ahat.fit_linear_a_hat_model

fit_linear_a_hat_model(X, y, xlog=False, ylog=False)

Fits a simple linear regression model according to the standard a-hat vs a method.

Enforces a linear fit and a constant variance (homoskedasticity) assumption across all inputs. It allows for optional logarithmic transformations to help linearize the data.

Parameters

Name	Type	Description	Default
X	np.ndarray	1D array of input parameter values (e.g., flaw size, a).	required
y	np.ndarray	1D array of observed responses (e.g., signal amplitude, a-hat).	required
xlog	bool	If True, applies a natural logarithm transformation to X.	False
ylog	bool	If True, applies a natural logarithm transformation to y.	False

Returns

Name	Type	Description
	Tuple[LinearRegression, float]	Tuple[LinearRegression, float]: - model: The fitted sklearn LinearRegression object. - tau: The constant standard deviation of the residuals.

Examples

import numpy as np
X = np.linspace(1, 10, 50)
y = 2.5 * np.log(X) + np.random.normal(0, 0.5, 50)

# Fit the standard model, taking the log of X to achieve linearity
model, tau = fit_linear_a_hat_model(X, y, xlog=True, ylog=False)
print(f"Constant Standard Deviation: {tau:.4f}")