# Questions tagged [orthogonal]

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### How do you know if MANOVA syntax requests for a set of orthogonal contrasts on SPSS? [closed]

How do you know if MANOVA syntax requests for a set of orthogonal contrasts on SPSS? What should be included in the code? What output should there be in the SS?
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### In Probabilistic PCA, Where does the arbitrary orthogonal matrix(rotation matrix) come from?

I'm working on studying Probabilistic PCA based on the paper (Tipping & Bishop, 1999), I can follow the idea that the maximum likelihood function would reach the stationary point when the the ...
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### Alternatives to PCA with orthogonal datasets?

http://blog.audio-tk.com/2008/02/04/dimensionality-reduction-principal-components-analysis/ "It is obvious that PCA does not respect the manifold structure. One has to use 3 dimensions to describe ...
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### Using varimax – rotated PCA for clustering via Gaussian Mixture Model?

After extracting the Principle Components of my data, I apply Gaussian Mixture Models for clustering. I used a subset of the orthogonal basis of the Principle Components and projected my data onto ...
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### Orthogonal contrasts for coefficients of regression

Suppose that we want to test the following hypothesis $H_{0}:b_{1}+b_{3}-2b_{2}=0$ where $b_{1},b_{2},b_{3}$ are coefficient derived from a linear regression.We can see that $H_{0}$ is similar to ...
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### Orthogonality of residuals in linear regression

In multiple linear regression, I came across the statement that both $e$(residual) and predicted $y$ are projections of actual y and $e$ is orthogonal to predicted $y$. I was trying to visualize the ...
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### Which rotation type for principal component regression?

I would like to perform a principal component regression (PCR), but feel a little confused about the rotation type to be used in the principal component analysis (PCA) step. First I perform a PCA to ...