From cebc33633f63351ef802ccc539df4ff56a3d1f61 Mon Sep 17 00:00:00 2001
From: HubertRonald <hubert.ronald@gmail.com>
Date: Tue, 9 Jun 2026 22:34:52 -0500
Subject: [PATCH 1/7] Add Student t distribution and regression helpers

---
 src/luasf.lua               |   5 +-
 src/luasf/distributions.lua |  15 ++-
 src/luasf/regression.lua    | 209 ++++++++++++++++++++++++++++++++++++
 3 files changed, 227 insertions(+), 2 deletions(-)
 create mode 100644 src/luasf/regression.lua

diff --git a/src/luasf.lua b/src/luasf.lua
index 9fc63b5..8dd3abc 100644
--- a/src/luasf.lua
+++ b/src/luasf.lua
@@ -1,7 +1,9 @@
 --[[
 LuaSF : Lua Statistics Functions
 
-A lightweight, pure-Lua library for basic statistics and random variables.
+LuaSF is a small, lightweight, pure-Lua library for descriptive statistics,
+shape statistics, bivariate statistics, probability helpers, sampling utilities,
+pseudo-random variable generation, and simple formula-based regression summaries.
 
 MIT License
 
@@ -39,5 +41,6 @@ merge(M, require(prefix .. "sampling"))
 merge(M, require(prefix .. "distributions"))
 merge(M, require(prefix .. "bivariate"))
 merge(M, require(prefix .. "probability"))
+merge(M, require(prefix .. "regression"))
 
 return M
diff --git a/src/luasf/distributions.lua b/src/luasf/distributions.lua
index 0282d81..84aee8d 100644
--- a/src/luasf/distributions.lua
+++ b/src/luasf/distributions.lua
@@ -189,6 +189,16 @@ local function chiSquareVA(n)
   return value
 end
 
+local function studentTVA(df)
+  df = df or 1
+  validation.assert_positive_integer(df, "df")
+
+  local z = normalVA(0, 1)
+  local v = chiSquareVA(df)
+
+  return z / sqrt(v / df)
+end
+
 local function gamVA(alpha, lambda)
   alpha = alpha or 1
   lambda = lambda or 1
@@ -254,6 +264,7 @@ M.binomialVA = binomialVA
 M.geometricVA = geometricVA
 M.poissonVA = poissonVA
 M.chiSquareVA = chiSquareVA
+M.studentTVA = studentTVA
 M.gamVA = gamVA
 M.lognoVA = lognoVA
 M.lognoRandVA = lognoVA
@@ -270,7 +281,9 @@ M.binomial = binomialVA
 M.geometric = geometricVA
 M.poisson = poissonVA
 M.chi_square = chiSquareVA
+M.student_t = studentTVA
+M.t_student = studentTVA
 M.gamma = gamVA
 M.lognormal = lognoVA
 
