An R Introduction to Statistics

Multiple Linear Regression

  A multiple linear regression (MLR) model that describes a dependent variable y by independent variables x1, x2, ..., xp (p > 1) is expressed by the equation as follows, where the numbers α and βk (k = 1, 2, ..., p) are the parameters, and ϵ is the error term.

y = α+ ∑  β x  + ϵ
        k  k k

For example, in the built-in data set stackloss from observations of a chemical plant operation, if we assign stackloss as the dependent variable, and assign Air.Flow (cooling air flow), Water.Temp (inlet water temperature) and Acid.Conc. (acid concentration) as independent variables, the multiple linear regression model is:

Stack.Loss = α + β1 * Air.F low + β2 * W ater.T emp + β3 *Acid.Conc.+ ϵ

Further detail of the stackloss data set can be found in the R documentation.

> help(stackloss)