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The design matrix contains data on the independent variables (also called explanatory variables), in a statistical model that is intended to explain observed data on a response variable (often called a dependent variable). The theory relating to such models uses the design matrix as input to some linear algebra : see for example linear regression.
For example, if A is a 3-by-0 matrix and B is a 0-by-3 matrix, then AB is the 3-by-3 zero matrix corresponding to the null map from a 3-dimensional space V to itself, while BA is a 0-by-0 matrix. There is no common notation for empty matrices, but most computer algebra systems allow creating and computing with them.
The following is an age-based Leslie matrix for this species. Each row in the first and third matrices corresponds to animals within a given age range (0–1 years, 1–2 years and 2–3 years). In a Leslie matrix the top row of the middle matrix consists of age-specific fertilities: F 1, F 2 and F 3. Note, that F 1 = S i ×R i in the matrix
Synonym for (0,1)-matrix, binary matrix or Boolean matrix. Can be used to represent a k-adic relation. Markov matrix: A matrix of non-negative real numbers, such that the entries in each row sum to 1. Metzler matrix: A matrix whose off-diagonal entries are non-negative. Monomial matrix: A square matrix with exactly one non-zero entry in each ...
In this example, the dimension, k, equals 2. As another example, suppose that the data consists of points (x, y) that we assume are distributed according to a straight line with i.i.d. Gaussian residuals (with zero mean): this leads to the same statistical model as was used in the example with children's heights. The dimension of the ...
A doubly stochastic matrix is a square matrix of nonnegative real numbers with each row and column summing to 1. A substochastic matrix is a real square matrix whose row sums are all ; In the same vein, one may define a probability vector as a vector whose elements are nonnegative real numbers which sum to 1. Thus, each row of a right ...
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The Burt table is the symmetric matrix of all two-way cross-tabulations between the categorical variables, and has an analogy to the covariance matrix of continuous variables. Analyzing the Burt table is a more natural generalization of simple correspondence analysis , and individuals or the means of groups of individuals can be added as ...