Projection matrix

For the linear transformation, see Projection (linear algebra).

In statistics, the projection matrix ,[1] sometimes also called the influence matrix[2] or hat matrix , maps the vector of response values (dependent variable values) to the vector of fitted values (or predicted values). It describes the influence each response value has on each fitted value.[3][4] The diagonal elements of the projection matrix are the leverages, which describe the influence each response value has on the fitted value for that same observation.

  1. ^ Basilevsky, Alexander (2005). Applied Matrix Algebra in the Statistical Sciences. Dover. pp. 160–176. ISBN 0-486-44538-0.
  2. ^ "Data Assimilation: Observation influence diagnostic of a data assimilation system" (PDF). Archived from the original (PDF) on 2014-09-03.
  3. ^ Hoaglin, David C.; Welsch, Roy E. (February 1978). "The Hat Matrix in Regression and ANOVA" (PDF). The American Statistician. 32 (1): 17–22. doi:10.2307/2683469. hdl:1721.1/1920. JSTOR 2683469.
  4. ^ David A. Freedman (2009). Statistical Models: Theory and Practice. Cambridge University Press.