# What is Multiple variables: Definition and 49 Discussions

In statistics, the coefficient of multiple correlation is a measure of how well a given variable can be predicted using a linear function of a set of other variables. It is the correlation between the variable's values and the best predictions that can be computed linearly from the predictive variables.The coefficient of multiple correlation takes values between 0 and 1. Higher values indicate higher predictability of the dependent variable from the independent variables, with a value of 1 indicating that the predictions are exactly correct and a value of 0 indicating that no linear combination of the independent variables is a better predictor than is the fixed mean of the dependent variable.The coefficient of multiple correlation is known as the square root of the coefficient of determination, but under the particular assumptions that an intercept is included and that the best possible linear predictors are used, whereas the coefficient of determination is defined for more general cases, including those of nonlinear prediction and those in which the predicted values have not been derived from a model-fitting procedure.

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1. ### I Chain Rule in Multiple Variables

The following link leads to a question I asked on the mathematics Stack Exchange site. https://math.stackexchange.com/questions/3790900/chain-rule-with-a-function-depending-on-functions-of-different-variables/3791017?noredirect=1#comment7809514_3791017 I want to understand how the chain rule...
2. ### MHB Objective function of a linear program with multiple variables.

Hello, Please I need help to find the objective function of a linear program (attachement : example). I tried to figure it out from the formula provided in (attachement : formula) but I couldn't understand it, it's written (MIN(lambda)wj) I think it's the key to resolve my question ! ( Full file...
3. ### Objective function of a linear program with multiple variables

Hello, Please I need help to find the objective function of a linear program (attachement : example). I tried to figure it out from the formula provided in (attachement : formula) but I couldn't understand it, it's written (MIN(lambda)wj) I think it's the key to my question ! ( Full file is...
4. ### How to Solve a Derivative Presented in a Non-Standard Format?

I have attached a word document demonstrating the working out cos i was too lazy to learn how Latex primer works and writing it like I did above would've been too hard too read. I tried to make it as understandable as possible, presenting fractions as ' a ' instead of ' a / b ' . ------ b
5. ### I Test for dependence/independence of multiple variables

I don't think this is related to linear dependence/independence of linear algebra. I am talking about multi-variable calculus. I am getting confused with being able to quickly tell which variables depend on others when there are 4+ variables involved. For example, suppose I have w(r,s)...
6. ### Scalar in terms of multiple variables, Nyquist & Bode Plot

Homework Statement A scalar is given by It is controlled by With step time h = 0.2 s 1. Find the discrete equivalent model 2. Check the stability of closed loop (K = +1) 3. Obtain the via the Bode plot Homework EquationsThe Attempt at a Solution So for question 1. This is where I'm...
7. ### Two Limit exercises of functions of two variables.

(I) Find the limit (x,y)->(0,0) of F, then prove it by definition. (II) Find the limit and prove it by definition of: as (x,y) approach (C,0), C different from zero. I have previously asked it on Quora, but it doesn't appear to have answers any...
8. ### Extrems values on armonic function

Homework Statement f[/B] is an armonic function and C2(R2) a) Suposse a point P0 / fxx(P0) > 0. Prove that P0 is not a extreme value. b) consider D = {(x,y) / x2 + y2 < 1} and suposse fxx > 0 for all (x,y) in D. Prove that: if f(x,y) = 0 in x2 + y2 = 1, so f(x,y) = 0 for all (x,y) in D...
9. ### A Statistical analysis for comparing trends among multiple variables

In our study, we measured the seasonal abundance of selected genes from two sites. We want to make a comparison between the seasonal trends between the genes (i.e. which genes had similar trends and which didn't). What would be the best statistical analysis for this purpose? Thanks!
10. ### Factoring binomials with multiple variables p, x, and q

Homework Statement Question: "If p and q are constants and x2+px+12 is equivalent to (x+3)(x+q), what is the value of p?" I was told that the answer was 7 but I am not sure how to reach this value myself. 2. Homework Equations I am not quite sure if this is applicable. The Attempt at a...
11. ### 3D graph plot of a function of multiple variables.

