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If the data points are normally distributed with mean 0 and variance , then the residual sum of squares has a scaled chi-squared distribution (scaled by the factor ), with n − 1 degrees of freedom. The degrees-of-freedom, here a parameter of the distribution, can still be interpreted as the dimension of an underlying vector subspace.
The set of all velocities through a given point of space is known as the tangent space, and so df gives a linear function on the tangent space: a differential form. With this interpretation, the differential of f is known as the exterior derivative , and has broad application in differential geometry because the notion of velocities and the ...
df (abbreviation for disk free) is a standard Unix command used to display the amount of available disk space for file systems on which the invoking user has appropriate read access. df is typically implemented using the statfs or statvfs system calls .
df (Unix), a Unix command to report disk space usage by a filesystem; Dairy free, identifying products that contain no milk; Decapacitation factor, in biochemistry; Degrees of freedom, various measures in statistics, mathematics and physics; Density function, a mathematical function with a wide range of applications; Dielectric loss
The original notation employed by Gottfried Leibniz is used throughout mathematics. It is particularly common when the equation y = f(x) is regarded as a functional relationship between dependent and independent variables y and x.
In physics, the dissipation factor (DF) is a measure of loss-rate of energy of a mode of oscillation (mechanical, electrical, or electromechanical) in a dissipative system. It is the reciprocal of quality factor, which represents the "quality" or durability of oscillation.
Note that at each p, the differential df p is not a real number, but a linear functional on tangent vectors, and a prototypical example of a differential 1-form. Since any vector v is a linear combination Σ v j e j of its components, df is uniquely determined by df p (e j) for each j and each p ∈ U, which are just the partial derivatives of ...
In mathematics, the derivative is a fundamental tool that quantifies the sensitivity to change of a function's output with respect to its input. The derivative of a function of a single variable at a chosen input value, when it exists, is the slope of the tangent line to the graph of the function at that point.