least one element"))
+  else:
+    diffs = map2(lam(x1, x2): x1 - x2 end, l1, l2)
+    diffs-mean = mean(diffs)
+    s-hat = stdev-sample(diffs)
+    diffs-mean / (s-hat / num-sqrt(n1))
+  end
+end
+
+fun t-test-pooled(l1 :: List, l2 :: List) -> Number:
+  doc: "t-test-pooled"
+  n1 = l1.length()
+  n2 = l2.length()
+  m1 = mean(l1)
+  m2 = mean(l2)
+  v1 = variance-sample(l1)
+  v2 = variance-sample(l2)
+  (m1 - m2) / (((((n1 - 1) * num-expt(v1, 2)) + ((n2 - 1) * num-expt(v2, 2))) / ((n1 + n2) - 2)) * num-sqrt((1 / n1) + (1 / n2)))
+end
+
+fun t-test-independent(l1 :: List, l2 :: List) -> Number:
+  doc: "t-test-independent"
+  n1 = l1.length()
+  n2 = l2.length()
+  m1 = mean(l1)
+  m2 = mean(l2)
+  v1 = variance-sample(l1)
+  v2 = variance-sample(l2)
+  (m1 - m2) / num-sqrt((v1 / n1) + (v2 / n2))
+end
+
+fun chi-square(obs :: List, exp :: List) -> Number:
+  doc: "chi-square"
+  math.sum(map2(lam(o, e): num-expt(o - e, 2) / e end, obs, exp))
+end

From 2ba6dd10f8957e78ca49793c9728cb07b61c2586 Mon Sep 17 00:00:00 2001
From: Dorai Sitaram <ds26gte@gmail.com>
Date: Sat, 13 Apr 2024 09:14:53 -0400
Subject: [PATCH 02/14] - test-statistics.arr: added tests for the new stats
 functions #1732 - statistics.arr: added exceptions for t-test-{pooled,
 independent}

---
 src/arr/trove/statistics.arr          | 30 +++++++++++++++++----------
 tests/pyret/tests/test-statistics.arr | 28 ++++++++++++++++++++++---
 2 files changed, 44 insertions(+), 14 deletions(-)

diff --git a/src/arr/trove/statistics.arr b/src/arr/trove/statistics.arr
index 01db5d7abe..7354a277d9 100644
--- a/src/arr/trove/statistics.arr
+++ b/src/arr/trove/statistics.arr
@@ -229,7 +229,7 @@ fun t-test-paired(l1 :: List, l2 :: List) -> Number:
   if n1 <> n2:
     raise(E.message-exception("t-test-paired: input lists must have equal lengths"))
   else if n1 == 0:
-    raise(E.message-exception("t-test-paired: input lists should have at least one element"))
+    raise(E.message-exception("t-test-paired: input lists must have at least one element"))
   else:
     diffs = map2(lam(x1, x2): x1 - x2 end, l1, l2)
     diffs-mean = mean(diffs)
@@ -242,22 +242,30 @@ fun t-test-pooled(l1 :: List, l2 :: List) -> Number:
   doc: "t-test-pooled"
   n1 = l1.length()
   n2 = l2.length()
-  m1 = mean(l1)
-  m2 = mean(l2)
-  v1 = variance-sample(l1)
-  v2 = variance-sample(l2)
-  (m1 - m2) / (((((n1 - 1) * num-expt(v1, 2)) + ((n2 - 1) * num-expt(v2, 2))) / ((n1 + n2) - 2)) * num-sqrt((1 / n1) + (1 / n2)))
+  if (n1 == 0) or (n2 == 0):
+    raise(E.message-exception("t-test-pooled: input lists must have at least one element"))
+  else:
+    m1 = mean(l1)
+    m2 = mean(l2)
+    v1 = variance-sample(l1)
+    v2 = variance-sample(l2)
+    (m1 - m2) / (((((n1 - 1) * num-expt(v1, 2)) + ((n2 - 1) * num-expt(v2, 2))) / ((n1 + n2) - 2)) * num-sqrt((1 / n1) + (1 / n2)))
+  end
 end
 
 fun t-test-independent(l1 :: List, l2 :: List) -> Number:
   doc: "t-test-independent"
   n1 = l1.length()
   n2 = l2.length()
-  m1 = mean(l1)
-  m2 = mean(l2)
-  v1 = variance-sample(l1)
-  v2 = variance-sample(l2)
-  (m1 - m2) / num-sqrt((v1 / n1) + (v2 / n2))
+  if (n1 == 0) or (n2 == 0):
+    raise(E.message-exception("t-test-independent: input lists must have at least one element"))
+  else:
+    m1 = mean(l1)
+    m2 = mean(l2)
+    v1 = variance-sample(l1)
+    v2 = variance-sample(l2)
+    (m1 - m2) / num-sqrt((v1 / n1) + (v2 / n2))
+  end
 end
 
 fun chi-square(obs :: List, exp :: List) -> Number:
diff --git a/tests/pyret/tests/test-statistics.arr b/tests/pyret/tests/test-statistics.arr
index 46e4502f67..fad4226c40 100644
--- a/tests/pyret/tests/test-statistics.arr
+++ b/tests/pyret/tests/test-statistics.arr
@@ -49,18 +49,40 @@ check "numeric helpers":
   modes([list: -1, 2, -1, 2, -1]) is [list: -1]
   modes([list: 1, 1, 2, 2, 3, 3, 3]) is [list: 3]
 
+  variance([list:]) raises "empty"
+  variance([list: 5]) is 0
+  variance([list: 3, 4, 5, 6, 7]) is%(within(0.01)) 2.0
+  variance([list: 1, 1, 1, 1]) is-roughly ~0
+
   stdev([list:]) raises "empty"
   stdev([list: 5]) is 0
-
   stdev([list: 3, 4, 5, 6, 7]) is%(within(0.01)) 1.41
   stdev([list: 1, 1, 1, 1]) is-roughly ~0
-  stdev([list:]) raises "empty"
-  
+
+  variance-sample([list: 3, 4, 5, 6, 7]) is%(within(0.01)) (10 / 4)
+  variance-sample([list: 3]) raises "division by zero"
+  variance-sample([list: 1, 1, 1, 1]) is-roughly ~0
+  variance-sample([list:]) raises "empty"
+
   stdev-sample([list: 3, 4, 5, 6, 7]) is%(within(0.01)) num-sqrt(10 / 4)
   stdev-sample([list: 3]) raises "division by zero"
   stdev-sample([list: 1, 1, 1, 1]) is-roughly ~0
   stdev-sample([list:]) raises "empty"
 
+  t-test-paired([list: 1], [list: 2, 3]) raises "lists must have equal lengths"
+  t-test-paired([list:], [list:]) raises "lists must have at least one element"
+  t-test-paired([list: 1, 2, 3], [list: 4, 6, 8]) is%(within(0.01)) -6.928
+
+  t-test-pooled([list:], [list: 1, 2, 3]) raises "lists must have at least one element"
+  t-test-pooled([list: 1, 2, 3], [list: 4, 5, 6]) is%(within(0.01)) -3.674
+  t-test-pooled([list: 1, 2, 3], [list: 4, 5, 6, 7]) is%(within(0.01)) -2.217
+
+  t-test-independent([list:], [list: 1, 2, 3]) raises "lists must have at least one element"
+  t-test-independent([list: 1, 2, 3], [list: 4, 5, 6]) is%(within(0.01)) -3.674
+  t-test-independent([list: 1, 2, 3], [list: 4, 5, 6, 7]) is%(within(0.01)) -4.041
+
+  chi-square([list: 1, 2, 3, 4], [list: 1, 2, 3, 4]) is 0
+  chi-square([list: 1, 2, 3, 4], [list: 0.9, 1.8, 3.5, 4.7]) is%(within(0.01)) 0.209
 end
 
 check "linear regression":

From 363038c81a89d9515154ab898712a6238a02b286 Mon Sep 17 00:00:00 2001
From: Dorai Sitaram <ds26gte@gmail.com>
Date: Mon, 15 Apr 2024 09:56:29 -0400
Subject: [PATCH 03/14] Added z-test impl & test #1732

---
 src/arr/trove/statistics.arr          | 10 ++++++++++
 tests/pyret/tests/test-statistics.arr |  2 ++
 2 files changed, 12 insertions(+)

diff --git a/src/arr/trove/statistics.arr b/src/arr/trove/statistics.arr
index 7354a277d9..84c49dbfba 100644
--- a/src/arr/trove/statistics.arr
+++ b/src/arr/trove/statistics.arr
@@ -17,6 +17,7 @@ provide {
     t-test-paired: t-test-paired,
     t-test-pooled: t-test-pooled,
     t-test-independent: t-test-independent,
+    z-test: z-test,
     chi-square: chi-square
 } end
 provide-types *
@@ -268,6 +269,15 @@ fun t-test-independent(l1 :: List, l2 :: List) -> Number:
   end
 end
 