I am searching for a site that enables me to plot a function of multiple variables in 3D form. Say f(x1,x2,x3,x4) and I wish to plot this function as a 3D graph for x1 and x2 where x3 and x4 are kept constant.
12. ### Integration of Multiple Variables

Hi There, I'm a new member, so apologies if I've posted this in the wrong area. I've been working through the ASME STS-1-2006 Steel Stack Standard, particularly the Vortex Shedding section. I've come across this nasty integral which is doing my head in, and we wondering if anyone would mind...
13. ### Find a Rigorous Calculus of Multiple Variables Book for Advanced Learners

Hi! I am looking for a very rigorous book on some of the topics covered in Calculus of Multiple Variables. My University uses the last part of Adams "Calculus: a complete course" and I found the presentation therein more fit for people needing to know enough to perform the calculations than for...
14. ### Calculus of variations: multiple variables, functions of one variable

Simply put, can you find the function which extremizes the integral J[f]=\iint L\left(x,y,f(x),f(y),f'(x),f'(y)\right) \,dx \,dy Where ##f## is the function to be extremized, and ##x## and ##y## are independent variables? A result seems possible by using the usual calculus of variation...
15. ### Partial differentiation problem, multiple variables (chain rule?)

Homework Statement if z = x2 + 2y2 , x = r cos θ , y = r sin θ , find the partial derivative \left(\frac{\partial z}{\partial \theta}\right)_{x} Homework Equations z = x2 + 2y2 x = r cos θ y = r sin θ The Attempt at a Solution The textbook says that the equation should be...
16. ### Projectile Motion with multiple variables

Homework Statement As shown in the figure below, a particle is moving in a circle of radius R with constant speed v. At some location, the particle is detached from the circle and falls with a parabola path to point A. What is the horizontal range x of the projectile?Homework Equations Writing...
17. ### Deriving with multiple variables

Homework Statement I'm stuck at one of the derivations for relativistic energy. I've figured out every other single step, but I just can't wrap my head around this one: Prove that: {\frac{d}{dt}} {\frac {mu} {\sqrt{1-u^2/c^2}}} = {\frac {m {\frac{du} {dt}}} {(1-u^2/c^2)^{3/2}}}...
18. ### Rigorously determining differentiability in multiple variables

Homework Statement Determine if f(x,y) = ((x-y)4 +x3 +xy2)/(x2+y2) [f(x,y = 0 @ (0,0)] is differentiable at the origin. Homework Equations x = (0,0) The Attempt at a Solution A function is differentiable at x if f(x+Δx) - f(x) = AΔx + |Δx|R(x) Where A are constant...
19. ### Definition of Integral in Multiple Variables

Dyadic Cube C_{k,N} = X \in\ \mathbb{R}^{n} \frac{k_{i}}{2^{N}} \leq x_{i} < \frac{k_{i}+1}{2^{N}} for 1 \leq i \leq n Where k = \pmatrix { k_{1} \cr k_{2} \cr \vdots \cr k_{i} \cr } I understand that N is the level of the cubes, but what does k equal? I'm having trouble...
20. ### Integrate with multiple variables in denominator?

Hey everyone, I need to do the following integral. I just need a little help getting this started, I'm not sure where I need to go. Here is the problem: \int_{0}^{1-v} du \int_{0}^{\frac{1}{2}} dv \frac{1}{1+u^2-v^2} I think I have the boundaries for the integral set up correctly, {0≤v≤1/2...
21. ### Implicit differentiation in multiple variables

So, as the title may have given away, I'm trying to figure out implicit differentiation in the multiple variable context. I thought a good practice would be the law of cosines, aka c^2 = a^2 + b^2 - 2abcosθ. So I'm trying to find ∂θ/∂a, ∂θ/db, ∂θ/dc. I tried solving for θ and then taking...
22. ### Solving by substitution for multiple variables

Homework Statement I have four equations and have four variables. I need to solve for each of the variables. I am having difficulty figuring out how to do this. My equations are here. http://imgur.com/EOA8I Homework Equations \frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b^2} = 1 The Attempt...
23. ### Matlab: creating a table of equations using multiple variables

Homework Statement I have an equation that looks like func=sin(pi*x*n)*sin(pi*y*m) I was wondering if there was any method (possibly involving for loops) where I could get a plottable function along xy for all the different combinations of n and m i.e. m= 1 n =1 so the function would be...
24. ### Finding the maximum height given multiple variables

