test-statistics.arr: brownplt#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

@@ -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()

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
-
-
-