+fun z-test(l1 :: List, l2 :: List, sd1 :: Number, sd2 :: Number) -> Number:
+  doc: "z-test"
+  n1 = l1.length()
+  n2 = l2.length()
+  x-bar-1 = mean(l1)
+  x-bar-2 = mean(l2)
+  (x-bar-1 - x-bar-2) / num-sqrt((num-expt(sd1, 2) / n1) + (num-expt(sd2, 2) / n2))
+end
+
 fun chi-square(obs :: List, exp :: List) -> Number:
   doc: "chi-square"
   math.sum(map2(lam(o, e): num-expt(o - e, 2) / e end, obs, exp))
diff --git a/tests/pyret/tests/test-statistics.arr b/tests/pyret/tests/test-statistics.arr
index fad4226c40..b55fddfbc7 100644
--- a/tests/pyret/tests/test-statistics.arr
+++ b/tests/pyret/tests/test-statistics.arr
@@ -81,6 +81,8 @@ check "numeric helpers":
   t-test-independent([list: 1, 2, 3], [list: 4, 5, 6]) is%(within(0.01)) -3.674
   t-test-independent([list: 1, 2, 3], [list: 4, 5, 6, 7]) is%(within(0.01)) -4.041
 
+  z-test([list: 1, 2, 3], [list: 4, 5, 6], 1.58, 2.58) is%(within(0.01)) -1.718
+
   chi-square([list: 1, 2, 3, 4], [list: 1, 2, 3, 4]) is 0
   chi-square([list: 1, 2, 3, 4], [list: 0.9, 1.8, 3.5, 4.7]) is%(within(0.01)) 0.209
 end

From bcdfd0ee4c0c515d526473527bf19eac757e6bbe Mon Sep 17 00:00:00 2001
From: Dorai Sitaram <ds26gte@gmail.com>
Date: Thu, 16 May 2024 16:16:49 -0400
Subject: [PATCH 04/14] - arr/trove/statistics.arr: added
 multiple-regression(): takes a list of   list of known x-inputs, and a list
 of the corresponding known   y-outputs, and returns a predictor function that
 takes a list of   x-inputs and returns its estimated y-output #1732 -
 js/trove/multiple-regression.js contains the JS implementation of  
 multiple-regression and all its matrix subroutines -
 tests/test-statistics.arr: added a basic test (can add more from   curriculum
 examples, when these are added)

---
 src/arr/trove/statistics.arr          |   7 +
 src/js/trove/multiple-regression.js   | 182 ++++++++++++++++++++++++++
 tests/pyret/tests/test-statistics.arr |   9 ++
 3 files changed, 198 insertions(+)
 create mode 100644 src/js/trove/multiple-regression.js

diff --git a/src/arr/trove/statistics.arr b/src/arr/trove/statistics.arr
index 84c49dbfba..3b9d684279 100644
--- a/src/arr/trove/statistics.arr
+++ b/src/arr/trove/statistics.arr
@@ -13,6 +13,7 @@ provide {
     variance-sample: variance-sample,
     stdev-sample: stdev-sample,
     linear-regression: linear-regression,
+    multiple-regression: multiple-regression,
     r-squared: r-squared,
     t-test-paired: t-test-paired,
     t-test-pooled: t-test-pooled,
@@ -26,6 +27,7 @@ include lists
 import error as E
 import math as math
 import string-dict as SD
+import multiple-regression as MR
 
 fun mean(l :: List<Number>) -> Number:
   doc: "Find the average of a list of numbers"
@@ -208,6 +210,11 @@ fun linear-regression(x :: List<Number>, y :: List<Number>) -> (Number -> Number
   end
 end
 
+fun multiple-regression(x_s_s :: List<List<Number>>, y_s :: List<Number>) -> (List<Number> -> Number):
+  doc: "multiple-regression"
+  MR.multiple-regression(x_s_s, y_s)
+end
+
 fun r-squared(x :: List<Number>, y :: List<Number>, f :: (Number -> Number)) -> Number:
   shadow x = map(num-to-roughnum, x)
   shadow y = map(num-to-roughnum, y)
diff --git a/src/js/trove/multiple-regression.js b/src/js/trove/multiple-regression.js
new file mode 100644
index 0000000000..ae9300fa85
--- /dev/null
+++ b/src/js/trove/multiple-regression.js
@@ -0,0 +1,182 @@
+({
+  requires: [],
+  nativeRequires: ["pyret-base/js/namespace"],
+  provides: {
+    values: {
+      "multiple-regression": "tany"
+    }
+  },
+  theModule: function(runtime, namespace, uri) {
+
+    function makeColumnMatrix(y_s) {
+      let n = y_s.length;
+      let M = new Array(n);
+      for (let i = 0; i < n; i++) {
+        M[i][0] = y_s[i];
+      }
+      return M;
+    }
+
+    function matrixTranspose(m) {
+      let numrows = m.length;
+      let numcols = m[0].length;
+      let mT = new Array(numcols);
+      for (let i = 0; i < numcols; i++) {
+        mT[i] = new Array(m);
+        for (let j = 0; j < numrows; j++) {
+          mT[i][j] = m[j][i];
+        }
+      }
+      return mT;
+    }
+
+    function matrixDeterminant(m) {
+      let size = m.length;
+      if (size === 0) {
+        return 0;
+      }
+      if (m[0].length !== size) {
+        return 0;
+      }
+      if (size === 1) {
+        return m[0][0];
+      }
+      if (size === 2) {
+        return (m[0][0] * m[1][1] - m[1][0] * m[0][1]);
+      }
+      let det = 0;
+      for (let i = 0; i < size; i++) {
+        det += m[0][i] * matrixCofactor(m, 0, i);
+      }
+      return det;
+    }
+
+    function matrixCofactor(m, i, j) {
+      let size = m.length;
+      if (size === 0) {
+        return 0;
+      }
+      if (m[0].length !== size) {
+        return 0;
+      }
+      let mm = new Array(size - 1);
+      for (let ii = 0; ii < size; ii++) {
+        if (ii === i) { continue; }
+        let iii = (ii > i ? ii - 1 : ii)
+        mm[iii] = new Array(size - 1);
+        for (let jj = 0; jj < size; jj++) {
+          if (jj === j) { continue; }
+          let jjj = (jj > j ? jj - 1 : jj)
+          mm[iii][jjj] = m[ii][jj];
+        }
+      }
+      let sign = (i + j) % 2;
+      sign = (sign === 0) ? 1 : -1;
+      return sign * matrixDeterminant(mm)
+    }
+
+    function matrixAdjoint(m) {
+      let size = m.length;
+      let mc = new Array(size);
+      for (let i = 0; i < size; i++) {
+        mc[i] = new Array(size);
+        for (let j = 0; j < size; j++) {
+          mc[i][j] = matrixCofactor(m, i, j);
+        }
+      }
+      return matrixTranspose(mc)
+    }
+
+    function matrixInverse(m) {
+      let det = matrixDeterminant(m);
+      let mI = matrixAdjoint(m);
+      let k = m.length;
+      for (let i = 0; i < k; i++) {
+        for (let j = 0; j < k; j++) {
+          let x = mI[i][j]
+          mI[i][j] = x/det
+        }
+      }
+      return mI;
+    }
+
+    function matrixMultiply2(m1, m2) {
+      let m1r = m1.length;
+      let m1c = m1[0].length;
+      let m2c = m2[0].length;
+      let mP = new Array(m1r);
+      for (let i = 0; i < m1r; i++) {
+        mP[i] = new Array(m2c);
+        for (let j = 0; j < m2c; j++) {
+          let x = 0;
+          for (let k = 0; k < m1c; k++) {
+            x += m1[i][k] * m2[k][j];
+          }
+          mP[i][j] = x;
+        }
+      }
+      return mP;
+    }
+
+    function multipleRegression(x_s_s, y_s) {
+      runtime.ffi.checkArity(2, arguments, "multiple-regression", false);
+      runtime.checkList(x_s_s);
+      runtime.checkList(y_s);
+      let js_x_s_s = runtime.ffi.toArray(x_s_s);
+      let js_y_s = runtime.ffi.toArray(y_s);
+      let num_mappings = js_x_s_s.length;
+      if (js_y_s.length !== num_mappings) {
+        throw runtime.ffi.throwMessageException("multiple-regression: number of mappings incorrect");
+      }
+      let X = new Array(num_mappings);
+      let Y = new Array(num_mappings);
+      let x_s_len = false;
+      js_x_s_s.forEach(function(x_s, i) {
+        runtime.checkList(x_s);
+        let js_x_s = runtime.ffi.toArray(x_s);
+        let x_s_n = js_x_s.length;
+        if (x_s_len === false) {
+          x_s_len = x_s_n;
+        } else if (x_s_n !== x_s_len) {
+          throw runtime.ffi.throwMessageException("multiple-regression: bad mapping");
+        }
+        X[i] = new Array(x_s_len + 1)
+        let Xi = X[i];
+        Xi[0] = 1;
+        js_x_s.forEach(function(x, j) {
+          runtime.checkNumber(x);
+          Xi[j+1] = runtime.num_to_fixnum(x);
+        });
+      });
+      js_y_s.forEach(function(y, i) {
+        runtime.checkNumber(y);
+        Y[i] = [runtime.num_to_fixnum(y)];
+      });
+
+      let XT = matrixTranspose(X);
+      let B = matrixMultiply2(matrixInverse(matrixMultiply2(XT, X)), matrixMultiply2(XT, Y));
+      let Bfunc = function(x_s) {
+        runtime.checkList(x_s);
+        let js_x_s = runtime.ffi.toArray(x_s);
+        if (js_x_s.length !== x_s_len) {
+          throw runtime.ffi.throwMessageException("predictor: wrong number of arguments");
+        }
+        let result = B[0][0];
+        for (let i = 0; i < x_s_len; i++) {
+          result += runtime.num_to_fixnum(js_x_s[i]) * B[i+1][0]
+        }
+        return runtime.makeNumber(result);
+      }
+      return runtime.makeFunction(Bfunc, "predictor");
+    }
+
+    let vals = {
+
+      "multiple-regression": runtime.makeFunction(multipleRegression, "multiple-regression")
+
+    };
+
+    return runtime.makeModuleReturn(vals, {});
+  }
+})
+
diff --git a/tests/pyret/tests/test-statistics.arr b/tests/pyret/tests/test-statistics.arr
index b55fddfbc7..6d6f86441e 100644
--- a/tests/pyret/tests/test-statistics.arr
+++ b/tests/pyret/tests/test-statistics.arr
@@ -113,3 +113,12 @@ check "linear regression":
 
