Multivariate Definition and 135 Threads

Multivariate statistics is a subdivision of statistics encompassing the simultaneous observation and analysis of more than one outcome variable.
Multivariate statistics concerns understanding the different aims and background of each of the different forms of multivariate analysis, and how they relate to each other. The practical application of multivariate statistics to a particular problem may involve several types of univariate and multivariate analyses in order to understand the relationships between variables and their relevance to the problem being studied.
In addition, multivariate statistics is concerned with multivariate probability distributions, in terms of both

how these can be used to represent the distributions of observed data;
how they can be used as part of statistical inference, particularly where several different quantities are of interest to the same analysis.Certain types of problems involving multivariate data, for example simple linear regression and multiple regression, are not usually considered to be special cases of multivariate statistics because the analysis is dealt with by considering the (univariate) conditional distribution of a single outcome variable given the other variables.

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  1. T

    Testing Hypotheses in Multivariate Linear Regression Using SAS?

    I have a model y= beta0 + beta1 x1 + beta2 x2 + eps, eps~N(0,1). How to test hypothesis beta1=0 ? Is the same test for beta2=0?
  2. K

    Multivariate IBP Homework: Evaluating ∫ukduiP(u,y,t) du

    Homework Statement For u \in \mathbb R^n and P(u,y,t): \mathbb R^n \times U \times \mathbb R \to \mathbb R^n for some undisclosed set U, we want to evaluate \int u_k \frac{\partial}{\partial u_i} \left[ u_j P(u,y,t) \right] du where integration is component wise and du = du_1 du_2...
  3. A

    SOLUTION Multivariate SDE with repeated Eigenvalues

    I am looking forward the solution of multivariate Ornstein–Uhlenbeck differential stochastic equation with repeated eigenvalues. In particular with dy=A(y-c)dt +DdW y is a vector nx1 A is nxn matrix with repeated eigenvalues c is vector of nx1 of constant D is a nxm matrix of...
  4. I

    Multivariate Inverse Functions: Understanding Equations with Multiple Variables

    Homework Statement If I am asked to find the inverse functions of two functions: a=f(x, y) b=g(x,y) Does this mean find the two equations: x=m(a, b) y=n(a,b) If so, how do m, and n compare to f and g? Inverses of single variables mirror their inverse on a graph. How does this...
  5. R

    Multivariate regression for project cost estimates

    Hi All, Hope this is the right sub-forum for this. I currently work for an engineering consultancy and am doing some project management what for what are essentially site investigation reports (sites are quite small, typically a few acres/hectares). Our clients are mostly developers who have...
  6. R

    Multivariate quartic function help

    Homework Statement I am a Turkish student bogged down by a very difficult question (at least for me). Here's the question: Given that xy= 1, find all solutions for X4 + y4 - z4 + 4z2 - 2 = 0. I've spent many hours on this equation. It even prevents me from sleep. I would...
  7. A

    Multivariate distribution : Mean vector?

    Hello friends.My English is bad :) .I'll try to explain my trouble. In question: Q function according to x1 and x2 are substitutes when the joint comes out of solution. Of the solution in theory I do not understand where they come from.Is there another solution or the problem? Where is the...
  8. S

    Determining the covariance matrix of a multivariate normal distribution

    Hi all, I have a stats problem I'm trying to figure out. Suppose I have a very large population (~millions) of colored balls with exactly 50% red, 30% green, 20% blue. If I take a random sample of 1000 of these balls, the distribution of colors I end up with can be modeled as a multivariate...
  9. C

    Multivariate Normal Distribution

    Homework Statement http://img16.imageshack.us/img16/7703/ass1lx.jpg Homework Equations The Attempt at a Solution I know that f(x_1, x_2, x_3) = \frac{1}{(2 \pi)^{3/2}|\Sigma|^{1/2}}exp(-\frac{1}{2}x \Sigma^{-1} x) since n = 3 and mu = 0. I've never used the multivariate...
  10. E

