Statistics is the science which studies methods for learning from imperfect data. Regression is a statistical model of functional relationships between variables. Getting relationships right means being able to predict well. The least-squares optimal prediction is the expectation value; the conditional expectation function is the regression function. The regression function must be estimated from data; the bias-variance trade-off controls this estimation. Ordinary least squares revisited as a smoothing method. Other linear smoothers: nearest-neighbor averaging, kernel-weighted averaging.
Readings: Notes, chapter 1; Faraway, chapter 1, through page 17.
Posted by crshalizi at January 17, 2012 10:30 | permanent link