 end
 
+check "multiple regression":
+  x-s-s = [list: [list: 4], [list: 4.5], [list: 5], [list: 5.5], [list: 6], [list: 6.5], [list: 7]]
+  y-s   = [list: 33, 42, 45, 51, 53, 61, 62]
+  pf = multiple-regression(x-s-s, y-s)
+  pf([list: 8]) is%(within-abs(0.001)) 73.3214
+end
+
+
+

From 7cf32b95e5090e97fb7502240d046369cc28293f Mon Sep 17 00:00:00 2001
From: Dorai Sitaram <ds26gte@gmail.com>
Date: Fri, 17 May 2024 10:03:23 -0400
Subject: [PATCH 05/14] multiple-regression(): first arg is now a list of
 N-tuples (each N-tuple representing one input (setting of indep vars to
 values). The returned predictor fn also takes an N-tuple #1732

---
 src/js/trove/multiple-regression.js   | 8 ++++----
 tests/pyret/tests/test-statistics.arr | 4 ++--
 2 files changed, 6 insertions(+), 6 deletions(-)

diff --git a/src/js/trove/multiple-regression.js b/src/js/trove/multiple-regression.js
index ae9300fa85..1484e12791 100644
--- a/src/js/trove/multiple-regression.js
+++ b/src/js/trove/multiple-regression.js
@@ -132,8 +132,8 @@
       let Y = new Array(num_mappings);
       let x_s_len = false;
       js_x_s_s.forEach(function(x_s, i) {
-        runtime.checkList(x_s);
-        let js_x_s = runtime.ffi.toArray(x_s);
+        runtime.checkTuple(x_s);
+        let js_x_s = x_s.vals;
         let x_s_n = js_x_s.length;
         if (x_s_len === false) {
           x_s_len = x_s_n;
@@ -156,8 +156,8 @@
       let XT = matrixTranspose(X);
       let B = matrixMultiply2(matrixInverse(matrixMultiply2(XT, X)), matrixMultiply2(XT, Y));
       let Bfunc = function(x_s) {
-        runtime.checkList(x_s);
-        let js_x_s = runtime.ffi.toArray(x_s);
+        runtime.checkTuple(x_s);
+        let js_x_s = x_s.vals;
         if (js_x_s.length !== x_s_len) {
           throw runtime.ffi.throwMessageException("predictor: wrong number of arguments");
         }
diff --git a/tests/pyret/tests/test-statistics.arr b/tests/pyret/tests/test-statistics.arr
index 6d6f86441e..b3c227376c 100644
--- a/tests/pyret/tests/test-statistics.arr
+++ b/tests/pyret/tests/test-statistics.arr
@@ -114,10 +114,10 @@ check "linear regression":
 end
 
 check "multiple regression":
-  x-s-s = [list: [list: 4], [list: 4.5], [list: 5], [list: 5.5], [list: 6], [list: 6.5], [list: 7]]
+  x-s-s = [list: {4}, {4.5}, {5}, {5.5}, {6}, {6.5}, {7}]
   y-s   = [list: 33, 42, 45, 51, 53, 61, 62]
   pf = multiple-regression(x-s-s, y-s)
-  pf([list: 8]) is%(within-abs(0.001)) 73.3214
+  pf({8}) is%(within-abs(0.001)) 73.3214
 end
 
 

From 7501262b2a8ec1459d43d42e6bf8d026cad2ca14 Mon Sep 17 00:00:00 2001
From: Dorai Sitaram <ds26gte@gmail.com>
Date: Fri, 17 May 2024 13:42:53 -0400
Subject: [PATCH 06/14] statistics.arr: Correct type of multiple-regression()
 #1732 multiple-regression.js: clean-up w/ better row/col indexing names

---
 src/arr/trove/statistics.arr        |   7 +-
 src/js/trove/multiple-regression.js | 100 ++++++++++++++--------------
 2 files changed, 55 insertions(+), 52 deletions(-)

diff --git a/src/arr/trove/statistics.arr b/src/arr/trove/statistics.arr
index 3b9d684279..34a2a5138e 100644
--- a/src/arr/trove/statistics.arr
+++ b/src/arr/trove/statistics.arr
@@ -210,7 +210,7 @@ fun linear-regression(x :: List<Number>, y :: List<Number>) -> (Number -> Number
   end
 end
 
-fun multiple-regression(x_s_s :: List<List<Number>>, y_s :: List<Number>) -> (List<Number> -> Number):
+fun multiple-regression(x_s_s :: List<Any>, y_s :: List<Number>) -> (Any -> Number):
   doc: "multiple-regression"
   MR.multiple-regression(x_s_s, y_s)
 end
@@ -257,7 +257,10 @@ fun t-test-pooled(l1 :: List, l2 :: List) -> Number:
     m2 = mean(l2)
     v1 = variance-sample(l1)
     v2 = variance-sample(l2)
-    (m1 - m2) / (((((n1 - 1) * num-expt(v1, 2)) + ((n2 - 1) * num-expt(v2, 2))) / ((n1 + n2) - 2)) * num-sqrt((1 / n1) + (1 / n2)))
+    v1-squared = num-sqr(v1)
+    v2-squared = num-sqr(v2)
+    (m1 - m2) / (((((n1 - 1) * v1-squared) + ((n2 - 1) * v2-squared)) / ((n1 + n2) - 2)) *
+                 num-sqrt((1 / n1) + (1 / n2)))
   end
 end
 
diff --git a/src/js/trove/multiple-regression.js b/src/js/trove/multiple-regression.js
index 1484e12791..c0b58192c5 100644
--- a/src/js/trove/multiple-regression.js
+++ b/src/js/trove/multiple-regression.js
@@ -9,22 +9,22 @@
   theModule: function(runtime, namespace, uri) {
 
     function makeColumnMatrix(y_s) {
-      let n = y_s.length;
-      let M = new Array(n);
-      for (let i = 0; i < n; i++) {
-        M[i][0] = y_s[i];
+      let size = y_s.length;
+      let M = new Array(size);
+      for (let r = 0; r < size; r++) {
+        M[r][0] = y_s[r];
       }
       return M;
     }
 
     function matrixTranspose(m) {
-      let numrows = m.length;
-      let numcols = m[0].length;
-      let mT = new Array(numcols);
-      for (let i = 0; i < numcols; i++) {
-        mT[i] = new Array(m);
-        for (let j = 0; j < numrows; j++) {
-          mT[i][j] = m[j][i];
+      let numRows = m.length;
+      let numCols = m[0].length;
+      let mT = new Array(numCols);
+      for (let r = 0; r < numCols; r++) {
+        mT[r] = new Array(numRows);
+        for (let c = 0; c < numRows; c++) {
+          mT[r][c] = m[c][r];
         }
       }
       return mT;
@@ -45,13 +45,13 @@
         return (m[0][0] * m[1][1] - m[1][0] * m[0][1]);
       }
       let det = 0;
-      for (let i = 0; i < size; i++) {
-        det += m[0][i] * matrixCofactor(m, 0, i);
+      for (let c = 0; c < size; c++) {
+        det += m[0][c] * matrixCofactor(m, 0, c);
       }
       return det;
     }
 
