week5 additional notes#
Principal component regression is especially used to overcome the problem with collinearity in linear regression by combining explanatory variables to a smaller set of uncorrelated variables.
Main idea of PCR#
The linear regression model:
\[
Z_i = m(X_i) + \epsilon_i = \beta^TX_i + \epsilon_i
\]
degenerates to:
\[
Z_i = \beta^T \Gamma Y + \epsilon_i = m_PC (Y)\Gamma + \epsilon_i
\]