Simple Linear Regression

Simple linear regression analysis provides bivariate statistical tools essential

to the applied researcher in many instances. Regression is a methodology that

is grounded in the relationship between two quantitative variables (y, x) such that the value of y (dependent variable) can be predicted based on the value of x (independent variable). Determining the mathematical relationship between these two variables, such as exposure time and lethality or wash time and

log10 microbial reductions, is very common in applied research. From a

mathematical perspective, two types of relationships must be discussed: (1)

a functional relationship and (2) a statistical relationship. Recall that, math-

ematically, a functional relationship has the form

y ¼ f (x),

where y is the resultant value, on the function of x ( f(x)), and f(x) is any set of mathematical procedure or formula such as xþ 1, 2xþ 10, or 4x3 2x2þ 5x – 10, or log10 x2þ 10, and so on. Let us look at an example in which y¼ 3x. Hence,

y x 3 1

6 2

9 3

Graphing the function y on x, we have a linear graph (Figure 2.1). Given a particular value of x, y is said to be determined by x.