-    function matrixCofactor(m, i, j) {
+    function matrixCofactor(m, r, c) {
       let size = m.length;
       if (size === 0) {
         return 0;
@@ -60,17 +60,17 @@
         return 0;
       }
       let mm = new Array(size - 1);
-      for (let ii = 0; ii < size; ii++) {
-        if (ii === i) { continue; }
-        let iii = (ii > i ? ii - 1 : ii)
-        mm[iii] = new Array(size - 1);
-        for (let jj = 0; jj < size; jj++) {
-          if (jj === j) { continue; }
-          let jjj = (jj > j ? jj - 1 : jj)
-          mm[iii][jjj] = m[ii][jj];
+      for (let ri = 0; ri < size; ri++) {
+        if (ri === r) { continue; }
+        let rii = (ri > r ? ri - 1 : ri)
+        mm[rii] = new Array(size - 1);
+        for (let ci = 0; ci < size; ci++) {
+          if (ci === c) { continue; }
+          let cii = (ci > c ? ci - 1 : ci)
+          mm[rii][cii] = m[ri][ci];
         }
       }
-      let sign = (i + j) % 2;
+      let sign = (r + c) % 2;
       sign = (sign === 0) ? 1 : -1;
       return sign * matrixDeterminant(mm)
     }
@@ -78,10 +78,10 @@
     function matrixAdjoint(m) {
       let size = m.length;
       let mc = new Array(size);
-      for (let i = 0; i < size; i++) {
-        mc[i] = new Array(size);
-        for (let j = 0; j < size; j++) {
-          mc[i][j] = matrixCofactor(m, i, j);
+      for (let r = 0; r < size; r++) {
+        mc[r] = new Array(size);
+        for (let c = 0; c < size; c++) {
+          mc[r][c] = matrixCofactor(m, r, c);
         }
       }
       return matrixTranspose(mc)
@@ -90,29 +90,29 @@
     function matrixInverse(m) {
       let det = matrixDeterminant(m);
       let mI = matrixAdjoint(m);
-      let k = m.length;
-      for (let i = 0; i < k; i++) {
-        for (let j = 0; j < k; j++) {
-          let x = mI[i][j]
-          mI[i][j] = x/det
+      let size = m.length;
+      for (let r = 0; r < size; r++) {
+        for (let c = 0; c < size; c++) {
+          let x = mI[r][c]
+          mI[r][c] = x/det
         }
       }
       return mI;
     }
 
     function matrixMultiply2(m1, m2) {
-      let m1r = m1.length;
-      let m1c = m1[0].length;
-      let m2c = m2[0].length;
-      let mP = new Array(m1r);
-      for (let i = 0; i < m1r; i++) {
-        mP[i] = new Array(m2c);
-        for (let j = 0; j < m2c; j++) {
+      let m1numRows = m1.length;
+      let m1numCols = m1[0].length; // this will be === m2numRows
+      let m2numCols = m2[0].length;
+      let mP = new Array(m1numRows);
+      for (let r = 0; r < m1numRows; r++) {
+        mP[r] = new Array(m2numCols);
+        for (let c = 0; c < m2numCols; c++) {
           let x = 0;
-          for (let k = 0; k < m1c; k++) {
-            x += m1[i][k] * m2[k][j];
+          for (let k = 0; k < m1numCols; k++) {
+            x += m1[r][k] * m2[k][c];
           }
-          mP[i][j] = x;
+          mP[r][c] = x;
         }
       }
       return mP;
@@ -131,7 +131,7 @@
       let X = new Array(num_mappings);
       let Y = new Array(num_mappings);
       let x_s_len = false;
-      js_x_s_s.forEach(function(x_s, i) {
+      js_x_s_s.forEach(function(x_s, r) {
         runtime.checkTuple(x_s);
         let js_x_s = x_s.vals;
         let x_s_n = js_x_s.length;
@@ -140,17 +140,17 @@
         } else if (x_s_n !== x_s_len) {
           throw runtime.ffi.throwMessageException("multiple-regression: bad mapping");
         }
-        X[i] = new Array(x_s_len + 1)
-        let Xi = X[i];
-        Xi[0] = 1;
-        js_x_s.forEach(function(x, j) {
+        X[r] = new Array(x_s_len + 1)
+        let Xr = X[r];
+        Xr[0] = 1;
+        js_x_s.forEach(function(x, c) {
           runtime.checkNumber(x);
-          Xi[j+1] = runtime.num_to_fixnum(x);
+          Xr[c+1] = runtime.num_to_fixnum(x);
         });
       });
-      js_y_s.forEach(function(y, i) {
+      js_y_s.forEach(function(y, r) {
         runtime.checkNumber(y);
-        Y[i] = [runtime.num_to_fixnum(y)];
+        Y[r] = [runtime.num_to_fixnum(y)];
       });
 
       let XT = matrixTranspose(X);

From d341e3392060286432b1fa689b1834f2636e2849 Mon Sep 17 00:00:00 2001
From: Dorai Sitaram <ds26gte@gmail.com>
Date: Fri, 17 May 2024 14:45:51 -0400
Subject: [PATCH 07/14] test-statistics.arr: #1732 - check mulreg test on 1 var
 matches our linreg on same var - add mulreg test for 2 vars statistics.arr:
 add pointers to docs for formulas used

---
 src/arr/trove/statistics.arr          |  6 ++++++
 tests/pyret/tests/test-statistics.arr | 19 ++++++++++++++-----
 2 files changed, 20 insertions(+), 5 deletions(-)

diff --git a/src/arr/trove/statistics.arr b/src/arr/trove/statistics.arr
index 34a2a5138e..933b76f012 100644
--- a/src/arr/trove/statistics.arr
+++ b/src/arr/trove/statistics.arr
@@ -210,6 +210,8 @@ fun linear-regression(x :: List<Number>, y :: List<Number>) -> (Number -> Number
   end
 end
 
+# please see: https://online.stat.psu.edu/stat462/
+
 fun multiple-regression(x_s_s :: List<Any>, y_s :: List<Number>) -> (Any -> Number):
   doc: "multiple-regression"
   MR.multiple-regression(x_s_s, y_s)
@@ -246,6 +248,10 @@ fun t-test-paired(l1 :: List, l2 :: List) -> Number:
   end
 end
 
+# please see:
+#   https://en.wikipedia.org/wiki/Student's_t-test
+#   https://www.investopedia.com/terms/t/t-test.asp
+
 fun t-test-pooled(l1 :: List, l2 :: List) -> Number:
   doc: "t-test-pooled"
   n1 = l1.length()
diff --git a/tests/pyret/tests/test-statistics.arr b/tests/pyret/tests/test-statistics.arr
index b3c227376c..b2eb5bb826 100644
--- a/tests/pyret/tests/test-statistics.arr
+++ b/tests/pyret/tests/test-statistics.arr
@@ -114,11 +114,20 @@ check "linear regression":
 end
 
 check "multiple regression":
+  # multiple-regression function for single independent variable
   x-s-s = [list: {4}, {4.5}, {5}, {5.5}, {6}, {6.5}, {7}]
   y-s   = [list: 33, 42, 45, 51, 53, 61, 62]
-  pf = multiple-regression(x-s-s, y-s)
-  pf({8}) is%(within-abs(0.001)) 73.3214
+  pf1   = multiple-regression(x-s-s, y-s)
+  pf1({8}) is-roughly 73.3214
+  #
+  # check it matches linear-regression function on the same single variable
+  x-s = [list: 4, 4.5, 5, 5.5, 6, 6.5, 7]
+  pf2 = linear-regression(x-s, y-s)
+  pf2(8) is-roughly 73.3214
+  #
+  # multiple-regression with two independent variables
+  x-s-s-i = [list: {4; 3}, {4.5; 2}, {5; 1.2}, {5.5; 4.5}, {6; 3.3}, {6.5; 10}, {7; 0}]
+  y-s-i   = [list: 33, 42, 45, 51, 53, 61, 62]
+  pf-i    = multiple-regression(x-s-s-i, y-s-i)
+  pf-i({8; 9}) is-roughly 74.52888
 end
-
-
-

