By Phoebus J. Dhrymes (auth.)
This booklet has taken shape over a number of years because of a few classes taught on the collage of Pennsylvania and at Columbia collage and a chain of lectures i've got given on the foreign financial Fund. certainly, i started writing down my notes systematically in the course of the educational yr 1972-1973 whereas on the collage of California, la. the various personality of the viewers, in addition to my very own perception of what an introductory and infrequently terminal acquaintance with formal econometrics should surround, have made up our minds the fashion and content material of this quantity. the choice of subject matters and the extent of discourse supply enough sort in order that the publication can function the root for various kinds of classes. for instance, a comparatively hassle-free one-semester path could be according to Chapters one via 5, omitting the appendices to those chapters and some sections in a number of the chapters so indicated. this could acquaint the scholar with the elemental concept of the final linear version, a number of the prob lems frequently encountered in empirical examine, and a few proposed options. For the sort of path, I must also suggest a short day trip into bankruptcy seven (logit and professional bit research) in view of the expanding availability of information units for which this sort of research is more advantageous than that according to the final linear model.
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Extra resources for Introductory Econometrics
It was, also, variously interpreted as a (relative) measure ofthe reduction in the variability of the dependent variable, when account is taken of the explanatory variables, or as the square of the (sample) correlation coefficient between actual and predicted dependent variables (within the sample). In this section we shall formalize the use of R2 in goodness of fit considerations by showing that a simple transformation of R2 will yield a test statistic for testing the hypothesis that the coefficients of all the bona fide variables are (simultaneously) equal to zero.
1. ], be the ith row OfL I2 · We have: Xi - y'X2 is un correlated with X2. PROOF. ; is a k-element (column) vector all of whose elements are zero except 31 Appendix: A Geometric Interpretation of the GLM the ith, which is unity. The covariance matrix of the left member above is -I Y'] [:Ell :E21 [e' 0]I :E12] i :E22 -Y = [e: i :E l1 e' i - 2e:i:E 12 y + y':E 22 y e: i:E 12 - y':t22] :E22 :E 2I e. i - :E 22 y But and the conclusion follows immediately. d. 2. I. PROOF. We may write, for any (n - k)-element vector a, Var(x i - a'x2) = Var[(xi - Y'X2) + (y - a)'x2] = Var(x i - Y'X2) + Var[(y - a)'x2].
9. Show that the quantity (y - eji)'(y - eji) - (ta derived from Equation (26) is nonnegative. Under what conditions, if ever, will it be zero? Show also that its magnitude will depend on the units in which the variables are measured. 10. Show that R2 lies in the interval [0, 1]. 11. Let X k = (x. I, ... k) and suppose we regress y on X k , obtaining the coefficient of determination of mUltiple regression (unadjusted) Rf. " ... HI) and regress y on X HI ' obtaining Rf+l. Show that it is always true that Rf + 1 ~ Rf.
Introductory Econometrics by Phoebus J. Dhrymes (auth.)