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  2. Degrees of freedom - Wikipedia

    en.wikipedia.org/wiki/Degrees_of_freedom

    In many scientific fields, the degrees of freedom of a system is the number of parameters of the system that may vary independently. For example, a point in the plane has two degrees of freedom for translation: its two coordinates; a non-infinitesimal object on the plane might have additional degrees of freedoms related to its orientation.

  3. Degrees of freedom (statistics) - Wikipedia

    en.wikipedia.org/wiki/Degrees_of_freedom...

    Here, the degrees of freedom arises from the residual sum-of-squares in the numerator, and in turn the n − 1 degrees of freedom of the underlying residual vector {¯}. In the application of these distributions to linear models, the degrees of freedom parameters can take only integer values. The underlying families of distributions allow ...

  4. Degrees of freedom (physics and chemistry) - Wikipedia

    en.wikipedia.org/wiki/Degrees_of_freedom_(physics...

    In physics and chemistry, a degree of freedom is an independent physical parameter in the chosen parameterization of a physical system.More formally, given a parameterization of a physical system, the number of degrees of freedom is the smallest number of parameters whose values need to be known in order to always be possible to determine the values of all parameters in the chosen ...

  5. Generalized coordinates - Wikipedia

    en.wikipedia.org/wiki/Generalized_coordinates

    A degree of freedom corresponds to one quantity that changes the configuration of the system, for example the angle of a pendulum, or the arc length traversed by a bead along a wire. If it is possible to find from the constraints as many independent variables as there are degrees of freedom, these can be used as generalized coordinates. [5]

  6. Degrees of freedom (mechanics) - Wikipedia

    en.wikipedia.org/wiki/Degrees_of_freedom_(mechanics)

    A mechanism or linkage containing a number of connected rigid bodies may have more than the degrees of freedom for a single rigid body. Here the term degrees of freedom is used to describe the number of parameters needed to specify the spatial pose of a linkage. It is also defined in context of the configuration space, task space and workspace ...

  7. Chi-squared distribution - Wikipedia

    en.wikipedia.org/wiki/Chi-squared_distribution

    For the chi-squared distribution, only the positive integer numbers of degrees of freedom (circles) are meaningful. By the central limit theorem , because the chi-squared distribution is the sum of k {\displaystyle k} independent random variables with finite mean and variance, it converges to a normal distribution for large k {\displaystyle k} .

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  9. Analysis of variance - Wikipedia

    en.wikipedia.org/wiki/Analysis_of_variance

    The textbook method is to compare the observed value of F with the critical value of F determined from tables. The critical value of F is a function of the degrees of freedom of the numerator and the denominator and the significance level (α). If F ≥ F Critical, the null hypothesis is rejected.