From 6f09230cd8fa26dafbb0f8be6f6043d883d0a93a Mon Sep 17 00:00:00 2001
From: Dorai Sitaram <ds26gte@gmail.com>
Date: Fri, 17 May 2024 14:52:15 -0400
Subject: [PATCH 08/14] multiple-regression.js: gen'd predictor function shd
 check that all its arg tuple's elts are numbers #1732

---
 src/js/trove/multiple-regression.js | 4 +++-
 1 file changed, 3 insertions(+), 1 deletion(-)

diff --git a/src/js/trove/multiple-regression.js b/src/js/trove/multiple-regression.js
index c0b58192c5..6c95bd4916 100644
--- a/src/js/trove/multiple-regression.js
+++ b/src/js/trove/multiple-regression.js
@@ -163,7 +163,9 @@
         }
         let result = B[0][0];
         for (let i = 0; i < x_s_len; i++) {
-          result += runtime.num_to_fixnum(js_x_s[i]) * B[i+1][0]
+          let x = js_x_s[i];
+          runtime.checkNumber(x);
+          result += runtime.num_to_fixnum(x) * B[i+1][0]
         }
         return runtime.makeNumber(result);
       }

From cb49a3f750971b55ee6f45824bb06c2b81a3dbd3 Mon Sep 17 00:00:00 2001
From: Dorai Sitaram <ds26gte@gmail.com>
Date: Fri, 17 May 2024 15:01:59 -0400
Subject: [PATCH 09/14] multiple-regression.js: better exception msgs #1732

---
 src/js/trove/multiple-regression.js | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/src/js/trove/multiple-regression.js b/src/js/trove/multiple-regression.js
index 6c95bd4916..2e4740899d 100644
--- a/src/js/trove/multiple-regression.js
+++ b/src/js/trove/multiple-regression.js
@@ -126,7 +126,7 @@
       let js_y_s = runtime.ffi.toArray(y_s);
       let num_mappings = js_x_s_s.length;
       if (js_y_s.length !== num_mappings) {
-        throw runtime.ffi.throwMessageException("multiple-regression: number of mappings incorrect");
+        throw runtime.ffi.throwMessageException("multiple-regression: number of inputs doesn't match number of outputs");
       }
       let X = new Array(num_mappings);
       let Y = new Array(num_mappings);
@@ -138,7 +138,7 @@
         if (x_s_len === false) {
           x_s_len = x_s_n;
         } else if (x_s_n !== x_s_len) {
-          throw runtime.ffi.throwMessageException("multiple-regression: bad mapping");
+          throw runtime.ffi.throwMessageException("multiple-regression: lengths of input tuples are different");
         }
         X[r] = new Array(x_s_len + 1)
         let Xr = X[r];

From b9ea62d21bac290262e1014855ed765cb1114d86 Mon Sep 17 00:00:00 2001
From: Dorai Sitaram <ds26gte@gmail.com>
Date: Sun, 19 May 2024 11:50:49 -0400
Subject: [PATCH 10/14] redefine linear-regression() as a special case of
 multiple-regression() #1732

---
 src/arr/trove/statistics.arr        | 42 +++++++++++------------------
 src/js/trove/multiple-regression.js | 15 ++++++-----
 2 files changed, 25 insertions(+), 32 deletions(-)

diff --git a/src/arr/trove/statistics.arr b/src/arr/trove/statistics.arr
index 933b76f012..4aabb05c58 100644
--- a/src/arr/trove/statistics.arr
+++ b/src/arr/trove/statistics.arr
@@ -184,32 +184,6 @@ fun stdev-sample(l :: List) -> Number:
   num-sqrt(variance-sample(l))
 end
 
-fun linear-regression(x :: List<Number>, y :: List<Number>) -> (Number -> Number):
-  doc: "returns a linear predictor function calculated with ordinary least squares regression"
-  if x.length() <> y.length():
-    raise(E.message-exception("linear-regression: input lists must have equal lengths"))
-  else if x.length() < 2:
-    raise(E.message-exception("linear-regression: input lists must have at least 2 elements each"))
-  else:
-    shadow y = map(num-to-roughnum, y)
-    shadow x = map(num-to-roughnum, x)
-    xpt-xy = math.sum(map2(lam(xi, yi): xi * yi end, x, y))
-    xpt-x-xpt-y = (math.sum(x) * math.sum(y)) / x.length()
-    covariance = xpt-xy - xpt-x-xpt-y
-    v1 = math.sum(map(lam(n): n * n end, x))
-    v2 = (math.sum(x) * math.sum(x)) / x.length()
-    variance1 = v1 - v2
-    beta = covariance / variance1
-    alpha = mean(y) - (beta * mean(x))
-
-    fun predictor(in :: Number) -> Number:
-      (beta * in) + alpha
-    end
-
-    predictor
-  end
-end
-
 # please see: https://online.stat.psu.edu/stat462/
 
 fun multiple-regression(x_s_s :: List<Any>, y_s :: List<Number>) -> (Any -> Number):
@@ -217,6 +191,22 @@ fun multiple-regression(x_s_s :: List<Any>, y_s :: List<Number>) -> (Any -> Numb
   MR.multiple-regression(x_s_s, y_s)
 end
 
+fun linear-regression(x-s :: List<Number>, y-s :: List<Number>) -> (Number -> Number):
+  doc: "returns a linear predictor function for a single independent variable"
+  x-s-n = x-s.length()
+  if x-s-n <> y-s.length():
+    raise(E.message-exception("linear-regression: input lists must have equal lengths"))
+  else if x-s-n < 2:
+    raise(E.message-exception("linear-regression: input lists must have at least 2 elements each"))
+  else:
+    predictor1 = MR.multiple-regression(x-s.map(lam(x1 :: Number): {x1} end), y-s)
+    fun predictor2(x2 :: Number) -> Number:
+      predictor1({x2})
+    end
+    predictor2
+  end
+end
+
 fun r-squared(x :: List<Number>, y :: List<Number>, f :: (Number -> Number)) -> Number:
   shadow x = map(num-to-roughnum, x)
   shadow y = map(num-to-roughnum, y)
diff --git a/src/js/trove/multiple-regression.js b/src/js/trove/multiple-regression.js
index 2e4740899d..dccd0f55b6 100644
--- a/src/js/trove/multiple-regression.js
+++ b/src/js/trove/multiple-regression.js
@@ -72,7 +72,7 @@
       }
       let sign = (r + c) % 2;
       sign = (sign === 0) ? 1 : -1;
-      return sign * matrixDeterminant(mm)
+      return sign * matrixDeterminant(mm);
     }
 
     function matrixAdjoint(m) {
@@ -84,7 +84,7 @@
           mc[r][c] = matrixCofactor(m, r, c);
         }
       }
-      return matrixTranspose(mc)
+      return matrixTranspose(mc);
     }
 
     function matrixInverse(m) {
@@ -93,8 +93,8 @@
       let size = m.length;
       for (let r = 0; r < size; r++) {
         for (let c = 0; c < size; c++) {
-          let x = mI[r][c]
-          mI[r][c] = x/det
+          let x = mI[r][c];
+          mI[r][c] = x/det;
         }
       }
       return mI;
@@ -126,7 +126,10 @@
       let js_y_s = runtime.ffi.toArray(y_s);
       let num_mappings = js_x_s_s.length;
       if (js_y_s.length !== num_mappings) {
-        throw runtime.ffi.throwMessageException("multiple-regression: number of inputs doesn't match number of outputs");
+        throw runtime.ffi.throwMessageException("multiple-regression: lists must have equal lengths");
+        if (num_mappings < 2) {
+          throw runtime.ffi.throwMessageException("multiple-regression: lists must have at least 2 elements each");
+        }
       }
       let X = new Array(num_mappings);
       let Y = new Array(num_mappings);
@@ -140,7 +143,7 @@
         } else if (x_s_n !== x_s_len) {
           throw runtime.ffi.throwMessageException("multiple-regression: lengths of input tuples are different");
         }
-        X[r] = new Array(x_s_len + 1)
+        X[r] = new Array(x_s_len + 1);
         let Xr = X[r];
         Xr[0] = 1;
         js_x_s.forEach(function(x, c) {

