feat: documents linear models

src/linear/mod.rs

@@ -1,2 +1,23 @@
+//! # Linear Models
+//! Linear models describe a continuous response variable as a function of one or more predictor variables.
+//! The model describes the relationship between a dependent variable y (also called the response) as a function of one or more independent, or explanatory variables \\(X_i\\). The general equation for a linear model is:
+//! \\[y = \beta_0 + \sum_{i=1}^n \beta_iX_i + \epsilon\\]
+//!
+//! where \\(\beta_0 \\) is the intercept term (the expected value of Y when X = 0), \\(\epsilon \\) is an error term that is is independent of X and \\(\beta_i \\)
+//! is the average increase in y associated with a one-unit increase in \\(X_i\\)
+//!
+//! Model assumptions:
+//! * _Linearity_. The relationship between X and the mean of y is linear.
+//! * _Constant variance_. The variance of residual is the same for any value of X.
+//! * _Normality_. For any fixed value of X, Y is normally distributed.
+//! * _Independence_. Observations are independent of each other.
+//!
+//! ## References:
+//!
+//! * ["An Introduction to Statistical Learning", James G., Witten D., Hastie T., Tibshirani R., 3. Linear Regression](http://faculty.marshall.usc.edu/gareth-james/ISL/)
+//! * ["The Statistical Sleuth, A Course in Methods of Data Analysis", Ramsey F.L., Schafer D.W., Ch 7, 8, 3rd edition, 2013](http://www.statisticalsleuth.com/)
+//!
+//! <script type="text/javascript" src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.0/MathJax.js?config=TeX-AMS_CHTML"></script>
+
 pub mod linear_regression;
 pub mod logistic_regression;