-return M
\ No newline at end of file
+return M
diff --git a/src/luasf/regression.lua b/src/luasf/regression.lua
new file mode 100644
index 0000000..9961205
--- /dev/null
+++ b/src/luasf/regression.lua
@@ -0,0 +1,209 @@
+local module_name = ... or "luasf.regression"
+local prefix = module_name:match("^src%.") and "src.luasf." or "luasf."
+
+local validation = require(prefix .. "validation")
+local descriptive = require(prefix .. "descriptive")
+local core = require(prefix .. "core")
+
+local sqrt = math.sqrt
+
+local M = {}
+
+local function clamp_near_zero(value)
+  if value < 0 and value > -1e-12 then
+    return 0
+  end
+
+  if value > 0 and value < 1e-12 then
+    return 0
+  end
+
+  return value
+end
+
+local function divide_or_nil(numerator, denominator)
+  if denominator == nil or denominator == 0 then
+    return nil
+  end
+
+  return numerator / denominator
+end
+
+local function validate_model(model)
+  assert(type(model) == "table", "model must be a table")
+  validation.assert_number(model.slope, "model.slope")
+  validation.assert_number(model.intercept, "model.intercept")
+end
+
+local function simple_linear_regression(x, y)
+  validation.assert_same_length_numeric_arrays(x, y, "x", "y")
+  assert(#x >= 3, "x and y must contain at least three values")
+
+  local n = #x
+  local mean_x = descriptive.mean(x)
+  local mean_y = descriptive.mean(y)
+  local sxx = 0
+  local syy = 0
+  local sxy = 0
+
+  for i = 1, n do
+    local dx = x[i] - mean_x
+    local dy = y[i] - mean_y
+
+    sxx = sxx + dx * dx
+    syy = syy + dy * dy
+    sxy = sxy + dx * dy
+  end
+
+  assert(sxx > 0, "x values must not be constant")
+
+  local slope = sxy / sxx
+  local intercept = mean_y - slope * mean_x
+  local fitted = {}
+  local residual_values = {}
+  local sse = 0
+  local ssr = 0
+
+  for i = 1, n do
+    local y_hat = intercept + slope * x[i]
+    local residual = y[i] - y_hat
+
+    fitted[i] = y_hat
+    residual_values[i] = residual
+
+    sse = sse + residual * residual
+    ssr = ssr + (y_hat - mean_y) * (y_hat - mean_y)
+  end
+
+  local sst = syy
+
+  sse = clamp_near_zero(sse)
+  ssr = clamp_near_zero(ssr)
+  sst = clamp_near_zero(sst)
+
+  local degrees_freedom = n - 2
+  local mse = sse / degrees_freedom
+  local rmse = sqrt(mse)
+  local residual_standard_error = rmse
+
+  local r
+  local r_squared
+  local adjusted_r_squared
+
+  if sst > 0 then
+    r = sxy / sqrt(sxx * syy)
+    r_squared = 1 - (sse / sst)
+    r_squared = clamp_near_zero(r_squared)
+    adjusted_r_squared = 1 - ((1 - r_squared) * (n - 1) / degrees_freedom)
+  else
+    r = nil
+    r_squared = nil
+    adjusted_r_squared = nil
+  end
+
+  local standard_error_slope = sqrt(mse / sxx)
+  local standard_error_intercept = sqrt(mse * ((1 / n) + ((mean_x * mean_x) / sxx)))
+
+  local t_slope = divide_or_nil(slope, standard_error_slope)
+  local t_intercept = divide_or_nil(intercept, standard_error_intercept)
+
+  local ms_regression = ssr
+  local ms_residual = mse
+  local f_statistic = divide_or_nil(ms_regression, ms_residual)
+
+  return {
+    n = n,
+    degrees_freedom = degrees_freedom,
+
+    slope = slope,
+    intercept = intercept,
+    coefficients = {
+      intercept = intercept,
+      slope = slope
+    },
+
+    mean_x = mean_x,
+    mean_y = mean_y,
+
+    r = r,
+    r_squared = r_squared,
+    adjusted_r_squared = adjusted_r_squared,
+
+    sxx = sxx,
+    syy = syy,
+    sxy = sxy,
+
+    sst = sst,
+    ssr = ssr,
+    sse = sse,
+    mse = mse,
+    rmse = rmse,
+    residual_standard_error = residual_standard_error,
+
+    standard_error_slope = standard_error_slope,
+    standard_error_intercept = standard_error_intercept,
+    t_slope = t_slope,
+    t_intercept = t_intercept,
+
+    fitted_values = fitted,
+    residuals = residual_values,
+
+    anova = {
+      regression = {
+        df = 1,
+        ss = ssr,
+        ms = ms_regression,
+        f = f_statistic
+      },
+      residual = {
+        df = degrees_freedom,
+        ss = sse,
+        ms = ms_residual
+      },
+      total = {
+        df = n - 1,
+        ss = sst
+      }
+    }
+  }
+end
+
+local function predict(model, x)
+  validate_model(model)
+
+  if type(x) == "table" then
+    local result = {}
+
+    for i = 1, #x do
+      validation.assert_number(x[i], "x value")
+      result[i] = model.intercept + model.slope * x[i]
+    end
+
+    return result
+  end
+
+  validation.assert_number(x, "x")
+
+  return model.intercept + model.slope * x
+end
+
+local function fitted_values(model)
+  assert(type(model) == "table", "model must be a table")
+  assert(type(model.fitted_values) == "table", "model.fitted_values must be a table")
+
+  return core.copy_array(model.fitted_values)
+end
+
+local function residuals(model)
+  assert(type(model) == "table", "model must be a table")
+  assert(type(model.residuals) == "table", "model.residuals must be a table")
+
+  return core.copy_array(model.residuals)
+end
+
+M.simple_linear_regression = simple_linear_regression
+M.predict = predict
+M.fitted_values = fitted_values
+M.residuals = residuals
+
+return M

From 94619d81935d77a57317614cd46b892055bccb33 Mon Sep 17 00:00:00 2001
From: HubertRonald <hubert.ronald@gmail.com>
Date: Tue, 9 Jun 2026 22:34:52 -0500
Subject: [PATCH 2/7] Add Student t and regression tests

---
 spec/test_regression.lua | 88 ++++++++++++++++++++++++++++++++++++++++
 spec/test_student_t.lua  | 46 +++++++++++++++++++++
 2 files changed, 134 insertions(+)
 create mode 100644 spec/test_regression.lua
 create mode 100644 spec/test_student_t.lua