From 207d18b3410d66ed36285f2e14cb0007e5cc373c Mon Sep 17 00:00:00 2001
From: Dorai Sitaram <ds26gte@gmail.com>
Date: Fri, 14 Jun 2024 13:02:23 -0400
Subject: [PATCH 11/14] statistics.arr: Corrected t-test, z-test, t-test-pooled
 Simplified def of t-test-paired, t-test-independent, chi-square (Still think
 the `test` in these names should be `score` or `value`)

---
 src/arr/trove/statistics.arr          | 86 +++++++++++++++------------
 tests/pyret/tests/test-statistics.arr |  7 ++-
 2 files changed, 53 insertions(+), 40 deletions(-)

diff --git a/src/arr/trove/statistics.arr b/src/arr/trove/statistics.arr
index 4aabb05c58..fafcd880da 100644
--- a/src/arr/trove/statistics.arr
+++ b/src/arr/trove/statistics.arr
@@ -15,10 +15,11 @@ provide {
     linear-regression: linear-regression,
     multiple-regression: multiple-regression,
     r-squared: r-squared,
+    z-test: z-test,
+    t-test: t-test,
     t-test-paired: t-test-paired,
     t-test-pooled: t-test-pooled,
     t-test-independent: t-test-independent,
-    z-test: z-test,
     chi-square: chi-square
 } end
 provide-types *
@@ -222,69 +223,78 @@ fun r-squared(x :: List<Number>, y :: List<Number>, f :: (Number -> Number)) ->
   end
 end
 
+fun z-test(sample-list :: List, population-sd :: Number, population-mean :: Number) -> Number:
+  doc: "z-test"
+  sample-size = sample-list.length()
+  sample-mean = mean(sample-list)
+  sd-of-mean = population-sd / num-sqrt(sample-size)
+  (sample-mean - population-mean) / sd-of-mean
+end
+
+fun t-test(sample-list :: List, population-mean :: Number) -> Number:
+  doc: "t-test"
+  sample-size = sample-list.length()
+  sample-mean = mean(sample-list)
+  estimated-population-variance = variance-sample(sample-list)
+  variance-of-mean = estimated-population-variance / sample-size
+  (sample-mean - population-mean) / num-sqrt(variance-of-mean)
+end
+
+# please see:
+#   https://en.wikipedia.org/wiki/Student's_t-test
+#   https://www.investopedia.com/terms/t/t-test.asp
+#     (this has a typo for the pooled t-test, corrected here)
+
 fun t-test-paired(l1 :: List, l2 :: List) -> Number:
   doc: "t-test-paired"
-  n1 = l1.length()
+  n = l1.length()
   n2 = l2.length()
-  if n1 <> n2:
+  if n <> n2:
     raise(E.message-exception("t-test-paired: input lists must have equal lengths"))
-  else if n1 == 0:
+  else if n == 0:
     raise(E.message-exception("t-test-paired: input lists must have at least one element"))
   else:
     diffs = map2(lam(x1, x2): x1 - x2 end, l1, l2)
     diffs-mean = mean(diffs)
     s-hat = stdev-sample(diffs)
-    diffs-mean / (s-hat / num-sqrt(n1))
+    diffs-mean / (s-hat / num-sqrt(n))
   end
 end
 
-# please see:
-#   https://en.wikipedia.org/wiki/Student's_t-test
-#   https://www.investopedia.com/terms/t/t-test.asp
-
-fun t-test-pooled(l1 :: List, l2 :: List) -> Number:
+fun t-test-pooled(sample-list-1 :: List, sample-list-2 :: List) -> Number:
   doc: "t-test-pooled"
-  n1 = l1.length()
-  n2 = l2.length()
+  n1 = sample-list-1.length()
+  n2 = sample-list-2.length()
   if (n1 == 0) or (n2 == 0):
     raise(E.message-exception("t-test-pooled: input lists must have at least one element"))
   else:
-    m1 = mean(l1)
-    m2 = mean(l2)
-    v1 = variance-sample(l1)
-    v2 = variance-sample(l2)
-    v1-squared = num-sqr(v1)
-    v2-squared = num-sqr(v2)
-    (m1 - m2) / (((((n1 - 1) * v1-squared) + ((n2 - 1) * v2-squared)) / ((n1 + n2) - 2)) *
-                 num-sqrt((1 / n1) + (1 / n2)))
+    m1 = mean(sample-list-1)
+    m2 = mean(sample-list-2)
+    v1 = variance-sample(sample-list-1)
+    v2 = variance-sample(sample-list-2)
+    v = (((n1 - 1) * v1) + ((n2 - 1) * v2)) / ((n1 + n2) - 2)
+    (m1 - m2) / num-sqrt((v / n1) + (v / n2))
   end
 end
 
-fun t-test-independent(l1 :: List, l2 :: List) -> Number:
+fun t-test-independent(sample-list-1 :: List, sample-list-2 :: List) -> Number:
   doc: "t-test-independent"
-  n1 = l1.length()
-  n2 = l2.length()
+  n1 = sample-list-1.length()
+  n2 = sample-list-2.length()
   if (n1 == 0) or (n2 == 0):
     raise(E.message-exception("t-test-independent: input lists must have at least one element"))
   else:
-    m1 = mean(l1)
-    m2 = mean(l2)
-    v1 = variance-sample(l1)
-    v2 = variance-sample(l2)
+    m1 = mean(sample-list-1)
+    m2 = mean(sample-list-2)
+    v1 = variance-sample(sample-list-1)
+    v2 = variance-sample(sample-list-2)
     (m1 - m2) / num-sqrt((v1 / n1) + (v2 / n2))
   end
 end
 
-fun z-test(l1 :: List, l2 :: List, sd1 :: Number, sd2 :: Number) -> Number:
-  doc: "z-test"
-  n1 = l1.length()
-  n2 = l2.length()
-  x-bar-1 = mean(l1)
-  x-bar-2 = mean(l2)
-  (x-bar-1 - x-bar-2) / num-sqrt((num-expt(sd1, 2) / n1) + (num-expt(sd2, 2) / n2))
-end
-
-fun chi-square(obs :: List, exp :: List) -> Number:
+fun chi-square(observed-values :: List, predicted-values :: List) -> Number:
   doc: "chi-square"
-  math.sum(map2(lam(o, e): num-expt(o - e, 2) / e end, obs, exp))
+  math.sum(map2(lam(observed-value, predicted-value):
+                  num-expt(observed-value - predicted-value, 2) / predicted-value end,
+                observed-values, predicted-values))
 end
diff --git a/tests/pyret/tests/test-statistics.arr b/tests/pyret/tests/test-statistics.arr
index b2eb5bb826..b2f158ddaf 100644
--- a/tests/pyret/tests/test-statistics.arr
+++ b/tests/pyret/tests/test-statistics.arr
@@ -69,19 +69,22 @@ check "numeric helpers":
   stdev-sample([list: 1, 1, 1, 1]) is-roughly ~0
   stdev-sample([list:]) raises "empty"
 
+  z-test([list: 1, 2, 3], 1.58, 2.58) is%(within(0.01)) -0.6358
+
+  t-test([list: 1, 2, 3], 2.58) is%(within(0.01)) -1.0046
+
   t-test-paired([list: 1], [list: 2, 3]) raises "lists must have equal lengths"
   t-test-paired([list:], [list:]) raises "lists must have at least one element"
   t-test-paired([list: 1, 2, 3], [list: 4, 6, 8]) is%(within(0.01)) -6.928
 
   t-test-pooled([list:], [list: 1, 2, 3]) raises "lists must have at least one element"
   t-test-pooled([list: 1, 2, 3], [list: 4, 5, 6]) is%(within(0.01)) -3.674
-  t-test-pooled([list: 1, 2, 3], [list: 4, 5, 6, 7]) is%(within(0.01)) -2.217
+  t-test-pooled([list: 1, 2, 3], [list: 4, 5, 6, 7]) is%(within(0.01)) -3.873
 
   t-test-independent([list:], [list: 1, 2, 3]) raises "lists must have at least one element"
   t-test-independent([list: 1, 2, 3], [list: 4, 5, 6]) is%(within(0.01)) -3.674
   t-test-independent([list: 1, 2, 3], [list: 4, 5, 6, 7]) is%(within(0.01)) -4.041
 