    Good source of problems for multivariate calculus

    Hi, I have this qualifying exam coming up in about a month for my Ph.D. program in math. I just noticed that my European undergraduate education covered nothing about actually calculating any tricky integrals. It was only about Riemann sums and proving properties of the integral which I know...
  11. J

    How to derive the multivariate normal distribution

    If the covariance matrix \mathbf{\Sigma} of the multivariate normal distribution is invertible one can derive the density function: f(x_1,...,x_n) = f(\mathbf{x}) =...
  12. N

    How to take the limit of a multivariate function that goes to 0

    Title says it all. Examples from class I am looking at include: lim(x,y) -> (0,0) of functions such as: 6yx^3 / 2x^4 + y^4 or (x^2)(sin^2 (y)) / x^2 + 2y^2 My professor did a bad job of explaining it (or at least I did not understand). Thanks, Nkk
  13. X

    Layperson's description of multivariate gaussian distributions?

    I am a Computer Science student who wants to implement the EM statistical clustering algorithm. I'm doing this on my spare time outside of any classes that I'm taking. I've been doing a lot of reading and understand almost everything I need to fully. However, I only understand univariable normal...
  14. P

    Common roots of multivariate polynomials

    I was wondering if it were possible to efficiently solve the common root of 4 polynomials in 4 variables algebraically. I am currently using a gradient descent method, which can find these roots in a couple seconds; however, I am concerned about local minima. So far I have attempted to use...
  15. C

    How Do You Compute the Most Successful Recipe Using Multivariate Testing?

    Homework Statement My goal is to have enough info that I could sit down with a piece of paper and actually compute a pretend test from start to end. All the examples and docs I have found online are not nearly in layman's terms.. oh, please excuse my math-lameness btw. :-) If I have 5-7...
  16. W

    Evaluate multivariate integral over a simplex - help

    I would need to evaluate the integral \int\limits_{x\in S}[x+x_A]^TA[x+x_A]\exp\left(-\frac{1}{4}[x+x_B]^TB[x+x_B]\right)dx where x is a column n-vector x_A and x_B are column n-vector constants A and B are n\times n (symmetrical) matrices taken over the volume S, which is a n-simplex* in...
  17. A

    Help with multivariate Calculus

    Homework Statement Show that: max{a,b}=1/2*(a+b+|a-b|) Hence or otherwise, show that if f,g:R ----> R are continuous, then the function h:R ----> R defined by h(x) = max{f(x),g(x)} is also continuos. Suppose the f:(0,inf) ---> R is differentiable and f(x) ---> 0 as x---> inf. Set...
  18. M

    Multivariate Calculus question

    Hi, could anyone tell me the steps to solve the following question: Find the solution of x'=Ax with the initial value -------1---------2 0 0 x(0)=( 0 ), if A=( 0 1 -1 ) -------1---------1 1 1
  19. G

    Multivariate Normal Distribution

    Homework Statement Z = (Z1, Z2, ... Zd) is a d-dimensional normal variable with distribution N(0, E). Let A be invertible matrix such that AA' = E. (E = sigma = covariance matrix). Find the distribution of Y = (A^-1)*Z. The Attempt at a Solution I'm pretty sure the solution is normal...
  20. K

    Multivariate probability distributions?

    Homework Statement Let Y be the number of customers entering a ABC bank in a day. It is known that Y has a Poisson distribution with some unknown mean lambda. Suppose that 1% of the customers entering the branch in a day open a new ABC bank account. Find the mean and variance of the number of...
  21. N

    L'Hôpítal's rule for multivariate functions

    In my math class lectures at the university while studying multivariable functions the lecturer never mentioned L'hopital's rule for these multivariate functions..But in a tutorial class,a tutorial assistant approached this question..find lim (x,y)-->(0,0) [sin(x^2+y^2)]/(x^2+y^2)..by implicitly...
  22. L

    Multi-start iterative multivariate constrained nonlinear programming

    Hi, I need to solve a multi-start iterative multivariate constrained nonlinear programming problem. But I can't seem to be find any package that will solve it for me. I have been wondering if anyone would be kind enough to tell me some packages that can solve the problem. (C/C++ packages...
  23. L

    Textbook recommendation for multivariate calculus?

