Add simple regression summaries and Student t random variable

[HubertRonald]

Summary

This PR prepares LuaSF for v0.8.0 by adding a Student's t random variable generator and formula-based simple linear regression summaries.

It builds on the modular source layout, bivariate statistics, shape statistics, and probability helpers introduced in previous releases.

What changed

Added Student's t random variable generator

Added:

stats.studentTVA(df)
stats.student_t(df)
stats.t_student(df)

The Student's t random variable is generated using the standard relationship:

T = Z / sqrt(V / df)

where Z is an approximately standard normal random variable and V is a chi-square random variable with df degrees of freedom.

Added simple regression module

Added:

src/luasf/regression.lua

The module exposes:

stats.simple_linear_regression(x, y)
stats.predict(model, x)
stats.fitted_values(model)
stats.residuals(model)

Regression summary output

simple_linear_regression(x, y) returns a formula-based regression summary including:

• Slope
• Intercept
• R
• R squared
• Adjusted R squared
• SSE
• SSR
• SST
• MSE
• RMSE
• Residual standard error
• Standard error for slope
• Standard error for intercept
• T statistic for slope
• T statistic for intercept
• Fitted values
• Residuals
• ANOVA-style summary without p-values

Added tests

Added:

spec/test_student_t.lua
spec/test_regression.lua

The tests cover:

• Student's t random variable aliases
• Degrees of freedom validation
• Perfect simple linear regression
• Regression with intercept
• Prediction helper
• Fitted values helper
• Residuals helper
• Regression summary fields
• Input validation

Added examples

Added:

examples/student_t_distribution.lua
examples/simple_linear_regression.lua

Added LuaRocks rockspec

Added:

rockspec/luasf-0.8.0-1.rockspec

Updated workflows

Updated GitHub Actions workflows to include:

lua spec/test_student_t.lua
lua spec/test_regression.lua
lua examples/student_t_distribution.lua
lua examples/simple_linear_regression.lua

The LuaRocks publishing workflow now defaults to:

rockspec/luasf-0.8.0-1.rockspec

Updated documentation

Updated:

README.md
docs/api.md
CHANGELOG.md
CONTRIBUTING.md

Compatibility notes

This PR does not remove or rename existing public functions.

Existing usage remains supported:

local stats = require("luasf")
local stats = require("LuaSF")
local stats = require("LuaStat")

Legacy LuaSF names remain available.

Testing

Tested locally with:

lua spec/test_stats.lua
lua spec/test_distributions.lua
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

Examples can be run with:

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/poisson_arrivals.lua
lua examples/binomial_coin_flips.lua
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

Release target

This PR prepares LuaSF for:

v0.8.0 - Simple Regression Summaries and Student's t Random Variable

Scope note

LuaSF now includes formula-based simple regression summaries, but it does not compute p-values, confidence intervals, critical values, multiple regression, non-linear regression, or machine learning workflows.

The goal remains to keep LuaSF lightweight, pure Lua, readable, and useful for statistics, probability, simulation, and teaching.