Microsoft Office Tutorials and References

In Depth Information

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
ð Þ
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

ð
7
:
1
Þ

7.1 Multiple Regression Equation

The multiple regression equation follows a similar format and is:

Y
¼
a
þ
b
1
X
1
þ
b
2
X
2
þ
b
3
X
3

þ
etc
:
depending on the number of predictors used

ð
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
Chap. 6
.
(See
Sect. 6.5.1
). If you

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

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

DOI: 10.1007/978-1-4614-5779-4_7,

Springer Science+Business Media New York 2013

149

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