diff --git a/spec/test_regression.lua b/spec/test_regression.lua
new file mode 100644
index 0000000..4634cb0
--- /dev/null
+++ b/spec/test_regression.lua
@@ -0,0 +1,88 @@
+local luaunit = require("luaunit")
+local stats = require("luasf")
+
+TestRegression = {}
+
+function TestRegression:test_simple_linear_regression_perfect_line()
+  local x = {1, 2, 3, 4, 5}
+  local y = {2, 4, 6, 8, 10}
+
+  local model = stats.simple_linear_regression(x, y)
+
+  luaunit.assertAlmostEquals(model.slope, 2, 0.000001)
+  luaunit.assertAlmostEquals(model.intercept, 0, 0.000001)
+  luaunit.assertAlmostEquals(model.r, 1, 0.000001)
+  luaunit.assertAlmostEquals(model.r_squared, 1, 0.000001)
+  luaunit.assertAlmostEquals(model.sse, 0, 0.000001)
+  luaunit.assertAlmostEquals(model.ssr, 40, 0.000001)
+  luaunit.assertAlmostEquals(model.sst, 40, 0.000001)
+  luaunit.assertEquals(model.n, 5)
+  luaunit.assertEquals(model.degrees_freedom, 3)
+end
+
+function TestRegression:test_simple_linear_regression_with_intercept()
+  local x = {1, 2, 3, 4, 5}
+  local y = {3, 5, 7, 9, 11}
+
+  local model = stats.simple_linear_regression(x, y)
+
+  luaunit.assertAlmostEquals(model.slope, 2, 0.000001)
+  luaunit.assertAlmostEquals(model.intercept, 1, 0.000001)
+  luaunit.assertAlmostEquals(stats.predict(model, 6), 13, 0.000001)
+end
+
+function TestRegression:test_predict_accepts_array()
+  local x = {1, 2, 3, 4, 5}
+  local y = {3, 5, 7, 9, 11}
+
+  local model = stats.simple_linear_regression(x, y)
+  local predictions = stats.predict(model, {6, 7})
+
+  luaunit.assertAlmostEquals(predictions[1], 13, 0.000001)
+  luaunit.assertAlmostEquals(predictions[2], 15, 0.000001)
+end
+
+function TestRegression:test_non_perfect_regression_summary()
+  local x = {1, 2, 3, 4, 5}
+  local y = {2, 5, 5, 9, 10}
+
+  local model = stats.simple_linear_regression(x, y)
+  local fitted = stats.fitted_values(model)
+  local residuals = stats.residuals(model)
+
+  luaunit.assertEquals(#fitted, 5)
+  luaunit.assertEquals(#residuals, 5)
+  luaunit.assertTrue(model.r_squared > 0)
+  luaunit.assertTrue(model.r_squared <= 1)
+  luaunit.assertTrue(model.mse >= 0)
+  luaunit.assertTrue(model.rmse >= 0)
+  luaunit.assertEquals(model.anova.regression.df, 1)
+  luaunit.assertEquals(model.anova.residual.df, 3)
+  luaunit.assertEquals(model.anova.total.df, 4)
+end
+
+function TestRegression:test_requires_same_length_arrays()
+  luaunit.assertError(function()
+    stats.simple_linear_regression({1, 2, 3}, {1, 2})
+  end)
+end
+
+function TestRegression:test_requires_at_least_three_values()
+  luaunit.assertError(function()
+    stats.simple_linear_regression({1, 2}, {2, 4})
+  end)
+end
+
+function TestRegression:test_rejects_constant_x_values()
+  luaunit.assertError(function()
+    stats.simple_linear_regression({1, 1, 1}, {2, 3, 4})
+  end)
+end
+
+function TestRegression:test_rejects_non_numeric_values()
+  luaunit.assertError(function()
+    stats.simple_linear_regression({1, 2, "x"}, {2, 4, 6})
+  end)
+end
+
+os.exit(luaunit.LuaUnit.run())
diff --git a/spec/test_student_t.lua b/spec/test_student_t.lua
new file mode 100644
index 0000000..c4e4d40
--- /dev/null
+++ b/spec/test_student_t.lua
@@ -0,0 +1,46 @@
+local luaunit = require("luaunit")
+local stats = require("luasf")
+
+TestStudentT = {}
+
+function TestStudentT:tearDown()
+  stats.reset_rng()
+end
+
+function TestStudentT:test_student_t_returns_number()
+  stats.seed(1234)
+
+  local value = stats.student_t(5)
+
+  luaunit.assertEquals(type(value), "number")
+end
+
+function TestStudentT:test_student_t_legacy_name_returns_number()
+  stats.seed(1234)
+
+  local value = stats.studentTVA(5)
+
+  luaunit.assertEquals(type(value), "number")
+end
+
+function TestStudentT:test_t_student_alias_returns_number()
+  stats.seed(1234)
+
+  local value = stats.t_student(5)
+
+  luaunit.assertEquals(type(value), "number")
+end
+
+function TestStudentT:test_student_t_rejects_zero_degrees_of_freedom()
+  luaunit.assertError(function()
+    stats.student_t(0)
+  end)
+end
+
+function TestStudentT:test_student_t_rejects_non_integer_degrees_of_freedom()
+  luaunit.assertError(function()
+    stats.student_t(2.5)
+  end)
+end
+
+os.exit(luaunit.LuaUnit.run())

From 058eba67c785bf2abc1181485d38013fb34c180f Mon Sep 17 00:00:00 2001
From: HubertRonald <hubert.ronald@gmail.com>
Date: Tue, 9 Jun 2026 22:34:52 -0500
Subject: [PATCH 3/7] Add Student t and simple regression examples

---
 examples/simple_linear_regression.lua | 27 +++++++++++++++++++++++++++
 examples/student_t_distribution.lua   | 15 +++++++++++++++
 2 files changed, 42 insertions(+)
 create mode 100644 examples/simple_linear_regression.lua
 create mode 100644 examples/student_t_distribution.lua

diff --git a/examples/simple_linear_regression.lua b/examples/simple_linear_regression.lua
new file mode 100644
index 0000000..2b7bad5
--- /dev/null
+++ b/examples/simple_linear_regression.lua
@@ -0,0 +1,27 @@
+local stats = require("luasf")
+
+local study_hours = {1, 2, 3, 4, 5, 6}
+local exam_scores = {52, 55, 61, 66, 72, 75}
+
+local model = stats.simple_linear_regression(study_hours, exam_scores)
+local prediction = stats.predict(model, 7)
+
+print("Simple linear regression example")
+print("Formula: y = intercept + slope * x")
+print("Intercept:", model.intercept)
+print("Slope:", model.slope)
+print("R:", model.r)
+print("R squared:", model.r_squared)
+print("Adjusted R squared:", model.adjusted_r_squared)
+print("SSE:", model.sse)
+print("SSR:", model.ssr)
+print("SST:", model.sst)
+print("MSE:", model.mse)
+print("RMSE:", model.rmse)
+print("Residual standard error:", model.residual_standard_error)
+print("Standard error slope:", model.standard_error_slope)
+print("Standard error intercept:", model.standard_error_intercept)
+print("T slope:", model.t_slope)
+print("T intercept:", model.t_intercept)
+print("ANOVA F statistic:", model.anova.regression.f)
+print("Prediction for 7 study hours:", prediction)
diff --git a/examples/student_t_distribution.lua b/examples/student_t_distribution.lua
new file mode 100644
index 0000000..d621e41
--- /dev/null
+++ b/examples/student_t_distribution.lua
@@ -0,0 +1,15 @@
+local stats = require("luasf")
+
+local degrees_of_freedom = 10
+local draws = {}
+
+for i = 1, 10 do
+  draws[i] = stats.student_t(degrees_of_freedom)
+end
+
+print("Student's t random values")
+print("Degrees of freedom:", degrees_of_freedom)
+
+for i = 1, #draws do
+  print(i, draws[i])
+end

