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Chapter 6

Correlation and Simple Linear Regression

There are many different types of ‘‘correlation coefﬁcients,’’ but the one we will

use in this topic is the Pearson product-moment correlation which we will call: r.

6.1 What is a ‘‘Correlation?’’

Basically, a correlation is a number between -1 and +1 that summarizes the

relationship between two variables, which we will call X and Y.

A correlation can be either positive or negative. A positive correlation means

that as X increases, Y increases. A negative correlation means that as X increases,

Y decreases. In statistics books, this part of the relationship is called the direction

of the relationship (i.e., it is either positive or negative).

The correlation also tells us the magnitude of the relationship between X and Y.

As the correlation approaches closer to +1, we say that the relationship is strong

and positive.

As the correlation approaches closer to -1, we say that the relationship is

strong and negative.

A zero correlation means that there is no relationship between X and Y. This

means that neither X nor Y can be used as a predictor of the other.

A good way to understand what a correlation means is to see a ‘‘picture’’ of the

scatterplot of points produced in a chart by the data points. Let’s suppose that you

want to know if variable X can be used to predict variable Y. We will place the

predictor variable X on the x-axis (the horizontal axis of a chart) and the criterion

variable Y on the y-axis (the vertical axis of a chart). Suppose, further, that you

have collected data given in the scatterplots below (see Fig.
6.1
through Fig.
6.6
).

Figure
6.1
shows the scatterplot for a perfect positive correlation of r = +1.0.

This means that you can perfectly predict each y-value from each x-value because

T. J. Quirk et al., Excel 2010 for Biological and Life Sciences Statistics,

DOI: 10.1007/978-1-4614-5779-4_6,

Springer Science+Business Media New York 2013

109

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