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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