From 759a7915f4bdd4aede9f89e9a273cfc28023376d Mon Sep 17 00:00:00 2001
From: HubertRonald <hubert.ronald@gmail.com>
Date: Tue, 9 Jun 2026 22:34:52 -0500
Subject: [PATCH 4/7] Add LuaRocks rockspec for v0.8.0

---
 rockspec/luasf-0.8.0-1.rockspec | 43 +++++++++++++++++++++++++++++++++
 1 file changed, 43 insertions(+)
 create mode 100644 rockspec/luasf-0.8.0-1.rockspec

diff --git a/rockspec/luasf-0.8.0-1.rockspec b/rockspec/luasf-0.8.0-1.rockspec
new file mode 100644
index 0000000..52a7602
--- /dev/null
+++ b/rockspec/luasf-0.8.0-1.rockspec
@@ -0,0 +1,43 @@
+package = "luasf"
+version = "0.8.0-1"
+
+source = {
+  url = "git://github.com/HubertRonald/LuaSF.git",
+  tag = "v0.8.0"
+}
+
+description = {
+  summary = "Lua Statistics Functions",
+  detailed = [[
+LuaSF is a lightweight, pure-Lua library for descriptive statistics,
+shape statistics, bivariate statistics, probability helpers, sampling
+utilities, simulation examples, random variable generation, and simple
+formula-based regression summaries.
+  ]],
+  homepage = "https://github.com/HubertRonald/LuaSF",
+  license = "MIT",
+  maintainer = "Hubert Ronald"
+}
+
+dependencies = {
+  "lua >= 5.1"
+}
+
+build = {
+  type = "builtin",
+  modules = {
+    luasf = "src/luasf.lua",
+    ["luasf.core"] = "src/luasf/core.lua",
+    ["luasf.validation"] = "src/luasf/validation.lua",
+    ["luasf.rng"] = "src/luasf/rng.lua",
+    ["luasf.descriptive"] = "src/luasf/descriptive.lua",
+    ["luasf.shape"] = "src/luasf/shape.lua",
+    ["luasf.sampling"] = "src/luasf/sampling.lua",
+    ["luasf.distributions"] = "src/luasf/distributions.lua",
+    ["luasf.bivariate"] = "src/luasf/bivariate.lua",
+    ["luasf.probability"] = "src/luasf/probability.lua",
+    ["luasf.regression"] = "src/luasf/regression.lua",
+    LuaSF = "LuaSF.lua",
+    LuaStat = "LuaStat.lua"
+  }
+}

From 0a21b48ac26f422eea37feeac23b472736d69e78 Mon Sep 17 00:00:00 2001
From: HubertRonald <hubert.ronald@gmail.com>
Date: Tue, 9 Jun 2026 22:34:52 -0500
Subject: [PATCH 5/7] Add regression release checks to workflows

---
 .github/workflows/ci.yml               | 4 ++++
 .github/workflows/publish-luarocks.yml | 7 +++++--
 2 files changed, 9 insertions(+), 2 deletions(-)

diff --git a/.github/workflows/ci.yml b/.github/workflows/ci.yml
index 930d22e..73d2b4d 100644
--- a/.github/workflows/ci.yml
+++ b/.github/workflows/ci.yml
@@ -60,6 +60,8 @@ jobs:
           lua spec/test_bivariate.lua
           lua spec/test_shape.lua
           lua spec/test_probability.lua
+          lua spec/test_student_t.lua
+          lua spec/test_regression.lua
 
       - name: Run examples
         run: |
@@ -74,3 +76,5 @@ jobs:
           lua examples/covariance_correlation.lua
           lua examples/skewness_kurtosis.lua
           lua examples/probability_helpers.lua
+          lua examples/student_t_distribution.lua
+          lua examples/simple_linear_regression.lua
diff --git a/.github/workflows/publish-luarocks.yml b/.github/workflows/publish-luarocks.yml
index 8c03841..5e342fd 100644
--- a/.github/workflows/publish-luarocks.yml
+++ b/.github/workflows/publish-luarocks.yml
@@ -6,7 +6,7 @@ on:
       rockspec:
         description: "Rockspec file to validate or publish"
         required: true
-        default: "rockspec/luasf-0.7.0-1.rockspec"
+        default: "rockspec/luasf-0.8.0-1.rockspec"
         type: string
       publish:
         description: "Publish to LuaRocks after validation"
@@ -52,7 +52,10 @@ jobs:
 
