Makes sense out of regression analysis

books:

	• The Geometry of Multivariate Statistics Thomas D. Wickens Lawrence Erlbaum, 1994 - 176 pages average customer review:based on 2 reviews
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Makes sense out of regression analysis

Well, actually, this book is applicable to much more than regression analysis, e.g., ANOVA and "general linear statistical models". It also helps make sense of univariate statistics, not just multivariate. Regression analysis, though, is the main application of the methods in this book. It will not substitute for Neter, et al. or any of the numerous texts on techniques of regression analysis; what it does is provide a simple geometric model for understanding regression. A couple of teasers: why does SSTO = SSR + SSE work in terms of degrees of freedom as well as the actual sums of squares? Where does that term, "degrees of freedom," come from anyway? The DF is the dimension of a vector subspace, as Wickens explains. What does the correlation coefficient really mean? Dig into that old linear algebra text, and you'll notice that it has the mathematical form of the cosine of the angle between two vectors in n-space - no coincidence. This geometric viewpoint was the basis for much or R. A. Fisher's early work, and has been unfortunately obscured since then. If you have a modicum of familiarity with vector spaces, and the ability to visualize, this book is an epiphany!

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not as hard as it looks

The only book multivariate stats books Ive found that bases its approach on a geometrical interpretation of what is being done. It succeeds in imparting an intuitive picture of the ideas behind the math - very clearly written, and informative.

A traditional approach to developing multivariate statistical theory is algebraic. Sets of observations are represented by matrices, linear combinations are formed from these matrices by multiplying them by coefficient matrices, and useful statistics are found by imposing various criteria of optimization on these combinations. Matrix algebra is the vehicle for these calculations. A second approach is computational. Since many users find that they do not need to know the mathematical basis of the techniques as long as they have a way to transform data into results, the computation can be done by a package of computer programs that somebody else has written. An approach from this perspective emphasizes how the computer packages are used, and is usually coupled with rules that allow one to extract the most important numbers from the output and interpret them. Useful as both approaches are--particularly when combined--they can overlook an important aspect of multivariate analysis. To apply it correctly, one needsa way to conceptualize the multivariate relationships that exist among variables.

This book is designed to help the reader develop a way of thinking about multivariate statistics, as well as to understand in a broader and more intuitive sense what the procedures do and how their results are interpreted. Presenting important procedures of multivariate statistical theory geometrically, the author hopes that this emphasis on the geometry will give the reader a coherent picture into which all the multivariate techniques fit.

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