LinearRegressor

regressors.LinearRegressor(self)

A class used to represent a Simple Linear Regressor.

\[ Y = \beta_0 + \beta_1 \cdot x + \epsilon \]

Attributes

Name	Type	Description
weights	`ndarray`	The weights of the linear regression model. Here, the weights are represented by the \(\beta\) vector which for univariate regression is a 1D vector of length two, \(\beta = [\beta_0, \beta_1]\), where \(\beta_0\) is the slope and \(\beta_1\) is the intercept.

Name	Description
fit	Trains the linear regression model using the given training data.
predict	Makes predictions for input data.

regressors.LinearRegressor.fit(X, y)

Trains the linear regression model using the given training data.

In other words, the fit method learns the weights, represented by the \(\beta\) vector. To learn the \(\beta\) vector, use:

\[ \hat{\beta} = \left( X^\top X \right)^{-1}X^\top y \]

Here, \(X\) is the so-called design matrix, which, to include a term for the intercept, has a column of ones appended to the input X matrix.

\[ X = \begin{bmatrix} 1 & x_{1} \\ 1 & x_{2} \\ \vdots & \vdots \\ 1 & x_{n} \end{bmatrix} \]

Name	Type	Description	Default
`X`	`ndarray`	The training data, which is a 2D array of shape `(n_samples, 1)` where each row is a sample and each column is a feature.	required
`y`	`ndarray`	The target values, which is a 1D array of shape `(n_samples, )`.	required

regressors.LinearRegressor.predict(X)

Makes predictions for input data.

\[ \hat{y} = X \hat{\beta} \]

Name	Type	Description	Default
`X`	`ndarray`	Input data, a 2D array of shape `(n_samples, 1)`, with which to make predictions.	required

Type	Description
`ndarray`	The predicted target values as a 1D array with the same length as `X`.