Homework Statement A 4.27-kg object is thrown vertically upward from the surface of Mercury, where the acceleration due to gravity is g1 = 3.70 m/s2. The initial velocity is v1, and the object reaches a maximum height of y1. What is the maximum height, y2, if the object is thrown with a...
25. ### Problems with propagation of error for multiple variables

please help by telling me whether my approach to solve the problems are right or wrong. please refer to the ATTACHMENT for the questions and my approaches... your help is highly appreciated!
26. ### Chain rule with multiple variables

I was reading over a textbook that stated the following, where y(s,t) = v(x(s,t),t) \frac{\partial y}{\partial t} = \frac{\partial v}{\partial x}\frac{\partial x}{\partial t} + \frac{\partial v}{\partial t} and \frac{\partial^2y}{\partial t^2} = \frac{\partial^2 v}{\partial x^2}\left (...
27. ### Analyzing a 7-variable data set where multiple variables changed at once

Hi, I have some experimental data from a colleague which has been collected with different values for 7 parameters. It isn't nice, as in it's not as if 6 of the parameters were held fixed while the seventh was adjusted. Beyond that, I don't have much data. I'm not up on my statistical...
28. ### Critical points with multiple variables

Homework Statement Locate and classify the critical points of f(x,y) = (x-y)(xy-1). Homework Equations The Attempt at a Solution I found the partial derivatives with respect to x and y and I got: ∂f/∂x = -y2+2xy-1 ∂f/∂y = x2-2xy+1 After setting them both equal to zero I can't...
29. ### Using multiple variables to generate a table or csv

Hi All, I am new to mathematica and this kind of work in general, and was looking to score a little help on this thread. I basically need to build a data set that contains city information, country information, coordinates, and weather information. I want to do this using Mathematica's...
30. ### Integration of multiple variables

Homework Statement Find the volume of the given solid. Under the plane x − 2y + z = 8 and above the region bounded by x + y = 1 and x2 + y = 1 The Attempt at a Solution Here's how I set it up. \int^1_0 \int^{1-x^2}_{1-x} (8-x+2y) dydx When I do the math, I get 21/20. I have...
31. ### Calc III - Graphing a Function of Multiple Variables by hand

I come across questions where I have to match the equation with its contour map and graph. Examples: z = sin(xy) z = sin(x-y) Right now I'm using Wolfram Alpha for all of these, but supposing these appear on an exam... how do I graph it by hand? :confused: For example, for z =...
32. ### Circular mass, finding multiple variables

A 4.0 N and 3.0 N force act simultaneously on a circular mass of .25 kg, initially at rest floating in space. a) Find the net force acting on the mass (magnitude and direction) I found the netforce (Resultant) = 5N b) Find the acceleration of the mass, magnitude and direction. The...
33. ### Limits of multiple variables along y=mx

This is an assignment problem I have. Can't seem to figure it out. It has two parts, one to prove that the function approaches 0 where y=mx and and one where the function approaches 0 from y=kx2... f(x,y) = (x3y)/(2x6+y2) I've attempted both parts and get stuck on what seems like the same...
34. ### MATLAB Matlab m file function with multiple variables

Hi, I have a MATLAB function m file and I want to integrate the function. function y = myfun(t,a,b) y = (1/(2*pi)).*(1./t)*(1i*(a+b)); endThen when I call the integration in MATLAB I don't know how to specify a and b whilst integrating over t. I need to be able to set a and b outside of the...
35. ### Mathematica Mathematica -> making multiple variables in one go?

[ANSWERED] Mathematica -> making multiple variables in one go? Ok so let's say i know how many variables i want: numberofvariables = 5; and then i want to create 5 different variables, say X1, X2, X3, X4, X5 based on some formula, say: Xi = 5+i^2 but i want this creation of...
36. ### Parity of function of multiple variables

Hi everyone I was wondering how to determine the parity of a function of multiple variables. Say the function is: f(x,z) = xz How would I determine its parity? For the above function it is true that #1 f(x,z) = f(-x,-z) but its also true that #2 \int_{-a}^{a}\int_{-a}^{a}xz \dx...
37. ### Sketching Multiple Variables: How to Represent 3-Dimensional Surfaces?

