Independent variables Definition and 26 Threads

Dependent and independent variables are variables in mathematical modeling, statistical modeling and experimental sciences. Dependent variables receive this name because, in an experiment, their values are studied under the supposition or hypothesis that they depend, by some law or rule (e.g., by a mathematical function), on the values of other variables. Independent variables, in turn, are not seen as depending on any other variable in the scope of the experiment in question. In this sense, some common independent variables are time, space, density, mass, fluid flow rate, and previous values of some observed value of interest (e.g. human population size) to predict future values (the dependent variable).Of the two, it is always the dependent variable whose variation is being studied, by altering inputs, also known as regressors in a statistical context. In an experiment, any variable that the experimenter manipulates can be called an independent variable. Models and experiments test the effects that the independent variables have on the dependent variables. Sometimes, even if their influence is not of direct interest, independent variables may be included for other reasons, such as to account for their potential confounding effect.

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  1. Ahmed1029

    I Degrees of freedom and constraints

    In case of P holonomic constraints and N particles, I have 3N-P degrees of freedom and I have to look for 3N-P generalized coordinates if I want them to vary independently, but what about non-holonomic constraints? I know if I have N particles and P non-holonomic constraints, I still need 3N...
  2. Ahmed1029

    I Can I always consider velocities and coordinates to be independent?

    It's a topic that's been giving be a headache for some time. I'm not sure if/why/whether I can always consider velocities and (independent) coordinates to be independent, whether in case of cartesian coordinates and velocities or generalized coordinates and velocities.
  3. megf

    I Probability Density Function of the Product of Independent Variables

    How do I find the probabilty density function of a variable y being y=ab, knowing the probabilty density functions of both a and b? I know how to use the method to calculate it for a/b - which gives 1/pi*(a²/b²+1) - using variable substitution and the jacobian matrix and determinant, but which...
  4. A

    A Independent variables in higher derivative Lagrangian

    Consider the following Lagrangian density $$\mathscr{L}=\mathbf{E}\cdot\left(\nabla^{2}\mathbf{E}\right)$$ where $$E_{i}=\partial_{i}\phi\;(i=x,y,z )$$. In th is case the potential and its 3rd derivatives are the independent variables. Acording to Barut's classical theory of fields book, for...
  5. M

    A Using standard deviation values as independent variables

    Hey. I am planning on doing some research, where I predict a change based on different types of risk. The question is simple. Can I use values of standard deviation as independent variables in a linear regression analysis (OLS)? The standard deviation values over time will be calculated in...
  6. Pushoam

    Avg. of sum of independent variables

    Homework Statement Homework EquationsThe Attempt at a Solution The probability that ##X_1 ## is between ## X_1 ## and ## X_1 + dX_1 ## and ##X_2 ## is between ## X_2 ## and ## X_2 + dX_2 ## and so on till the nth variable is dP(##X_1, X_2, ..., X_n) = p ( X_1) p( x_2) p(X_3)...p(X_n) dX_1...
  7. maistral

    A Nonlinear regression in two or more independent variables

    Hi. I wanted to learn more on this topic, but it seems all the available resources in the internet points to using R, SPSS, MINITAB or EXCEL. Is there an established numerical method for such cases? I am aware of the Levenberg-Marquardt, Gauss-Newton and such methods for nonlinear regression on...
  8. Dependent and independent variables exercise: the basics | Algebra I | Khan Academy

    Dependent and independent variables exercise: the basics | Algebra I | Khan Academy

    Here we have a problem that asks us to identify which variables are dependent and independent. Hint: independent variables are not influenced and remain unch...
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  9. Dependent and independent variables exercise: graphing the equation | Algebra I | Khan Academy

    Dependent and independent variables exercise: graphing the equation | Algebra I | Khan Academy

    It's helpful to express an equation on a graph where we plot at least 2 points. Watch and we'll show you. Practice this lesson yourself on KhanAcademy.org ri...
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  10. Dependent and independent variables exercise: express the graph as an equation | Khan Academy

    Dependent and independent variables exercise: express the graph as an equation | Khan Academy

    We're flipping the last video on its head and doing the opposite. This time we give you the graph and ask you to express it as an equation. Practice this les...
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  11. H

    Why are position and velocity independent variables in a phase space?

    Why do we take a particle's position ##x## and its velocity ##\dot{x}## as independent variables in a phase space when they are dependent in the sense that given the function ##x(t)##, we can get the function ##\dot{x}(t)##? I'm thinking they are independent variables but not independent...
  12. Coffee_

    E-L equations only hold for independent variables?

