4 Multiple Regression
The final section returns to \(\underline {Y}=XB+\underline {\varepsilon }\) with the columns of \(X\) now measured quantities rather than group indicators. The estimation theory is already done — Section 3.3 applies verbatim — so what is new here is everything that arises from the columns being observed rather than designed.
An experimenter chooses \(X\) and can make its columns orthogonal. A regression analyst takes the \(X\) that nature supplies, and its columns are generally correlated. Four consequences occupy this section: the coefficients change meaning depending on what else is in the model; near-dependence between columns makes them unstable; individual observations can dominate the fit; and there is no longer an obvious answer to which variables belong in the model at all.
4.2 Multiple Linear Regression Model With Two Independent (Regressor) Variables
4.3 General Multiple Line Regression
Introduction
4.4 Meaning of the Coefficients
4.5 Multicollinearity
4.6 Examination of Residuals(errors)
4.7 Practice Problems
4.8 Leverage, Outliers and Influential Observations
4.9 Variable Selection
4.10 Practice Problems
4.11 Hazards in the use of Regression
Course Outline
Prescribed Textbooks
Recommended Textbooks
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