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Chapter 7

Multiple Correlation and Multiple Regression

There are many times in science when you want to predict a criterion, Y, but you

want to ﬁnd out if you can develop a better prediction model by using
several

predictors
in combination (e.g.
X
1
,
X
2
,
X
3
, etc.) instead of a single predictor,
X
.

The resulting statistical procedure is called “multiple correlation” because it uses

two or more predictors in combination to predict Y, instead of a single predictor, X.

Each predictor is “weighted” differently based on its separate correlation with Y

and its correlation with the other predictors. The job of multiple correlation is to

produce a regression equation that will weight each predictor differently and in such

a way that the combination of predictors does a better job of predicting Y than any

single predictor by itself. We will call the multiple correlation:
R
xy
.

You will recall (see Sect. 6.5.3) that the regression equation that predicts Y when

only one predictor, X, is used is:

Y

¼

a

þ

bX

(7.1)

7.1 Multiple Regression Equation

The multiple regression equation follows a similar format and is:

Y

a

b
1
X
1
þ

b
2
X
2
þ

b
3
X
3

¼

þ

etc

depending on the number of predictors used

(7.2)

þ

:

The “weight” given to each predictor in the equation is represented by the letter

“b” with a subscript to correspond to the same subscript on the predictors.

Important note:
In order to do multiple regression, you need to have installed the

“Data Analysis ToolPak” that was described in Chapter 6 (see Sect. 6.5.1). If you

did not install this, you need to do so now
.

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

DOI 10.1007/978-1-4614-6003-9_7,
#
Springer Science+Business Media New York 2013

143

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