    I'm talking about this: http://www.cs.cornell.edu/courses/cs6650/2008fa/images/thumb_EL.jpg In the derivation when you minimize action you assume that all the variations in coordinates are independent and thus conclude that each term has to be zero. When this isn't the case anymore one doesn't...
  13. J

    Independent variables of the Lagrangian

    Why are y and y' treated as independent variables, while they are not? Another slightly related question: if ' = d/dt then df'/dg' = df/dg because f' = df/dg g', but if we differentiate f' to g' we implicitly assume that df/dg is independent of g', is it?
  14. I

    Calculating Error in Multiple Independent Variables

    Homework Statement Okay so I was given this question to start calculating error on other problems. Consider the equation F(x,y,z) = x^4+2y^3+5yz+5. Let the uncertainty in x be represented by the variable dx, the uncertainty in y be represented by the variable dy, and the uncertainty in z...
  15. C

    Statistics and independent variables

    Homework Statement Let's say the independent variable (in statistical terms) A depends on variables B, C and D. We perform tests, and find out that the variable A causes "something" with the values of B, C and D equal to B2, C2 and D2. Let's also say that A with variables B, C and D of B1...
  16. D

    Variance of the sum of random independent variables

    Homework Statement let x_{i} be a random variable, and let y_{j} = \sum x_{i}. The variance of the random distribution of the x_{i}'s is known, and each y is the sum of an equal amount of x_{i}'s, say N of them. How do I compute the variance of y in terms of \sigma^2_{x} and N? Homework...
  17. O

    Cubic equations with independent variables

    Hi colleages. can you help me to solve the cubic equation below: 2N(Ep-En)hp^3(x)-3[M(x,t)(Ep-En)-2NEnh]hp^2(x)-6Enh[M(x,t)+Nh]hp(x)+Enh^2[3M(x,t)+2Nh]=0 notice that all variables in the...
  18. T

    Laplace transform of function with independent variables OTHER than time

    Hi all Conventionally we used to seeing the Laplace transform applied to problems that use time as the independent variable, can anybody point me at some examples that do not use time as the independent variable? Thanks Tim
  19. D

    Independent variables in termodynamics

    Say I want to parametrize the plane. I can use cartesian (x,y) or polar (r,theta). But I cannot use x and r, because if I draw a circle and a vertical line, there are two points of intersection. I guess x and theta will do, because theta specifies a ray that will intersect any vertical line...
  20. C

    Finding joint pdf of independent variables.

    Homework Statement Suppose X1 and X2 are two independent gamma random variables, and X1~Gamma(a1, 1) and X2~(a2, 1). a) Find the joint pdf of Y1 = X1 + X2, and Y2 = X1/(X1 + X2). b) Show that Y1 and Y2 are independent. c) Find the marginal distributions of Y1 and Y2. The Attempt...
  21. M

    Uncorrelated Vs. Independent variables

    Hi, I am confused with respect to these two terms. In a book on regression analysis, I read the following statements. 1. For two normally distributed variables, zero covariance / correlation means independence of the two variables. 2. With the normality assumption, the following...
  22. R

    Correlation with two independent variables

    I would appreciate some help with this problem. Assuming X and Y are independent, I'm trying to find the correlation between XY and Y in terms of the means and standard deviations of X and Y. I'm not sure how to simplify cov(XY,Y)=E(XYY)-E(XY)E(Y) =E(XY^2)-E(X)E(Y)^2. If X and Y are...
  23. D

    Complex conjugate variables as independent variables in polynomial equations

    Hi, Is there any trick to treat complex conjugate variables in polynomial equations as independent variables by adding some other constraint equation ? Say, we have polynomial equation $f(x,x^{*},y,...) = 0$. where x^{*} is the complex conjugate of variable $x$. I might think of taking $x = r...
  24. E

    Ideal Gas Law: Exploring Independent Variables

    Homework Statement http://ocw.mit.edu/NR/rdonlyres/Physics/8-044Spring-2004/7A20B047-A049-44D6-96D2-75602F179856/0/notes_dfnitns.pdf There it says tht the number of independent variables of a simple fluid is 2 (see the "Complete Specification" section). But the ideal gas law is PV=NkT which...
  25. J

    Change of independent variables

    [SOLVED] Change of independent variables Homework Statement x = cos\theta Show (1-x^2)\frac{d^2y}{dx^2} - 2x\frac{dy}{dx} + 2y = 0 becomes \frac{d^2y}{d\theta ^2}+ cot(\theta) \frac{dy}{d\theta} + 2y = 0 Homework Equations The Attempt at a Solution dx = -sin(\theta) d\theta ... As a total...
  26. C

    Change of independent variables problem

    http://garciarussellchem.angelfire.com/Photo/Change_of_independent_variables_problem.jpg Homework Statement Homework Equations See Image at above adress The Attempt at a Solution See image at above adress
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