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56 views

What is the distribution of this ratio of quadratic forms?

I guess it's F-distribution but I don't know what the solving process it is
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1answer
38 views

Linear Kernel in Baysian Linear Regression

I came up with http://mlg.eng.cam.ac.uk/duvenaud/cookbook/index.html and it is actually very useful. At some point it says If you use just a linear kernel in a GP, you're simply doing Bayesian ...
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0answers
32 views

Comparison between normal glm and glm.nb regression with quadratic term?

Let's say I have a function to simulate data for negative binomial regression: ...
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0answers
11 views

What is “the smallest solution of an equation” mean?

Suppose you have an quadratic equation (n) of q, what's the meaning of this statement "...This implies that q is the smallest solution to equation (n)"? What is the ...
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0answers
13 views

How can a quadratic relationship be written two ways

In this answer, under: "Why include the linear term?" in the answer, it mentions the relationship can be written two ways. Later it says that the point where $x=b$ is the vertex of the parabola. ...
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2answers
61 views

Adding quadratic term changes the sign of the variable

Number of books published in a year (noBook) is my dependent variable and I have independent variables including the age of the author (age). The coefficient of age is positive and it is significant. ...
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1answer
127 views

Transforming a relationship from quadratic to linear

Assume that I'm running a path analysis and I have discovered that certain relationships, empirically, are quadratic rather than linear. In order to model the data as such, I want to transform the ...
2
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1answer
98 views

Comparison of two linear regression models with squared regressors

I need to compare two linear regression models that include the regressors in levels and in squares: $Y=a_1x^2+b_1x+c_1$ and $Y=a_2x^2+b_2x+c_2 $ Specifically, I need to test whether these ...
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2answers
228 views

How to include a linear and quadratic term when also including interaction with those variables?

When adding a numeric predictor with categorical predictors and their interactions, it is usually considered necessary to center the variables at 0 beforehand. The reasoning is that the main effects ...
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2answers
257 views

Sum of two normal products is Laplace?

It is apparently the case that if $X_i \sim N(0,1)$, then $X_1 X_2 + X_3 X_4 \sim \mathrm{Laplace(0,1)}$ I've seen papers on arbitrary quadratic forms, which always results in horrible non-central ...
4
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1answer
85 views

Quadratic form of a bivariate normal

This is a homework problem. Let $(X,Y)\sim N(\mu_1,\mu_2,\sigma^2_1,\sigma^2_2,\rho)$. Show that if $\sigma_1,\sigma_2 >0,|\rho|<1$, then $$ ...
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0answers
78 views

How to do centering if I have a quadratic term?

I have been trying to run a multilevel model with both a linear and a quadratic term for income as my main variables of interest. It looks something like: \begin{eqnarray} ...
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1answer
814 views

Quadratic models with R. The use of poly(..) and I(..) functions (R-language)

What causes the different results below? ...
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0answers
49 views

CVXOPT usage confusion

I am exploring the use of the CVXOPT to solve a constrained linear least square problem. The problem is a standard L2 form minimization problem, but with the condition that all coefficients are ...
0
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0answers
92 views

help deriving quadratic approximation to logistic regression cost function

I am reading Friedman et al's paper Regularization Paths for Generalized Linear Models via Coordinate Descent, specifically the portion on logistic regression. I'm trying to figure out how they ...
1
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2answers
766 views

Expected Value of Quadratic Form

On page 9 of Linear Regression Analysis 2nd Edition of Seber and Lee there is a proof for the expected value of a quadratic form that I don't understand. Let $X = (X_i)$ be an $n \times 1 $ random ...
5
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1answer
209 views

Adding a quadratic term: should I use the squared original (and not the squared standardized?)

In a multiple logistic regression I need to standardize one of the variables because I need to add a quadratic term. Whether I add the quadratic term as the squared original or the squared ...
3
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1answer
123 views

Covariance of $\mathbf{x}$ and $\mathbf{x}^\prime A \mathbf{x}$ when $\mathbf{x} \sim N_{m}(\mu, \Sigma)$

This is part of problem 5.23 in A First Course in Linear Model Theory, Dey and Ravishanker. It was on a previous midterm and I didn't know how to do it, but now I am studying for the final and would ...
5
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1answer
129 views

Optimal sampling to estimate a quadratic function

Suppose I have a quadratic function: $$ f(x) = a^T x + x^TBx $$ with $x \in \mathbb{R}^n$. Given a point $x$ I can measure $f(x)$ up to some noise, that is I can get a measurement: $$ \hat{f}(x) = ...
2
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2answers
309 views

Interpretation for simple slope analysis for curvilinear regression with interaction effects

When regressing income ($Y$) on age ($X$) moderated by gender ($Z$), I not only find significant effects for age ($X$), age squared ($X^2$), gender ($Z$), the interaction of age and gender ($XZ$), and ...
3
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1answer
246 views

Exponentiate a quadratic form, which MVN?

I read that if you have a quadratic $f(x) = ax^2+bx+c$ and providing the leading coefficient $a < 0$, then $e^{f(x)}$ is the pdf of a normal distribution with mean $\mu = -\frac{b}{2a}$ and ...
2
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1answer
78 views

How to specify and estimate the parameters of a model that is quadratic in several variables

I am trying to find how the quadratic model for a multiple featured dataset will be. Suppose that my training set is $X_1,...X_n$ with each $X$ of dimension $4$. Now suppose I want to fit a quadratic ...
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0answers
121 views

What is the distribution of the 'achieved' $R^2$?

I am interested in the distribution of/performing inference on the 'achieved' $R^2$ coefficient in multiple linear regression. Suppose that $y\sim x\beta + \epsilon$ with $\epsilon \sim ...