# Category:Regression Models

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This category contains results about Regression Models.

Definitions specific to this category can be found in Definitions/Regression Models.

Let $S$ be a stochastic process based on an equispaced time series.

Let the values of $S$ at timestamps $t, t - 1, t - 2, \dotsc$ be $z_t, z_{t - 1}, z_{t - 2}, \dotsc$

Let $\tilde z_t, \tilde z_{t - 1}, \tilde z_{t - 2}, \dotsc$ be deviations from a constant mean level $\mu$:

- $\tilde z_t = z_t - \mu$

Let $M$ be a linear filter model defined as

- $\tilde z_t = \phi_1 \tilde x_1 + \phi_2 \tilde x_2 + \dotsb + \phi_p \tilde x_p + a$

which relates a dependent variable $z$ to a set of independent variables $x_1, x_2, \dotsc, x_p$ plus an error term $a$.

$M$ is known as a **regression model**.