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1 vote

Understanding the multicollinearity issue in relation to linear regression

When $X$ is nearly multicollinear, $X^\top X$ will have at least one eigenvalue close to 0. As a consequence, $(X^\top X)^{-1}$ will have at least one very large eigenvalue. Since $(X^\top X)^{-1}$ ...
Steven Gubkin's user avatar
1 vote
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Understanding the multicollinearity issue in relation to linear regression

Maybe the two-regressor case helps to build intuition (let us omit the constant, which does not have covariances). Then, $$ X'X=\begin{pmatrix}\sum_ix_{i1}^2&\sum_ix_{i1}x_{i2}\\ \sum_ix_{i1}x_{i2}...
Christoph Hanck's user avatar
2 votes

Intuition behind between-group covariance matrix from MANOVA?

When considering the computationally efficient forms, let $L$ $(l=1,2,\ldots,L)$ be the number of treatment groups, $\mathbf{B}$ be the variable-by-variable $p \times p$ between-group sum of squares ...
Leif Peterson's user avatar
2 votes

Is there a way to use the covariance matrix to find coefficients for multiple regression?

The answer above is complete and great. The following aims to complement the answer with a different perspective. I also want to bring attention to the fact that using covariances to estimate ...
Tomas da Nobrega's user avatar

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