In Chapter
12, you learned how to use bivariate linear regression to build
simple linear models suitable for characterization of the relationship
between two variables (typically one dependent variable and one
independent variable). Clearly, many variables in the physical world can
have multiple IVs independently, accounting for some portion of variance
in the DV. Note the difference between “single linear regression” and
“multiple linear regression”—the former refers to a setting in which there
are multiple *responses* in a response vector
emphasizing that we are in the setting with a *single*
outcome but multiple predictors. This chapter discusses multiple linear
regression as an extension of simple linear regression. Assumptions
specific to multivariate regression, such as
*multicollinearity* among predictor variables, are
discussed and methods for model-building are presented.

The use of simple linear regression models and the bivariate correlation coefficient and its square (the coefficient of determination) are useful for illustrating simple examples; in reality, very few physical systems or fields of interest rely on a single independent and dependent variable pair. Consider models used to study climate change, such as General Circulation Models (GCMs) and even more sophisticated Atmosphere-Ocean General Circulation Models (AOGCMs). These models have been developed over the past 30 years to allow the increasingly accurate ...

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