![]() ![]() The matrix A is a 3x2 matrix, where element a 32is the number 3.35.Ī matrix with a single row is called a row vector, whereasone with a single column is called a column vector. In this course, we will work with afew matrices and most of them are composed of numbers or symbols that representnumbers. Forexample, a matrix may be composed of functions, and one can perform operationswithout having to evaluate the functions. The elements of matrices do not have to be numbers. Usually, boldface symbols areused to represent matrices. Thus element a 42represents the element in row 4 and column 2. In generic form thesesubscripts are usually represented by iand j. Each element in a matrix can be represented by a symbol witha subscript composed of two numbers, row and column. Number of rows always goes first, followed by thenumber of columns. The dimension of the matrix is given by the number of rowsand the number of columns. Matrices are used simply as a concise form to represent, manipulate,and operate with sets of numbers. For the most part, our use of matrix algebra does not involveany new concepts beyond the concept of numbers and operations with realnumbers. 3:1.1 Introductionto matrix algebra.Ī matrix is a rectangular array of elements arranged inrows and columns. As one may guess, part of theemphasis on linearity come from the fact that the distributions andprobabilities of linear combinations of normal variables can be worked outanalytically and eventually one ends up with a “table” distribution such asnormal, Student’s t, c 2or F. Where the l’s are coefficients that do not depend on anyv’s, and the v’s are the random variables. When does one need a “linear function of estimatedparameters”!? What is a “linearfunction of estimated parameters”!? A linear function or combination of randomvariables (such as the estimated parameters) is an equation that can beexpressed in the following way: In JMP these tests are performed using a menu item called “CustomTests.” In SAS, one uses the “estimate” statement. This introduction to matrix algebra is not supposed to besufficient for the student to learn how matrix algebra is used in statistics.The goal of the presentation is to give the reader the basic elements tounderstand that most hypothesis testing and estimations are performed byestimating the variances of l inear functions of estimated parameters.Statistical software includes direct commands or menu items that perform commonhypothesis testing by using pre-set linear functions of the parameters,however, for several practical aspects of regression, one needs to createcustom tests. 3:1 Data organization andMatrix approach to SLR.
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