       - name: Test probability helpers entry point
         run: lua -e 'local stats = require("luasf"); print(stats.factorial(5)); print(stats.combinations(5,2)); print(stats.permutations_with_repetition(10,4))'
-
+      
+      - name: Test LuaRocks package entry point
+        run: lua -e 'local stats = require("luasf"); print(stats.simple_linear_regression({1,2,3}, {2,4,6}).slope)'
+      
       - name: Test LuaSF compatibility entry point
         run: lua -e 'local stats = require("LuaSF"); print(stats.sumF({1,2,3}))'
 

From 61d2abc0809a9cff5cf69179a588b404e9112ddc Mon Sep 17 00:00:00 2001
From: HubertRonald <hubert.ronald@gmail.com>
Date: Tue, 9 Jun 2026 22:34:52 -0500
Subject: [PATCH 6/7] Document simple regression and Student t helpers

---
 CHANGELOG.md    |  39 ++++++++++++++--
 CONTRIBUTING.md |  30 ++++++++++---
 README.md       |  85 ++++++++++++++++++++++++++++-------
 docs/api.md     | 117 +++++++++++++++++++++++++++++++++++++++++++++++-
 4 files changed, 244 insertions(+), 27 deletions(-)

diff --git a/CHANGELOG.md b/CHANGELOG.md
index 0a1a800..2e3116f 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -10,13 +10,46 @@ This project follows a lightweight changelog format inspired by [Keep a Changelo
 
 ### Planned
 
+* Add more distribution and simulation-oriented examples.
 * Explore a lightweight cross-reference with LuaHMF as a related pure-Lua math helper project.
-* Add more distribution and simulation examples.
-* Evaluate optional formula-based simple regression summaries while keeping ML workflows outside the current scope.
+* Explore carefully scoped confidence interval or critical value helpers.
 
 ---
 
-## [0.7.0] - 2026-06-07
+## [0.8.0] - 2026-06-09
+
+### Added
+
+* Added Student's t random variable generator `studentTVA(df)`.
+* Added modern aliases `student_t(df)` and `t_student(df)`.
+* Added `src/luasf/regression.lua` for formula-based simple linear regression summaries.
+* Added `simple_linear_regression(x, y)`.
+* Added `predict(model, x)`.
+* Added `fitted_values(model)`.
+* Added `residuals(model)`.
+* Added regression summary fields for coefficients, R, R², adjusted R², SSE, SSR, SST, MSE, RMSE, residual standard error, standard errors, and t statistics.
+* Added ANOVA-style regression summary without p-values.
+* Added `spec/test_student_t.lua`.
+* Added `spec/test_regression.lua`.
+* Added `examples/student_t_distribution.lua`.
+* Added `examples/simple_linear_regression.lua`.
+* Added `rockspec/luasf-0.8.0-1.rockspec`.
+
+### Changed
+
+* Updated the public facade to expose regression helpers.
+* Updated GitHub Actions workflows to run Student's t and regression tests/examples.
+* Updated LuaRocks workflow default rockspec path to `rockspec/luasf-0.8.0-1.rockspec`.
+* Updated README, API documentation, and contributing notes.
+
+### Scope
+
+* LuaSF now includes formula-based simple regression summaries, but it does not compute p-values or confidence intervals.
+* Multiple regression, non-linear regression, optimization-based modeling, and machine learning workflows remain outside the current scope.
+
+---
+
+## [0.7.0] - 2026-06-09
 
 ### Added
 
diff --git a/CONTRIBUTING.md b/CONTRIBUTING.md
index 04bf184..8888fe3 100644
--- a/CONTRIBUTING.md
+++ b/CONTRIBUTING.md
@@ -17,6 +17,7 @@ LuaSF aims to provide:
 * Probability and combinatorics helpers
 * Pseudo-random variable generation
 * Sampling utilities
+* Formula-based simple regression summaries
 * A small and readable Lua codebase
 * Compatibility with the existing public API
 * Useful examples for simulations, teaching, small scripts, and game/mod scripting
@@ -36,17 +37,20 @@ Good fits for LuaSF:
 * Random variable generation
 * Sampling and simulation utilities
 * Formula-based statistical summaries
+* Small examples and tests
 
 Currently out of scope:
 
-* Machine learning pipelines
+* Large machine learning workflows
 * Optimization-based model training
-* Non-linear regression fitting
-* Deep learning
+* Non-linear regression engines
+* Multiple regression requiring a full matrix algebra subsystem
 * Native dependencies
-* Large framework-style APIs
+* Big integer dependencies
+* Full statistical inference engines with p-value/CDF approximations unless carefully scoped and tested
+
+For simple regression, LuaSF may report coefficients, R and R², sums of squares, standard errors, t statistics, and ANOVA-style summaries. Full p-values and confidence intervals are intentionally outside the current scope.
 
-Formula-based simple regression summaries may be considered in the future, but ML-style model training is intentionally outside the current scope.
 