Homework Statement Two separate problems: 1. Sketch f(x,y)=x+(y^2) 2. Sketch f(x,y)=sq rt (4-(x^2)-(y^2)) Homework Equations The Attempt at a Solution I honestly don't even know where to begin with sketching these two equations. In the first problem I can't find an example...
38. ### Taylor Series in Multiple Variables

Can anyone help me for the leading order terms in the taylor series for the function f(x,y) = Sqrt(a*x^8+b*x^4*y^4+y^8), centered at x=0,y = 0 and a,b,c constants?
39. ### Conditional expectation on multiple variables

How to compute E[X|Y1,Y2]? Assume all random variables are discrete. I tried E[X|Y1,Y2] = \sum_x{x p(x|y1,y2) but I'm not sure how to compute p(x|y1,y2] = \frac{p(x \cap y1 \cap y2)}{p(y1 \cap y2)} If it is correct, how can I simplify the expression if Y1 and Y2 are iid?
40. ### Return Multiple variables in Fortran

Hey Guys, I am converting my code from MATLAB to fortran. Now in MATLAB it is rather convenient to write a function which returns multiple variables. I believe a function in fortran can return only one variable. I think a subroutine can return multiple variables. I was not able to find any...
41. ### Approximation and error in functions of multiple variables - help needed

Homework Statement A baseball player is playing approximately 310 feet from a TV camera that is behind home plate. A batter hits a fly ball that goes to a wall 400 feet from the camera. (a) The Camera turns 12 degrees to follow the play. Approximate the number of feet the fielder has to make...
42. ### MATLAB Matlab Beginner: Equations with Multiple Variables

Im a begginer at Matlab and have a simple question. I have a equation with lots of variables that can be easily entered incorrectly. Therfore i was going to split up the term. For example if i have y = x^(6Z+2) i was going to put the m file as y=x^u u = 6Z + 2 then z = 3 for...
43. ### How to minimize a simple quadratic function of multiple variables ?

Hi everybody, I'm trying to minimize a function with multiple variables. My goal is to approximate on the L2 norm a matrix by the outer product of 2 vectors (or is it called tensor product ?). So I have to determine a vector y = (y1,...,yn) and a vector x = (x1,...,xm) such that their...
44. ### Differentiating with multiple variables

Homework Statement Find dw/dt. Check result by substitution and differentiation w = (x^2 + y^2)^1/2, x = e^2t , y = e^-2tHomework Equations The Attempt at a Solution dx/dw = x/(x^2 + y^2)^1/2 dy/dw = y/(x^2 + y^2)^1/2 Dont really know where to go with it
45. ### Multiple variables - check understanding

Homework Statement A function g(x,y) = 3x^2-x-y+y^2. I have to find the minimum and maximum of the function on D = [0,1] x [0,1]. The Attempt at a Solution First I have to check the ends; I mean (0,0), (0,1), (1,0) and (1,1). I also have to check the points, where the gradient is zero...
46. ### Gradient of functions with multiple variables

Homework Statement The gradient of f(x,y) = x^2-x+y is: gradient_f(x,y) = (2x-1 ; 1). To find gradient_f(x,y), I set 2x-1 = 0 and 1 = 0 - so there are no points, where gradient_f(x,y) is zero because of 1 != 0?
47. ### Functiosn with multiple variables

Homework Statement 1) I have a C1-function f(u,v), and f(0,0) = 1, df/du(0,0) = 3 and df/dv(0,0)=5. I have to find k'(1), when k(x) = f(x^2-1;x-1). 2) A function g(x,y) = 3x^2-x-y+y^2. I have to find the minimum and maximum of the function on D_1 = [0,1] x [0,1] and D_2 = [1,2] x [0,1]...
48. ### Functions with multiple variables

Homework Statement I have a function f(x,y,z) = 1/(x^2+y^2+z^2). I have to find the domain. It is R^3, but x^2+y^2+z^2 != 0. How do I write that and am I correct?
49. ### Continuous functions with multiple variables

I need to find a value for f at (0,0) to make this function continuous: f(x,y)=sqrt(x^2+y^2)/[abs(x) + abs(y)^(1/3)] With other functions in this problem I simply took the limit .. but taking the limit gives 0/0. In single-variable calculus I would apply l'hopital's rule to this, but I'm...