Definition:Multiple Regression

Definition

Multiple regression is an extension of regression in which there are $p$ explanatory variables where $p > 1$:

$x_1, x_2, \ldots, x_p$

Linear

Let $X$ and $Y$ be a random variable.

Let $X_1, X_2, \ldots, X_p$ also be random variables for $p \in \N_{>1}$

Let the regression of $Y$ on $X_1, X_2, \ldots, X_n$ be expressible in the form:

$\expect {Y \mid x_1, x_2, \ldots, x_p} = \beta_0 + \beta_1 x_2 + \beta_2 x_2 + \ldots + \beta_n x_n$

Then $\expect {Y \mid x_1, x_2, \ldots, x_p}$ is known as multiple linear regression.

Also see

• Results about multiple regression can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): multiple regression
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): multiple regression