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Unformatted text preview: A Quick Introduction to Factor Analysis From Data Analysis: A Statistical Primer for Psychology Students by Edward L. Wike: ... [T]here are elaborate extensions of r to multivariate data ... another case is k variables (factor analysis) . Fortunately, for both the student and author, none of these extensions will be considered here. From Linear Algebra and its Applications by Gilbert Strang: ... [T]he technique is so much needed that, even starting as an unwelcome black sheep of multi variate analysis, it has spread from psychology into biology and economics and the social sciences. From linear algebra: A “matrix” is a rectangular (in this discussion, usually square) array of numbers; e.g., 3 5 7 1 2 3  1 3 3 . 5 2 2 1 We can add two matrices of the same dimensions, by adding corresponding entries; and we can multiply a matrix by a number, by multiplying all the entries in the matrix by that number: 1 2 1 + 2 1 2 3 = 1 3 2 2 3 1 2 1 = 3 6 3 A square matrix is a “diagonal matrix” if the only nonzero entries (if any) are on the “main diagonal” (upper left to lower right): 5 1 0 The “transpose” of a matrix is the (new) matrix obtained turning the rows into columns (and vice versa): 3 5 7 1 2 3 T = 3 1 5 2 7 3  1 3 3 . 5 2 2 1 T =  1 3 3 . 5 2 2 1 If a (square) matrix A has the property that A T = A (as this one does), then A is called “symmet ric”. This just amounts to saying that, for each i and j , the entry in row i and column j is equal to the entry in row j and column i , i.e., the matrix is symmetric about its main diagonal. Relevant example: Suppose we have several variables, the scores on 4 exams, one in math, one in physics, one in English, and one in history — one list of 4 scores for each student in a class. Taking the exams 1 in pairs, we can find a correlation coefficient for each pair. We then form a matrix with the rows and columns labelled M(ath), P(hysics), E(nglish) and H(istory); the entry in the X row and Y column is the correlation coefficient between X and Y. The result is a symmetric matrix (since the correlation between X and Y is the correlation between Y and X) with 1’s on the main diagonal (since the correlation between X and X is 1):...
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This note was uploaded on 03/09/2008 for the course CALC 1,2,3 taught by Professor Varies during the Spring '08 term at Lehigh University .
 Spring '08
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 Calculus

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