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Least Squares Fitting--Polynomial -- from Wolfram MathWorld

Generalizing from a straight line (i.e., first degree polynomial) to a kth degree polynomial y=a_0+a_1x+...+a_kx^k, (1) the residual is given by R^2=sum_(i=1)^n[y_i-(a_0+a_1x_i+...+a_kx_i^k)]^2. (2) The partial derivatives (again dropping superscripts) are (partial(R^2))/(partiala_0) = -2sum_(i=1)^(n)[y-(a_0+a_1x+...+a_kx^k)]=0 (3) (partial(R^2))/(partiala_1) = -2sum_(i=1)^(n)[y-(a_0+a_1x+...+a_kx^k)]x=0 (4) (partial(R^2))/(partiala_k) =...



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Least Squares Fitting--Polynomial -- from Wolfram MathWorld

https://mathworld.wolfram.com/LeastSquaresFittingPolynomial.html

Generalizing from a straight line (i.e., first degree polynomial) to a kth degree polynomial y=a_0+a_1x+...+a_kx^k, (1) the residual is given by R^2=sum_(i=1)^n[y_i-(a_0+a_1x_i+...+a_kx_i^k)]^2. (2) The partial derivatives (again dropping superscripts) are (partial(R^2))/(partiala_0) = -2sum_(i=1)^(n)[y-(a_0+a_1x+...+a_kx^k)]=0 (3) (partial(R^2))/(partiala_1) = -2sum_(i=1)^(n)[y-(a_0+a_1x+...+a_kx^k)]x=0 (4) (partial(R^2))/(partiala_k) =...



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https://mathworld.wolfram.com/LeastSquaresFittingPolynomial.html

Least Squares Fitting--Polynomial -- from Wolfram MathWorld

Generalizing from a straight line (i.e., first degree polynomial) to a kth degree polynomial y=a_0+a_1x+...+a_kx^k, (1) the residual is given by R^2=sum_(i=1)^n[y_i-(a_0+a_1x_i+...+a_kx_i^k)]^2. (2) The partial derivatives (again dropping superscripts) are (partial(R^2))/(partiala_0) = -2sum_(i=1)^(n)[y-(a_0+a_1x+...+a_kx^k)]=0 (3) (partial(R^2))/(partiala_1) = -2sum_(i=1)^(n)[y-(a_0+a_1x+...+a_kx^k)]x=0 (4) (partial(R^2))/(partiala_k) =...

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      Least Squares Fitting--Polynomial -- from Wolfram MathWorld
    • DC.Title
      Least Squares Fitting--Polynomial
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    • DC.Description
      Generalizing from a straight line (i.e., first degree polynomial) to a kth degree polynomial y=a_0+a_1x+...+a_kx^k, (1) the residual is given by R^2=sum_(i=1)^n[y_i-(a_0+a_1x_i+...+a_kx_i^k)]^2. (2) The partial derivatives (again dropping superscripts) are (partial(R^2))/(partiala_0) = -2sum_(i=1)^(n)[y-(a_0+a_1x+...+a_kx^k)]=0 (3) (partial(R^2))/(partiala_1) = -2sum_(i=1)^(n)[y-(a_0+a_1x+...+a_kx^k)]x=0 (4) (partial(R^2))/(partiala_k) =...
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      Generalizing from a straight line (i.e., first degree polynomial) to a kth degree polynomial y=a_0+a_1x+...+a_kx^k, (1) the residual is given by R^2=sum_(i=1)^n[y_i-(a_0+a_1x_i+...+a_kx_i^k)]^2. (2) The partial derivatives (again dropping superscripts) are (partial(R^2))/(partiala_0) = -2sum_(i=1)^(n)[y-(a_0+a_1x+...+a_kx^k)]=0 (3) (partial(R^2))/(partiala_1) = -2sum_(i=1)^(n)[y-(a_0+a_1x+...+a_kx^k)]x=0 (4) (partial(R^2))/(partiala_k) =...

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      Least Squares Fitting--Polynomial -- from Wolfram MathWorld
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      Generalizing from a straight line (i.e., first degree polynomial) to a kth degree polynomial y=a_0+a_1x+...+a_kx^k, (1) the residual is given by R^2=sum_(i=1)^n[y_i-(a_0+a_1x_i+...+a_kx_i^k)]^2. (2) The partial derivatives (again dropping superscripts) are (partial(R^2))/(partiala_0) = -2sum_(i=1)^(n)[y-(a_0+a_1x+...+a_kx^k)]=0 (3) (partial(R^2))/(partiala_1) = -2sum_(i=1)^(n)[y-(a_0+a_1x+...+a_kx^k)]x=0 (4) (partial(R^2))/(partiala_k) =...

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      Least Squares Fitting--Polynomial -- from Wolfram MathWorld
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      Generalizing from a straight line (i.e., first degree polynomial) to a kth degree polynomial y=a_0+a_1x+...+a_kx^k, (1) the residual is given by R^2=sum_(i=1)^n[y_i-(a_0+a_1x_i+...+a_kx_i^k)]^2. (2) The partial derivatives (again dropping superscripts) are (partial(R^2))/(partiala_0) = -2sum_(i=1)^(n)[y-(a_0+a_1x+...+a_kx^k)]=0 (3) (partial(R^2))/(partiala_1) = -2sum_(i=1)^(n)[y-(a_0+a_1x+...+a_kx^k)]x=0 (4) (partial(R^2))/(partiala_k) =...
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