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[DOC File]Derivation of the Ordinary Least Squares Estimator
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where n is the total number of observations and ∑ is the summation operator. The above equation is known as the sum of squared residuals (sum of squared errors) and denoted SSE. Using the definitions of and , the SSE becomes ... Taking the partial derivative of equation (7) w.r.t. and setting the resulting equations equal to zero, the ...
derivative of a sum

[DOC File]Notes 10: Conductor sizing & an example
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Before differentiating, pull out the term from the summation that corresponds to the bus injection being computed. When differentiating a sum of terms with respect to a particular variable, the resulting derivative will be non-zero only for those terms in which the variable appears.
partial derivative of summation

[DOC File]University of Rhode Island
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Take the derivative of X(z) with respect to z: Thus, Homework 5a: (1%) Prove the Summation in time-domain property (#8): ROC: at least (Hint: Use the result from Example 1. Arrange the time-domain expression as the convolution between x[n] and u[n].) Signal Flow Graph. Example 1: For the pole-zero plot shown on the right, find H(z) and realize ...
derivative of summation formula

[DOC File]Solution of the Diffusion Equation
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For large times, the exponential term in the summation of equation [85] will vanish; removing this summation from equation [85] gives the large time limit for the solution shown in equation [87]. [87] At this point the change in u with time is . This derivative is not a function of x or t.
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[DOC File]Sums of Integer Powers--The Faulhaber Expansion
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The kernel of this latter summation can be expanded by the binomial theorem, and then the order of the two summations exchanged: Sp(n+1) = jk = jk. The limits of the summation variable k here are defaulted to – to +; since the binomial coefficient is zero outside the …
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[DOC File]California State University, Northridge
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We can make one further simplification to equation [1-44]. In the two derivatives on the left-hand side we have terms of the form ujduj. From the summation convention, we know that this term, with its implied summation, is equal to udu + vdv + wdw = d(u2/2) + d(v2/2)+d(w2/2) = …
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Derivative of a summation