Microsoft Office Tutorials and References

In Depth Information

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 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 and

þ

─

þ

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
).

Fig.
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 the

data points move “upward-and-to-the-right” along a perfectly-ﬁtting straight line

(see Fig.
6.1
)

¼þ

T.J. Quirk et al.,
Excel 2007 for Biological and Life Sciences Statistics
,

DOI 10.1007/978-1-4614-6003-9_6,
#
Springer Science+Business Media New York 2013

103

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