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//! Regression analysis
use crate::stats::bivariate::Data;
use crate::stats::float::Float;
/// A straight line that passes through the origin `y = m * x`
#[derive(Clone, Copy)]
pub struct Slope<A>(pub A)
where
A: Float;
impl<A> Slope<A>
where
A: Float,
{
/// Fits the data to a straight line that passes through the origin using ordinary least
/// squares
///
/// - Time: `O(length)`
pub fn fit(data: &Data<'_, A, A>) -> Slope<A> {
let xs = data.0;
let ys = data.1;
let xy = crate::stats::dot(xs, ys);
let x2 = crate::stats::dot(xs, xs);
Slope(xy / x2)
}
/// Computes the goodness of fit (coefficient of determination) for this data set
///
/// - Time: `O(length)`
pub fn r_squared(&self, data: &Data<'_, A, A>) -> A {
let _0 = A::cast(0);
let _1 = A::cast(1);
let m = self.0;
let xs = data.0;
let ys = data.1;
let n = A::cast(xs.len());
let y_bar = crate::stats::sum(ys) / n;
let mut ss_res = _0;
let mut ss_tot = _0;
for (&x, &y) in data.iter() {
ss_res = ss_res + (y - m * x).powi(2);
ss_tot = ss_res + (y - y_bar).powi(2);
}
_1 - ss_res / ss_tot
}
}
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