# Questions tagged [orthogonal]

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### The p value of my OPLS-DA model was -nan(ind), I don't know, what's mean, and the residual MS was infinite, I need help here?

I obtained for the first time strange cross-validation results of my OPLS-DA model, the CV ANOVA was -nan(ind), SD residual was inf, MS residual was inf also, moreover, F test equal to zero. The ...
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### Cross-covariance in context of Andrews plot

As shown in this Cross-Validated post Close curves on an Andrews plot I don't understand how, in the accepted answer, the cross-covariance can be defined as, $$\int_{-\pi}^{\pi}f_xf_ydt$$ Considering ...
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### Coefficients interpretation after recovering raw coefficients from a regression which used orthogonal regressors

I have an unbalanced panel of 747 observations and 15 years. After testing for Pooled, FE and RE, FE is the "best" model. However, I have multicollinearity problems. I can either remove one ...
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### some thought about independence and orthogonal, please comment on this if it's wrong

It seems that linearly independent is totally different from independent of random variable concept. Non-zero vectors Orthogonality must imply linearly independence. In Statistics, the relation of ...
1 vote
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### decision boundaries of random forests

I was told that decision boundaries of RandomForests can be non-orthogonal. See Figure 7-5 in Geron's book Hands-On Machine Learning with Scikit-Learn & TensorFlow p.g. 187 edition 1. This is not ...
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### Proving non-correlation with very disperse distributions

I'm fairly new to statistics and came up with a problem. I have a sample with a variation coefficient CV = 0.517 for variable x, and I want to prove this variable is not correlated with a second ...
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For example, if I have the data $$\begin{array}{l|l|l|l|l|l|l} A & low & & medium & & high & \\ \hline B & standard & new & ... 0 votes 0 answers 177 views ### 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 ... 1 vote 0 answers 190 views ### 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 ... 5 votes 2 answers 9k views ### 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 ... 0 votes 1 answer 421 views ### 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 ... 1 vote 0 answers 333 views ### How is multivariate Gaussian distribution is determined by its second moments alone? The following statement is given in Unsupervised Learning chapter of the book Elements of Statistical Learning. Since the multivariate Gaussian distribution is determined by its second moments ... 11 votes 2 answers 4k views ### The linear transformation of the normal gaussian vectors I am facing difficulty in proving the following statement. It is given in a research paper found on Google. I need help in proving this statement! Let X= AS, where A is orthogonal matrix and ... 1 vote 0 answers 94 views ### Statistics: orthogonality vs uncorrelatedness vs independence [duplicate] In this post I would like someone to summarize and relate these 3 concepts of statistics (in the context of stats). 1) I remember that uncorrelated does NOT imply independence (e.g. the case where ... 0 votes 1 answer 675 views ### Does orthogonal and zero mean of two RV X,Y imply that they are uncorrelated? I understand that two uncorrelated RV X,Y are orthogonal if at least one of both is of zero mean. But can you reverse this statement if you expand the preconditions to both RV X,Y being of zero mean? ... 1 vote 1 answer 243 views ### which angle and axis to chose to get a 90 degrees angle between those 2 vectors I am suddenly puzzled by ho to know (when in 3D) with respect to which axis is the vector being rotated when the dot product between then is =0. for example: if i rotate 90degrees (pi/2 radians) along ... 0 votes 2 answers 238 views ### orthogonality in 2D vs higher dim vectors considering that 2 vectors such as x_2=\begin{bmatrix}1 & 1 \end{bmatrix} and y_2=\begin{bmatrix} -1 & 1 \end{bmatrix} are orthogonal in 2D (i.e. their scalar product is 0) however ... 10 votes 3 answers 4k views ### Why are PCA eigenvectors orthogonal but correlated? I've seen some great posts explaining PCA and why under this approach the eigenvectors of a (symmetric) correlation matrix are orthogonal. I also understand the ways to show that such vectors are ... 1 vote 1 answer 2k views ### Orthogonal initialization of weight matrix Searching for the way to initialize the matrix weights as orthogonal (i.e. W*W^T = I and all the eigenvalues are equal either 1 or -1),(I was wrong) I found this ... 2 votes 0 answers 336 views ### Calculating orthogonalized impulse response functions for vector error corrrection models Background: I am working on orthogonal impuls response functions (OIRFs) for vector error correction models (VECMs). Its an exercise to develop understanding. I am given a bivariate VECM:$$ \Delta ...
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What is the sense or background of orthogonal polynomials (regarding using mixed models)? I would like to know why they shall or should be orthogonal. Is it to build independent sample points? On Is ...
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### How to standardize the data matrix before applying SVD for PCA?

I am trying to enhance the contrast in the images I get after scanning a surface using Thermography (Principal Component Thermography ~Rajic, which is basically an application of Principal Component ...
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### Balancing out in an orthogonal design

A definition of orthogonality in the context of statistics is An experimental design is orthogonal if the effects of any factor balance out (sum to zero) across the effects of the other factors. ...
1 vote
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### Statistically orthogonal - explanation?

I did see the related question here but my question is more related to the actual explanation of the orthogonality itself. So the following design is orthogonal (this is a latin square to be precise):...
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### What is the intercept term in a mixed effects model using orthogonal polynomials to model time?

I'm using a mixed effects model (lmer) in R to model eye-tracking data using orthogonal polynomials (poly(time,3)) for time. The response variable is log(looks to target/looks to competitor). The ...
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### Orthogonality in ANOVA and Regression Analysis

I read the following (Wikipedia) regarding contrast coding of categorical variables: Unlike when used in ANOVA, where it is at the researcher’s discretion whether they choose coefficient values ...
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### Distribution involving orthogonal matrix

If $Y∼N(\mu,I\sigma^2)$ and $Q$ is any orthogonal matrix of appropriate dimension, how do I find the distribution of $QY$?
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### Uses of the Helmert matrix

In chapter 8 of "Matrix Algebra from a Statistician's Perspective", the author describes the construction of an orthogonal matrix, the first row of which is proportional to some row vector of non-...
This post refers to a bivariate linear regression model, $Y_i = \beta_0 + \beta_1x_i$ . I have always taken the partitioning of total sum of squares (SSTO) into sum of squares for error (SSE) and sum ...