# Prediction and Estimation: The Role of Explanatory Variables

• Glen McPherson
Part of the Springer Texts in Statistics book series (STS)

## Abstract

In mathematics and mathematically related disciplines, scientists speak of functional relations between variables. The statement y = 3 + x for all positive values of x is an example of a functional relation between variables x and y. Through this relation it is possible to establish the exact value of y for any value of x. For example, if x takes the value 3 then y takes the value 6. In the physical sciences, functional relations may be referred to as Laws. Students of physics would recognize the relation between pressure (P) and volume (V) of a gas, P = k/V or PV = k as Boyle’s Law. This relation establishes that the product of the pressure and volume of an ideal gas is constant.

## Keywords

Explanatory Variable Simple Linear Regression Linear Regression Equation Regression Relation Variance Table

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