 ---
 
@@ -74,6 +78,7 @@ binomialVA
 geometricVA
 poissonVA
 chiSquareVA
+studentTVA
 gamVA
 lognoVA
 lognoRandVA
@@ -103,6 +108,7 @@ src/
     distributions.lua
     bivariate.lua
     probability.lua
+    regression.lua
     shape.lua
     validation.lua
     rng.lua
@@ -116,7 +122,8 @@ Recommended module ownership:
 * `bivariate.lua`: two-variable statistics such as covariance and correlation
 * `sampling.lua`: sampling helpers
 * `distributions.lua`: random variable generators
-* `probability.lua`: future probability/combinatorics helpers
+* `probability.lua`: probability/combinatorics helpers
+* `regression.lua`: simple regression
 * `validation.lua`: reusable input validation helpers
 * `shape.lua`: skewness and kurtosis helpers
 * `rng.lua`: random generator and seed helpers
@@ -155,6 +162,8 @@ lua spec/test_sampling.lua
 lua spec/test_bivariate.lua
 lua spec/test_shape.lua
 lua spec/test_probability.lua
+lua spec/test_student_t.lua
+lua spec/test_regression.lua
 ```
 
 Run examples:
@@ -171,6 +180,8 @@ lua examples/bootstrap_mean.lua
 lua examples/covariance_correlation.lua
 lua examples/skewness_kurtosis.lua
 lua examples/probability_helpers.lua
+lua examples/student_t_distribution.lua
+lua examples/simple_linear_regression.lua
 ```
 
 ---
@@ -284,6 +295,7 @@ Before opening a pull request, please check:
 * New modules are included in the rockspec draft when needed.
 * Code remains readable and dependency-light.
 * LuaRocks rockspec files are updated when preparing a package release.
+* Rockspec modules are updated when new source files are added.
 * CI workflows are updated when new tests or examples are added.
 
 
@@ -299,6 +311,7 @@ Prefer:
 * Minimal dependencies
 * Compatibility with Lua 5.1+
 * Explicit validation for public helpers
+* Small, focused modules
 * Formula-based helpers when appropriate
 
 Avoid:
@@ -308,12 +321,15 @@ Avoid:
 * Adding native dependencies
 * Overcomplicating the API
 * Turning LuaSF into a machine learning framework
+* Hidden behavior that makes examples harder to understand
 
 ---
 
 ## Future scope
 
-Simple formula-based regression summaries may be considered later, but optimization-based models and ML workflows are outside the current scope.
+* Explore carefully scoped confidence interval or critical value helpers.
+* Explore a lightweight cross-reference with LuaHMF as a related pure-Lua math helper project.
+* Add more distribution and simulation-oriented examples.
 
 ---
 
diff --git a/README.md b/README.md
index 583db29..addce95 100644
--- a/README.md
+++ b/README.md
@@ -31,9 +31,9 @@
 
 **LuaSF** stands for **Lua Statistics Functions**.
 
-LuaSF is a small, lightweight, pure-Lua library for descriptive statistics, shape statistics, bivariate statistics, probability helpers, sampling utilities, and pseudo-random variable generation.
+LuaSF is a small, lightweight, pure-Lua library for descriptive statistics, shape statistics, bivariate statistics, probability helpers, sampling utilities, pseudo-random variable generation, and simple formula-based regression summaries.
 
-The project started around 2014 and was later published under the MIT License. It has now been revived with compatibility improvements, tests, examples, documentation, a cleaner modular source structure, additional statistics helpers, sampling utilities, probability helpers, and LuaRocks packaging while preserving the existing public API.
+The project started around 2014 and was later published under the MIT License. It has now been revived with compatibility improvements, tests, examples, documentation, a cleaner modular source structure, additional statistics helpers, sampling utilities, probability helpers, LuaRocks packaging, and a compatibility-safe public API.
 
 ---
 
@@ -46,13 +46,16 @@ The project started around 2014 and was later published under the MIT License. I
 * Modular internal source layout
 * Basic descriptive statistics
 * Summary statistics helpers
+* Shape statistics helpers
 * Bivariate statistics helpers
 * Probability and combinatorics helpers
 * Sampling utilities
 * Discrete and continuous pseudo-random variables
+* Simple formula-based regression summaries
 * Compatible with the existing public LuaSF API
 * Useful for simulations, teaching, small scripts, game/mod scripting, and lightweight statistical utilities
 
+
 ---
 
 ## Installation
@@ -220,12 +223,24 @@ print(stats.stvF(values)) -- sample standard deviation
 | `geometricVA(p)`           | `geometric(p)`               | Geometric random variable        |
 | `poissonVA(lambda)`        | `poisson(lambda)`            | Poisson random variable          |
 | `chiSquareVA(n)`           | `chi_square(n)`              | Chi-square random variable       |
+| `studentTVA(df)`           | `student_t(df)`              | Student's t random variable      |
 | `gamVA(alpha, lambda)`     | `gamma(alpha, lambda)`       | Gamma random variable            |
 | `lognoVA(m, s)`            | `lognormal(m, s)`            | Log-normal random variable       |
 | `lognoRandVA(m, s)`        | `lognormal(m, s)`            | Log-normal random variable       |
 
 > `nomalVA` and `lognoRandVA` are preserved as compatibility aliases.
 
