Microsoft Office Tutorials and References
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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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