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@@ -621,8 +621,9 @@ $$
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<p>
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For a linear fit we don't need to invert a matrix!!
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Defining
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$$
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\gamma = \sum_{i=0}^{n-1}\frac{n-1}{\sigma_i^2},
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\gamma = \sum_{i=0}^{n-1}\frac{1}{\sigma_i^2},
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$$
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@@ -642,7 +643,7 @@ $$
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\gamma_{xy} = \sum_{i=0}^{n-1}\frac{y_ix_{i}}{\sigma_i^2},
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$$
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and show that
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we obtain
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$$
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\beta_0 = \frac{\gamma_{xx}\gamma_y-\gamma_x\gamma_y}{\gamma\gamma_{xx}-\gamma_x^2},
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$$
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@@ -652,7 +653,7 @@ $$
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$$
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<p>
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The LSM suffers often from both being underdetermined and overdetermined in the unknown coefficients \( \beta_i \). A better approach is to use the Singular Value Decomposition (SVD) method discussed below. Or using Lasso and Ridge regression. See below.
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This approach (different linear and non-linear regression) suffers often from both being underdetermined and overdetermined in the unknown coefficients \( \beta_i \). A better approach is to use the Singular Value Decomposition (SVD) method discussed below. Or using Lasso and Ridge regression. See below.
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</div>
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