    I am currently studying multivariate calculus, and quite frankly, I'm not doing well. I am currently using Thomas' Calculus, 11/e media upgrade by Pearson. I don't like this book. The text is 75% theory and 25% simple examples, too few exercise problems, and the explanation is just too difficult...
  24. J

    Estimating parameters from multivariate normal

    I need to estimate parameters from data that follow a mutinormal distribution. The parameters that I need to estimate are contained in the expression for the mean of the marginal normal distributions. That is each marginal distribution has mean: \frac{p_1*c_i + p_1*y}{p_1+p_2} where...
  25. I

    Constraint Equation? Multivariate calculus

    Homework Statement This is a second (university) year calculus problem dealing with calculus of multiple variables. In economics, utility is a measure of the relative satisfaction from, or desirability of, consumption of goods. A utility function u = u(a,b) gives the utility from consuming...
  26. G

    Taylor Polynomial of Order 3 for f(x,y,z) at (0,0,0)

    Homework Statement Calculate the taylor polynom of order 3 at (0,0,0) of the function with well-known series (that means I can't just take the derivatives) f(x,y,z)=\sqrt{e^{-x}+\sin y+z^{2}} Homework Equations The Attempt at a Solution I wrote the functions within the square...
  27. R

    Is the Multivariate Urn Problem Related to Discrete Distribution Theory?

    Hello, we are trying to solve a problem for which we would appreciate any reference that you could give us. The problem is as follows. We have two urns. Each urn contains balls in different colors. The exact number of balls of each color in each urn is known. Imagine that we extract a number...
  28. D

    Multivariate Linear Regression With Coefficient Constraint

    [SOLVED] Multivariate Linear Regression With Coefficient Constraint I'm attempting a multivariate linear regression (mvlr) by method of least squares. Basically, I'm solving a matrix of the following form for \beta_p, $ \begin{bmatrix} \sum y \\ \sum x_1 y \\ \sum x_2 y \\ \sum x_3 y...
  29. T

    Multivariate Exponential distribution

    Hi to all :) Does anyone have any idea how the expression for a multivariate exponential distribution looks like? If possible, can you post the source url? Commonly available is the multivariate normal distribution. thanks in advance :biggrin:
  30. D

    Multivariate and vector calculus

    Hi everyone I'm just about to begin a course in multivariate and vector calculus what prior knowledge in maths is good to go over to help me along the way in this course?
  31. C

    Multivariate Fourth Moment in Porbability

    I am not sure whether "Multivariate Fourth Moment" is the name for it. But basically, I have an N-dimensional vector x, which is Gaussian with mean 0 and covariance matrix R. I also have two N by N matrix A and B. What I what to do is to compute the expectation...
  32. M

    Is Multivariate Regression Suitable for Estimating Temperatures at Linked Sites?

    I have temperature data from two different sites, and I want to develop a relationship for temperature between those two sites. In that way, if I have temperature at just one of those sites, I can approximate the temperature at the other site. My question is whether or not a multivariate...
  33. benorin

    Def. Continuity in terms of sequences: How do I generalize to multivariate fcns?

    Working from "Principles of Mathematical Analysis", by Walter Rudin I have gleaned the following definition of continuity of a function (which maps a subset one metric space into another): Suppose f:E\rightarrow Y, where \left( X, d_{X}\right) \mbox{ and } \left( Y, d_{Y}\right) are metric...
  34. C

    Calculating Arc Length in Multivariate Calculus

    here is the problem, and I can't seem to get very far, compute the length of r(t) = <3t, 4cost, 4sint> from t=0 to t=1 i know the formula is integral from 0 to 1 of length of r'(t) but I keep coming up with 5, and it doesn't seem right, can someone please confirm or deny this. Thanks
  35. C

    Strict local minimizer (multivariate)

    I'm stuck on this question Show that f(x1,x2) has a strict local minimizer at t=0 along every line { x1=at { x2=bt through (0,0). Any hints or tips would be great thanks
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