Partitioning variation

Learning objectives

  • How a model partitions variation
  • Definition of R squared and correlation
  • Geometry of data and models.  Every model coefficient corresponds to an explanatory model vector.

Before class

In class

  • Geometry of a data frame.   Way 1, case-by-case:  Plot each case as a point on a coordinate system with 1 axis for each variable.  Way 2, variable-by-variable: Plot each variable as a vector on a coordinate system with 1 axis for each case.
  • Counting model vectors.  A linear model determines a set of explanatory vectors.
  • What is Rsquared for a linear model?
  • Quiz 5 (on models and their coefficients.)

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