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mhjensen
2018-08-24 06:35:38 +02:00
parent 3a6bdf1450
commit dc7ce90ee7
20 changed files with 159 additions and 2504 deletions
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@@ -621,8 +621,9 @@ $$
<p>
For a linear fit we don't need to invert a matrix!!
Defining
$$
\gamma = \sum_{i=0}^{n-1}\frac{n-1}{\sigma_i^2},
\gamma = \sum_{i=0}^{n-1}\frac{1}{\sigma_i^2},
$$
@@ -642,7 +643,7 @@ $$
\gamma_{xy} = \sum_{i=0}^{n-1}\frac{y_ix_{i}}{\sigma_i^2},
$$
and show that
we obtain
$$
\beta_0 = \frac{\gamma_{xx}\gamma_y-\gamma_x\gamma_y}{\gamma\gamma_{xx}-\gamma_x^2},
$$
@@ -652,7 +653,7 @@ $$
$$
<p>
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.
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.
</div>