6 The \(k\)-Variable Linear Model
Economic relationships rarely involve a single explanatory variable. Savings depend on the age structure of the population and on income and its growth; demand depends on own price, the prices of substitutes and income; output depends on labour and capital. This section develops least squares for any number of regressors. With the matrix tools of Section 5 the algebra is no harder than for one regressor, and the matrix form reveals two things the scalar formulas hide: what a multiple regression coefficient means, given by the Frisch–Waugh–Lovell theorem, and the geometry of least squares as an orthogonal projection.
6.1 The model in matrix form
6.2 Least squares
6.3 The decomposition of the sum of squares and \(R^2\)
6.4 Partitioned regression: the Frisch–Waugh–Lovell theorem
6.5 Partial correlation
6.6 The geometry of least squares
6.7 Multiple regression in software
6.8 Practice Problems
6.2 Least squares
6.3 The decomposition of the sum of squares and \(R^2\)
6.4 Partitioned regression: the Frisch–Waugh–Lovell theorem
6.5 Partial correlation
6.6 The geometry of least squares
6.7 Multiple regression in software
6.8 Practice Problems
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