+### Simple regression summaries
+
+| Function                         | Description                                      |
+| -------------------------------- | ------------------------------------------------ |
+| `simple_linear_regression(x, y)` | Formula-based simple linear regression summary   |
+| `predict(model, x)`              | Predicts one value or a list of values           |
+| `fitted_values(model)`           | Returns fitted values from a regression model    |
+| `residuals(model)`               | Returns residuals from a regression model        |
+
+LuaSF reports coefficients, R and R², sums of squares, mean squared error, residual standard error, standard errors, t statistics, and an ANOVA-style summary for simple regression. It does not compute p-values or confidence intervals.
+
 ---
 
 ## Examples
@@ -337,6 +352,30 @@ print(stats.choice({"first", "second", "third"})) -- first
 stats.reset_rng()
 ```
 
+### Student's t random variable
+
+```lua
+local stats = require("luasf")
+
+print(stats.student_t(10))
+```
+
+### Simple linear regression
+
+```lua
+local stats = require("luasf")
+
+local x = {1, 2, 3, 4, 5}
+local y = {3, 5, 7, 9, 11}
+
+local model = stats.simple_linear_regression(x, y)
+
+print(model.intercept) -- 1
+print(model.slope)     -- 2
+print(model.r_squared) -- 1
+print(stats.predict(model, 6)) -- 13
+```
+
 ---
 
 ## Project structure
@@ -353,6 +392,7 @@ LuaSF/
       distributions.lua
       bivariate.lua
       probability.lua
+      regression.lua
       validation.lua
       rng.lua
   spec/
@@ -362,6 +402,8 @@ LuaSF/
     test_bivariate.lua
     test_shape.lua
     test_probability.lua
+    test_student_t.lua
+    test_regression.lua
   examples/
     dice_simulation.lua
     normal_quality_control.lua
@@ -374,6 +416,8 @@ LuaSF/
     covariance_correlation.lua
     skewness_kurtosis.lua
     probability_helpers.lua
+    student_t_distribution.lua
+    simple_linear_regression.lua
   docs/
     api.md
   .github/
@@ -387,6 +431,7 @@ LuaSF/
     luasf-0.5.0-1.rockspec
     luasf-0.6.0-1.rockspec
     luasf-0.7.0-1.rockspec
+    luasf-0.8.0-1.rockspec
   LuaSF.lua
   LuaStat.lua
   README.md
@@ -409,11 +454,14 @@ eval "$(luarocks path --local)"
 Run tests:
 
 ```bash
-lua spec/test_stats.lua
-lua spec/test_distributions.lua
-lua spec/test_sampling.lua
 lua spec/test_bivariate.lua
+lua spec/test_distributions.lua
 lua spec/test_probability.lua
+lua spec/test_regression.lua
+lua spec/test_sampling.lua
+lua spec/test_shape.lua
+lua spec/test_stats.lua
+lua spec/test_student_t.lua
 ```
 
 ---
@@ -421,16 +469,19 @@ lua spec/test_probability.lua
 ## Running examples
 
 ```bash
+lua examples/binomial_coin_flips.lua
+lua examples/bootstrap_mean.lua
+lua examples/covariance_correlation.lua
 lua examples/dice_simulation.lua
-lua examples/normal_quality_control.lua
 lua examples/gamma_distribution.lua
-lua examples/weighted_loot_drop.lua
 lua examples/monte_carlo_pi.lua
+lua examples/normal_quality_control.lua
 lua examples/poisson_arrivals.lua
-lua examples/binomial_coin_flips.lua
-lua examples/bootstrap_mean.lua
-lua examples/covariance_correlation.lua
 lua examples/probability_helpers.lua
+lua examples/simple_linear_regression.lua
+lua examples/skewness_kurtosis.lua
+lua examples/student_t_distribution.lua
+lua examples/weighted_loot_drop.lua
 ```
 
 ---
@@ -450,24 +501,26 @@ lua examples/probability_helpers.lua
 * Summary statistics helpers
 * Shape statistics helpers
 * Bivariate statistics helpers
-* Probability helpers
+* Probability and combinatorics helpers
 * Sampling utilities
 * Deterministic simulation support
+* Student's t random variable generator
+* Formula-based simple linear regression summaries
 * LuaRocks publishing
 
-### Planned
+### Possible future work
 
-* Lightweight cross-reference with LuaHMF
 * More distribution and simulation examples
-* Optional simple formula-based regression summaries, without turning LuaSF into a machine learning framework
+* Lightweight cross-reference with LuaHMF
+* Carefully scoped confidence interval or critical value helpers
 
 ---
 
 ## Scope
 
-LuaSF is focused on lightweight statistics, probability, random variables, and simulation helpers.
+LuaSF is focused on lightweight statistics, probability, random variables, regression summaries, and simulation helpers.
 
-Optimization-based modeling, machine learning workflows, model training pipelines, and non-linear regression are intentionally outside the current scope of LuaSF.
+Optimization-based modeling, machine learning workflows, model training pipelines, non-linear regression, and full statistical inference engines are intentionally outside the current scope of LuaSF.
 
 ---
 
diff --git a/docs/api.md b/docs/api.md
index fd9561c..712984b 100644
--- a/docs/api.md
+++ b/docs/api.md
@@ -2,7 +2,7 @@
 
 LuaSF stands for **Lua Statistics Functions**.
 
-This document describes the public LuaSF API after the compatibility revival, Phase 3 statistics/sampling additions, and LuaRocks publishing.
+This document describes the public LuaSF API after the compatibility revival, modularization, statistics/sampling additions, probability helpers, and simple regression summaries.
 
 LuaSF keeps the legacy public API available while adding clearer modern aliases.
 
@@ -56,6 +56,7 @@ src/
     distributions.lua
     bivariate.lua
     probability.lua
+    regression.lua
     validation.lua
     rng.lua
 ```
@@ -715,6 +716,7 @@ LuaSF provides functions for discrete and continuous pseudo-random variables.
 | `geometricVA(p)` | `geometric(p)` | Geometric random variable |
 | `poissonVA(lambda)` | `poisson(lambda)` | Poisson random variable |
 | `chiSquareVA(n)` | `chi_square(n)` | Chi-square random variable |
+| `studentTVA(df)` | `student_t(df)` or `t_student(df)` | Student's t-distributed random variable |
 | `gamVA(alpha, lambda)` | `gamma(alpha, lambda)` | Gamma random variable |
 | `lognoVA(m, s)` | `lognormal(m, s)` | Log-normal random variable |
 | `lognoRandVA(m, s)` | `lognormal(m, s)` | Log-normal random variable |
@@ -964,6 +966,27 @@ stats.chi_square(n)
 
