Lecture: Regression: Predicting and Relating Quantitative Features (Advanced Data Analysis from an Elementary Point of View)

February 7, 2013

(This article was originally published at Three-Toed Sloth , and syndicated at StatsBlogs.)

Statistics is the branch of mathematical engineering which designs and analyzes 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.

Reading: Notes, chapter 1 (examples.dat for running example; ckm.csv data set for optional exercises)

Advanced Data Analysis from an Elementary Point of View

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