Models

Linear models can be built from a variety of types by using the ModelMatrix intermediate type. This allows us to get rid of some of the bloat from the previous example and create a fit on the iris data.

We can access the data from a fit via methods on the fit. For example below we use the parameters().estimate() methods to get the estimated parameters of the fit and parameters().confidence_interval() to get the confidence interval of each parameter.

use std::error::Error;  
  
use strafe::datasets::iris;  
use strafe::datasets::polars::prelude::*;  
use strafe::tests::two_way::LeastSquaresRegressionBuilder;  
use strafe::traits::{Model, ModelBuilder};  
use strafe::types::ModelMatrix;  
  
fn main() -> Result<(), Box<dyn Error>> {  
    let iris = iris()?;  
  
    let x = iris  
        .clone()  
        .lazy()  
        .filter(col("Species").eq(lit("setosa")))  
        .select(&[col("Sepal.Length")])  
        .collect()?;  
  
    let y = iris  
        .clone()  
        .lazy()  
        .filter(col("Species").eq(lit("setosa")))  
        .select(&[col("Sepal.Width")])  
        .collect()?;  
  
    let mut fit = LeastSquaresRegressionBuilder::new()  
        .with_x(&ModelMatrix::from(x))  
        .with_y(&ModelMatrix::from(y))  
        .build();  
  
    for p in fit.parameters()? {  
        println!("{} {:?}", p.estimate(), p.confidence_interval());  
    }
    
	Ok(())
}

-0.569432673039648 (-2.390925862499916, 1.2520605164206204)
0.7985283006471533 (0.43554707179202234, 1.1615095295022844)

Below is an example of fitting the model, printing the fit, and plotting some of the fit plots.

use std::error::Error;  
  
use strafe::datasets::iris;  
use strafe::datasets::polars::prelude::*;  
use strafe::plots::prelude::*;  
use strafe::tests::two_way::LeastSquaresRegressionBuilder;  
use strafe::traits::ModelBuilder;  
use strafe::types::ModelMatrix;  
  
fn main() -> Result<(), Box<dyn Error>> {  
    let iris = iris()?;  
  
    let x = iris  
        .clone()  
        .lazy()  
        .filter(col("Species").eq(lit("setosa")))  
        .select(&[col("Sepal.Length")])  
        .collect()?;  
  
    let y = iris  
        .clone()  
        .lazy()  
        .filter(col("Species").eq(lit("setosa")))  
        .select(&[col("Sepal.Width")])  
        .collect()?;  
  
    let mut fit = LeastSquaresRegressionBuilder::new()  
        .with_x(&ModelMatrix::from(x))  
        .with_y(&ModelMatrix::from(y))  
        .build();  
  
    println!("{fit}");  
  
    let root = SVGBackend::new("fit.svg", (1024, 768)).into_drawing_area();  
    fit.plot_fit(&root, &Default::default());  
  
    let root = SVGBackend::new("resid_lev.svg", (1024, 768)).into_drawing_area();  
    fit.plot_residual_leverage(&root, &Default::default());  
  
    let root = SVGBackend::new("qq.svg", (1024, 768)).into_drawing_area();  
    fit.plot_quantile_quantile(&root, &Default::default());  
  
    Ok(())  
}

Residuals:
┌─────────┬──────────────┬─────────┬──────────────┬─────────┐
│ Minimum │ 1st Quantile │ Median  │ 3rd Quantile │ Maximum │
╞═════════╪══════════════╪═════════╪══════════════╪═════════╡
│ -0.7239 │ -0.1827      │ -0.0030 │ 0.1573       │ 0.5170  │
└─────────┴──────────────┴─────────┴──────────────┴─────────┘

Coefficients:
┌────┬──────────┬─────────────────────────┬─────────────────────────┬─────────┬────────────┐
│    │ Estimate │ Confidence Interval (L) │ Confidence Interval (U) │ T-Value │ P-Value    │
╞════╪══════════╪═════════════════════════╪═════════════════════════╪═════════╪════════════╡
│ x0 │ -0.5694  │ -2.3909                 │ 1.2520                  │ -1.0914 │ 0.2805     │
│ x1 │ 0.7985   │ 0.4355                  │ 1.1615                  │ 7.6807  │ 6.7098e-10 │
└────┴──────────┴─────────────────────────┴─────────────────────────┴─────────┴────────────┘

Tests:
┌──────────────────────────────┬───────────┬────────────┬────────┐
│                              │ Statistic │ P-Value    │ Alpha  │
╞══════════════════════════════╪═══════════╪════════════╪════════╡
│ Multiple R-squared (Robust)  │ 0.9945    │ 0.0054     │ 0.1500 │
│ Significance of Regression   │ 58.993    │ 6.7098e-10 │ 0.05   │
│ Shapiro-Wilk Normal Residual │ 0.9868    │ 0.8459     │ 0.05   │
└──────────────────────────────┴───────────┴────────────┴────────┘