A quadratic form is a homogeneous polynomial of order two.

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### covariance of squared projections

Given a vector $x$ of independent mean-zero random variables, and two nonrandom orthogonal unit vectors $u,v$, does $u'v=0$ imply $cov(x'uu'x,x'vv'x)=0$? If so, what is the proof? If not, what happens ...
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### Ridge and Quadratic Programming for Portfolio Norm Optimization

Much like this post: Quadratic Programming and Lasso, I'm trying to integrate RIDGE Penalty in a dedicated quadratic solver. In my case, I am working with quadprog from MATLAB. Unlike LASSO where you ...
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### Interpreting moderated quadratic effect in mixed effect models

I study the effect of the same stimulus ($X$), displaced in 4 different conditions (categorical $M$, categories=High, Medium, Low, in addition there is "Control" condition, as a reference ...
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I'm conducting a multiple OLS regression. My main model contains a significant effect (p < .5) of x on y. I want to test in a robustness check whether x is related to y in a curvilinear/quadratic ...
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### Online estimation of a quadratic form

I have a functional form $y = x^T Q x + b^T x + c$, with $Q, b, c$ to be estimated, $x \in \mathbb{R}^n$ and $n$ varies around 10-20, depending on the problem. $x$ is sampled from a known Gaussian ...
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### How to plot quadratic model? [closed]

I have fit a polynomial glm in R with x and x^2 as the predictor of interest. ...
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### How to measure correlation in polynomial regression?

I have two variables that have a quadratic relationship. I can fit such an equation and get the R-squared, but how can I measure the degree to which the two variables are associated? Does a ...
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### Interpreting the results of using an ordered variable among independent variables in a model

I am running an ordered probit model since the dependent variable is ordered (using "MASS" package in R). Also, there is an ordered variable among the independent variable. It shows the results as L,...
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### When building a multiple linear regression model, is it possible to form models with both linear and non-linear (quadratic) relationships?

Through backward elimination, I have reduced my model from 6 linear factors to 1, accounting for 68% of variance. I have also found that by squaring one of the variables I previously included, that ...
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### Concavity of SVM dual formulation

These notes have derived the following dual formulation of the SVM optimisation problem using KKT conditions that I have followed It then states that the objective function is quadratic and concave (...
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### R: quadratic term in a beta regression

My hypothesis is that along a gradient of habitat structural complexity 'a', the fish diversity 'y' increases until an optimum level but decreases after that (which kinda I have noticed in the graphic ...
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### Why do we use quadratic form for random vectors? [closed]

I am studying linear regression. I have studied this in the past, but this is my first time exposing myself to the matrix form of multiple linear regression. My matrix algebra/linear algebra skills ...
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### Quadratic polynomial - how to test correlation between x and y?

I have one dependent variable (fish abundance) and one independet variable (time), both continuous. I would like to test the correlation between them because I expect that the abudance changes over ...
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### Mean and Variance of SSE

First, let \begin{equation} SSE = \overrightarrow{y}'(I - H) \overrightarrow{y} \end{equation} where \begin{equation} \overrightarrow{y} \sim MN(\textbf{X} \overrightarrow{\beta}, \sigma^{2}I) \\ H ...
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### Test of concavity for repeated measures data

First question here. I'm trying to figure out what statistical test is appropriate for testing whether a series of data is concave or convex. Specifically, this is coming from a human subjects ...
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### Interpretation of Cox Hazard Model with quadratic term

I am having trouble finding information on how to interpret coxph model hazard ratios with a quadratic term. Some of my variables are continuous count data, whereas others are continuous percentages. ...
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Is it possible to fit a quadratic or polynomial model with this type of data? Two inputs, input one is a temperature sensor: Input two is a valve opening on a scale from 0-100: This is a scatter ...
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