-  z-test([list: 1, 2, 3], [list: 4, 5, 6], 1.58, 2.58) is%(within(0.01)) -1.718
 
   chi-square([list: 1, 2, 3, 4], [list: 1, 2, 3, 4]) is 0
   chi-square([list: 1, 2, 3, 4], [list: 0.9, 1.8, 3.5, 4.7]) is%(within(0.01)) 0.209

From c5326d6394f2e080dab8e69d2bdcfd8c368628a6 Mon Sep 17 00:00:00 2001
From: Dorai Sitaram <ds26gte@gmail.com>
Date: Thu, 4 Jul 2024 11:20:58 -0400
Subject: [PATCH 12/14] - matrices.arr: Add fun list-to-vector -- method
 to-vector: typo fix (<> shd be or) - statistics.arr: use vector dot product
 instead of doing list manip - test-matrices.arr: add test for list-to-vector

---
 src/arr/trove/matrices.arr          | 8 +++++++-
 src/arr/trove/statistics.arr        | 7 ++++---
 tests/pyret/tests/test-matrices.arr | 2 ++
 3 files changed, 13 insertions(+), 4 deletions(-)

diff --git a/src/arr/trove/matrices.arr b/src/arr/trove/matrices.arr
index 3d9293f13b..ba7c97d18c 100644
--- a/src/arr/trove/matrices.arr
+++ b/src/arr/trove/matrices.arr
@@ -61,6 +61,7 @@ provide:
   make-matrix,
   build-matrix,
   vector-to-matrix,
+  list-to-vector,
   list-to-matrix,
   list-to-row-matrix,
   list-to-col-matrix,
@@ -351,7 +352,7 @@ sharing:
   
   method to-vector(self) -> Vector:
     doc: "Returns the one-row/one-column matrix as a vector"
-    if ((self.cols == 1) <> (self.rows == 1)):
+    if ((self.cols == 1) or (self.rows == 1)):
       vector-of-raw-array(self.elts)
     else:
       raise("Cannot convert non-vector matrix to vector")
@@ -974,6 +975,11 @@ where:
   [mk-mtx(1, 3): 1, 2, 3]
 end
 
+fun list-to-vector(lst :: List<Number>):
+  doc: "Converts the given list of numbers into a vector"
+  list-to-row-matrix(lst).to-vector()
+end
+
 fun list-to-matrix(rows :: NonZeroNat, cols :: NonZeroNat, lst :: List<Number>) block:
   doc: "Converts the given list of numbers into a matrix of the given size"
   when not(lst.length() == (rows * cols)):
diff --git a/src/arr/trove/statistics.arr b/src/arr/trove/statistics.arr
index f9d873b1f3..8123559a89 100644
--- a/src/arr/trove/statistics.arr
+++ b/src/arr/trove/statistics.arr
@@ -226,11 +226,12 @@ end
 
 fun multiple-regression(x_s_s :: List<List<Number>>, y_s :: List<Number>) -> (Any -> Number):
   doc: "multiple-regression"
-  mx_X = MX.lists-to-matrix(x_s_s.map(lam(x_s): x_s.push(1) end))
+  intercepts = MX.col-matrix.make(raw-array-of(1, y_s.length()))
+  mx_X = intercepts.augment(MX.lists-to-matrix(x_s_s))
   mx_Y = MX.lists-to-matrix(y_s.map(lam(y): [list: y] end))
-  B = MX.mtx-to-list(MX.mtx-least-squares-solve(mx_X, mx_Y))
+  B = MX.mtx-to-vector(MX.mtx-least-squares-solve(mx_X, mx_Y))
   fun B_pred_fn(x_s :: List<Number>) -> Number:
-    math.sum(map2(lam(b_i, x_i): b_i * x_i end, B, x_s.push(1)))
+    B.dot(MX.list-to-vector(x_s.push(1)))
   end
   B_pred_fn
 end
diff --git a/tests/pyret/tests/test-matrices.arr b/tests/pyret/tests/test-matrices.arr
index 7752cb7ae7..12b5685c99 100644
--- a/tests/pyret/tests/test-matrices.arr
+++ b/tests/pyret/tests/test-matrices.arr
@@ -57,6 +57,8 @@ check "Vector Operations":
 
   M.vec-normalize([vector: 1, 2, 3]) is%(vector-within(0.001))
   [vector: (1 / num-sqrt(14)), (2 / num-sqrt(14)), (3 / num-sqrt(14))]
+
+  M.list-to-vector([list: 1, 2, 3]) is [vector: 1, 2, 3]
 end
 
 check "Basic Matrix Accessors":

From bddb03f9408c4da48c070002dd3a75c538288625 Mon Sep 17 00:00:00 2001
From: Dorai Sitaram <ds26gte@gmail.com>
Date: Thu, 4 Jul 2024 23:50:50 -0400
Subject: [PATCH 13/14] efficiencies suggested by @blerner added

---
 src/arr/trove/matrices.arr   | 2 +-
 src/arr/trove/statistics.arr | 2 +-
 2 files changed, 2 insertions(+), 2 deletions(-)

diff --git a/src/arr/trove/matrices.arr b/src/arr/trove/matrices.arr
index ba7c97d18c..01415df976 100644
--- a/src/arr/trove/matrices.arr
+++ b/src/arr/trove/matrices.arr
@@ -977,7 +977,7 @@ end
 
 fun list-to-vector(lst :: List<Number>):
   doc: "Converts the given list of numbers into a vector"
-  list-to-row-matrix(lst).to-vector()
+  vector(raw-array-from-list(lst))
 end
 
 fun list-to-matrix(rows :: NonZeroNat, cols :: NonZeroNat, lst :: List<Number>) block:
diff --git a/src/arr/trove/statistics.arr b/src/arr/trove/statistics.arr
index 8123559a89..26e667e138 100644
--- a/src/arr/trove/statistics.arr
+++ b/src/arr/trove/statistics.arr
@@ -228,7 +228,7 @@ fun multiple-regression(x_s_s :: List<List<Number>>, y_s :: List<Number>) -> (An
   doc: "multiple-regression"
   intercepts = MX.col-matrix.make(raw-array-of(1, y_s.length()))
   mx_X = intercepts.augment(MX.lists-to-matrix(x_s_s))
-  mx_Y = MX.lists-to-matrix(y_s.map(lam(y): [list: y] end))
+  mx_Y = MX.col-matrix.make(raw-array-from-list(y_s))
   B = MX.mtx-to-vector(MX.mtx-least-squares-solve(mx_X, mx_Y))
   fun B_pred_fn(x_s :: List<Number>) -> Number:
     B.dot(MX.list-to-vector(x_s.push(1)))

From d36171ff510cba6d68c1de03fbb4d7894ee94a57 Mon Sep 17 00:00:00 2001
From: Dorai Sitaram <ds26gte@gmail.com>
Date: Fri, 5 Jul 2024 10:40:53 -0400
Subject: [PATCH 14/14] - statistics.arr: add more descriptive doc strings --
 multiple-regrssion output type made more specific -- multiple-regression:
 predictor fn raises exception on wrong # of args -- chi-square: simplify --
 use simpler is-roughly rather than is%(within(0.01)) - test-statistics.arr:
 add check for mult reg predictor arg# mismatch - test-matrices.arr: add
 additional tests for .to-vector()

---
 src/arr/trove/statistics.arr          | 33 ++++++++++++++++-----------
 tests/pyret/tests/test-matrices.arr   |  2 ++
 tests/pyret/tests/test-statistics.arr | 17 +++++++-------
 3 files changed, 31 insertions(+), 21 deletions(-)

diff --git a/src/arr/trove/statistics.arr b/src/arr/trove/statistics.arr
index 26e667e138..98f65a0294 100644
--- a/src/arr/trove/statistics.arr
+++ b/src/arr/trove/statistics.arr
@@ -224,20 +224,26 @@ end
 