 ---
 
+### `studentTVA(df)`
+
+Returns a Student's t-distributed random value with `df` degrees of freedom.
+
+LuaSF generates it from a standard normal random variable and an independent chi-square random variable:
+
+```text
+T = Z / sqrt(V / df)
+```
+
+where `Z` is approximately standard normal and `V` is chi-square with `df` degrees of freedom.
+
+Modern aliases:
+
+```lua
+stats.student_t(df)
+stats.t_student(df)
+```
+
+---
+
 ### `gamVA(alpha, lambda)`
 
 Returns a gamma-distributed random value.
@@ -1011,6 +1034,95 @@ stats.lognormal(m, s)
 
 ---
 
+## Simple regression summaries
+
+LuaSF provides formula-based simple linear regression summaries.
+
+These helpers are intended for lightweight statistics, teaching, small scripts, and simulation-style analysis. They are not a machine learning framework and do not perform iterative optimization.
+
+### `simple_linear_regression(x, y)`
+
+Returns a table with a formula-based simple linear regression summary.
+
+```lua
+local stats = require("luasf")
+
+local x = {1, 2, 3, 4, 5}
+local y = {3, 5, 7, 9, 11}
+
+local model = stats.simple_linear_regression(x, y)
+
+print(model.intercept) -- 1
+print(model.slope)     -- 2
+print(model.r_squared) -- 1
+```
+
+The returned table includes:
+
+```lua
+{
+  n = number,
+  degrees_freedom = number,
+
+  slope = number,
+  intercept = number,
+  coefficients = {
+    intercept = number,
+    slope = number
+  },
+
+  r = number or nil,
+  r_squared = number or nil,
+  adjusted_r_squared = number or nil,
+
+  sst = number,
+  ssr = number,
+  sse = number,
+  mse = number,
+  rmse = number,
+  residual_standard_error = number,
+
+  standard_error_slope = number,
+  standard_error_intercept = number,
+  t_slope = number or nil,
+  t_intercept = number or nil,
+
+  fitted_values = table,
+  residuals = table,
+
+  anova = {
+    regression = { df = 1, ss = number, ms = number, f = number or nil },
+    residual = { df = number, ss = number, ms = number },
+    total = { df = number, ss = number }
+  }
+}
+```
+
+### `predict(model, x)`
+
+Predicts one value or a list of values using a regression model.
+
+```lua
+local prediction = stats.predict(model, 6)
+local predictions = stats.predict(model, {6, 7, 8})
+```
+
+### `fitted_values(model)`
+
+Returns a copy of the model fitted values.
+
+### `residuals(model)`
+
+Returns a copy of the model residuals.
+
+### Scope note
+
+LuaSF reports simple regression coefficients, R and R², sums of squares, MSE, RMSE, residual standard error, standard errors, t statistics, and an ANOVA-style summary.
+
+LuaSF does not compute regression p-values, confidence intervals, critical values, multiple regression, non-linear regression, optimization-based modeling, or machine learning training pipelines.
+
+---
+
 ## Utility functions
 
 ### `rand()`
@@ -1070,6 +1182,7 @@ stats.binomialVA
 stats.geometricVA
 stats.poissonVA
 stats.chiSquareVA
+stats.studentTVA
 stats.gamVA
 stats.lognoVA
 stats.lognoRandVA
@@ -1133,6 +1246,8 @@ stats.binomial
 stats.geometric
 stats.poisson
 stats.chi_square
+stats.student_t
+stats.t_student
 stats.gamma
 stats.lognormal
 ```

From 3b55c2ec8389628ab4024e4443cf82687bbede3b Mon Sep 17 00:00:00 2001
From: HubertRonald <hubert.ronald@gmail.com>
Date: Tue, 9 Jun 2026 22:35:42 -0500
Subject: [PATCH 7/7] Add Student t and regression tests

---
 spec/test_stats.lua      | 2 +-
 src/luasf/validation.lua | 3 ++-
 2 files changed, 3 insertions(+), 2 deletions(-)

diff --git a/spec/test_stats.lua b/spec/test_stats.lua
index d8c016f..fd95b6c 100644
--- a/spec/test_stats.lua
+++ b/spec/test_stats.lua
@@ -43,7 +43,7 @@ end
 function TestStats:test_module_entry_points()
   local luasf_root = require("LuaSF")
   local luastat_root = require("LuaStat")
-  local luasf_src = require("src.luasf")
+  local luasf_src = require("luasf")
 
   luaunit.assertEquals(type(luasf_root), "table")
   luaunit.assertEquals(type(luastat_root), "table")
diff --git a/src/luasf/validation.lua b/src/luasf/validation.lua
index e2af90e..f807688 100644
--- a/src/luasf/validation.lua
+++ b/src/luasf/validation.lua
@@ -67,6 +67,7 @@ end
 function M.assert_positive_integer(value, name)
   M.assert_integer(value, name)
   assert(value >= 1, name .. " must be greater than or equal to 1")
+  assert(value == floor(value), name .. " must be an integer")
 end
 
-return M
\ No newline at end of file
+return M