The quadratic-form tag has no wiki summary.
1
vote
2answers
199 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 ...
4
votes
1answer
120 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
votes
1answer
100 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
votes
1answer
88 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
votes
2answers
204 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
votes
1answer
183 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
votes
1answer
72 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 ...
2
votes
0answers
86 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 ...