 # please see: https://online.stat.psu.edu/stat462/
 
-fun multiple-regression(x_s_s :: List<List<Number>>, y_s :: List<Number>) -> (Any -> Number):
-  doc: "multiple-regression"
+fun multiple-regression(x_s_s :: List<List<Number>>, y_s :: List<Number>) -> (List<Number> -> Number):
+  doc: "returns a predictor function given a list of list of independent inputs and the correspoinding list of outputs"
   intercepts = MX.col-matrix.make(raw-array-of(1, y_s.length()))
   mx_X = intercepts.augment(MX.lists-to-matrix(x_s_s))
   mx_Y = MX.col-matrix.make(raw-array-from-list(y_s))
   B = MX.mtx-to-vector(MX.mtx-least-squares-solve(mx_X, mx_Y))
+  B_n = B.length() - 1
   fun B_pred_fn(x_s :: List<Number>) -> Number:
-    B.dot(MX.list-to-vector(x_s.push(1)))
+    x_s_n = x_s.length()
+    if B_n <> x_s_n:
+      raise(E.message-exception("multiple-regression: the regression expected " + tostring(B_n) + " inputs, but received " + tostring(x_s_n) + " instead"))
+    else:
+      B.dot(MX.list-to-vector(x_s.push(1)))
+    end
   end
   B_pred_fn
 end
 
 fun linear-regression(x-s :: List<Number>, y-s :: List<Number>) -> (Number -> Number):
-  doc: "returns a linear predictor function for a single independent variable"
+  doc: "returns a linear predictor function given a list of single inputs and the corresponding list of outputs"
   x-s-n = x-s.length()
   if x-s-n <> y-s.length():
     raise(E.message-exception("linear-regression: input lists must have equal lengths"))
@@ -253,6 +259,7 @@ fun linear-regression(x-s :: List<Number>, y-s :: List<Number>) -> (Number -> Nu
 end
 
 fun r-squared(x :: List<Number>, y :: List<Number>, f :: (Number -> Number)) -> Number:
+  doc: "given a list of inputs, a list of outputs, and a model predictor, finds the r-squared of the model"
   shadow x = map(num-to-roughnum, x)
   shadow y = map(num-to-roughnum, y)
   y-mean = mean(y)
@@ -268,7 +275,7 @@ fun r-squared(x :: List<Number>, y :: List<Number>, f :: (Number -> Number)) ->
 end
 
 fun z-test(sample-list :: List, population-sd :: Number, population-mean :: Number) -> Number:
-  doc: "z-test"
+  doc: "given a sample and the population SD and mean, find the z-score of the sample's mean"
   sample-size = sample-list.length()
   sample-mean = mean(sample-list)
   sd-of-mean = population-sd / num-sqrt(sample-size)
@@ -276,7 +283,7 @@ fun z-test(sample-list :: List, population-sd :: Number, population-mean :: Numb
 end
 
 fun t-test(sample-list :: List, population-mean :: Number) -> Number:
-  doc: "t-test"
+  doc: "given a sample and the population mean, find the t-score of the sample's mean"
   sample-size = sample-list.length()
   sample-mean = mean(sample-list)
   estimated-population-variance = variance-sample(sample-list)
@@ -290,7 +297,7 @@ end
 #     (this has a typo for the pooled t-test, corrected here)
 
 fun t-test-paired(l1 :: List, l2 :: List) -> Number:
-  doc: "t-test-paired"
+  doc: "given two paired samples, find the t-score of the difference of their means"
   n = l1.length()
   n2 = l2.length()
   if n <> n2:
@@ -306,7 +313,7 @@ fun t-test-paired(l1 :: List, l2 :: List) -> Number:
 end
 
 fun t-test-pooled(sample-list-1 :: List, sample-list-2 :: List) -> Number:
-  doc: "t-test-pooled"
+  doc: "given two independent samples of different sizes or variances, find the t-score of the difference of their means"
   n1 = sample-list-1.length()
   n2 = sample-list-2.length()
   if (n1 == 0) or (n2 == 0):
@@ -322,7 +329,7 @@ fun t-test-pooled(sample-list-1 :: List, sample-list-2 :: List) -> Number:
 end
 
 fun t-test-independent(sample-list-1 :: List, sample-list-2 :: List) -> Number:
-  doc: "t-test-independent"
+  doc: "given two independent samples of similar size or variance, find the t-score of the difference of their means"
   n1 = sample-list-1.length()
   n2 = sample-list-2.length()
   if (n1 == 0) or (n2 == 0):
@@ -337,8 +344,8 @@ fun t-test-independent(sample-list-1 :: List, sample-list-2 :: List) -> Number:
 end
 
 fun chi-square(observed-values :: List, predicted-values :: List) -> Number:
-  doc: "chi-square"
-  math.sum(map2(lam(observed-value, predicted-value):
-                  num-expt(observed-value - predicted-value, 2) / predicted-value end,
-                observed-values, predicted-values))
+  doc: "given a list of observed and predicted values, returns the chi-square statistic"
+  for fold2(sum from 0, obs from observed-values, pred from predicted-values):
+    sum + (num-sqr(obs - pred) / pred)
+  end
 end
diff --git a/tests/pyret/tests/test-matrices.arr b/tests/pyret/tests/test-matrices.arr
index 12b5685c99..7a25792abb 100644
--- a/tests/pyret/tests/test-matrices.arr
+++ b/tests/pyret/tests/test-matrices.arr
@@ -97,6 +97,8 @@ check "Basic Matrix Accessors":
   M.mtx-row(mtx1, 0).to-vector() is [vector: 1, 2, 3]
   M.mtx-col(mtx1, 1).to-vector() is [vector: 2, 5]
 
+  [row-matrix: 1, 2, 3].to-vector() is [vector: 1, 2, 3]
+  [col-matrix: 1, 2, 3].to-vector() is [vector: 1, 2, 3]
 end
 
 check "Submatrices":
diff --git a/tests/pyret/tests/test-statistics.arr b/tests/pyret/tests/test-statistics.arr
index 13e685ea2e..79581ba2df 100644
--- a/tests/pyret/tests/test-statistics.arr
+++ b/tests/pyret/tests/test-statistics.arr
@@ -69,25 +69,25 @@ check "numeric helpers":
   stdev-sample([list: 1, 1, 1, 1]) is-roughly ~0
   stdev-sample([list:]) raises "empty"
 
-  z-test([list: 1, 2, 3], 1.58, 2.58) is%(within(0.01)) -0.6358
+  z-test([list: 1, 2, 3], 1.58, 2.58) is-roughly ~-0.635816119
 
-  t-test([list: 1, 2, 3], 2.58) is%(within(0.01)) -1.0046
+  t-test([list: 1, 2, 3], 2.58) is-roughly ~-1.004589468
 
   t-test-paired([list: 1], [list: 2, 3]) raises "lists must have equal lengths"
   t-test-paired([list:], [list:]) raises "lists must have at least one element"
-  t-test-paired([list: 1, 2, 3], [list: 4, 6, 8]) is%(within(0.01)) -6.928
+  t-test-paired([list: 1, 2, 3], [list: 4, 6, 8]) is-roughly ~-6.928203230
 
   t-test-pooled([list:], [list: 1, 2, 3]) raises "lists must have at least one element"
-  t-test-pooled([list: 1, 2, 3], [list: 4, 5, 6]) is%(within(0.01)) -3.674
-  t-test-pooled([list: 1, 2, 3], [list: 4, 5, 6, 7]) is%(within(0.01)) -3.873
+  t-test-pooled([list: 1, 2, 3], [list: 4, 5, 6]) is%(within(0.01)) -3.674234614
+  t-test-pooled([list: 1, 2, 3], [list: 4, 5, 6, 7]) is-roughly ~-3.872983346
 
   t-test-independent([list:], [list: 1, 2, 3]) raises "lists must have at least one element"
-  t-test-independent([list: 1, 2, 3], [list: 4, 5, 6]) is%(within(0.01)) -3.674
-  t-test-independent([list: 1, 2, 3], [list: 4, 5, 6, 7]) is%(within(0.01)) -4.041
+  t-test-independent([list: 1, 2, 3], [list: 4, 5, 6]) is-roughly ~-3.674234614
+  t-test-independent([list: 1, 2, 3], [list: 4, 5, 6, 7]) is-roughly ~-4.041451884
 
 
   chi-square([list: 1, 2, 3, 4], [list: 1, 2, 3, 4]) is 0
-  chi-square([list: 1, 2, 3, 4], [list: 0.9, 1.8, 3.5, 4.7]) is%(within(0.01)) 0.209
+  chi-square([list: 1, 2, 3, 4], [list: 0.9, 1.8, 3.5, 4.7]) is-roughly ~0.2090172239
 end
 
 check "polymorphic modes":
@@ -136,6 +136,7 @@ check "multiple regression":
   y-s   = [list: 33, 42, 45, 51, 53, 61, 62]
   pf1   = multiple-regression(x-s-s, y-s)
   pf1([list: 8]) is-roughly 73.3214
+  pf1([list: 8, 9]) raises "received"
   #
   # check it matches linear-regression function on the same single variable
   x-s = [list: 4, 4.5, 5, 5.5, 6, 6.5, 7]