# Questions tagged [regression]

This tag is for questions on (linear or nonlinear) regression, which is a way of describing how one variable, the outcome, is numerically related to predictor variables. The dependent variable is also referred to as $~Y~$, dependent or response and is plotted on the vertical axis (ordinate) of a graph.

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### Multilinear or Tensor Regression?

Given input data $x_t\in \mathbb{R}^n$ and output data $y_t\in\mathbb{R}^m$, the closed form solution to $\min_A \sum_t \|y_t - Ax_t\|^2_2$ is given by $A = (XX^T)^{-1}XY^T$ where $x_t$ form the ...
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### Estimating Spline curve by OLS. Is a good idea to fix the knots at Chebyshev sites?

I am writing my master's degree thesis on a novel method for fixing knots in an adaptive way and while reading the literature I've found many references to the so-called Chebyshev sites. This sites or ...
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### Deriving the odds ratio of a 3-way interaction logistic regression model

Suppose a logistic regression model has three binary explanatory variables $x_1$, $x_2$ and $x_3$ used to estimate the probability of success. This model includes all three main effects, the three $2$-...
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### Elastic Net as LASSO

Good evening everybody, I need help with an excercise on Regularised Regression. What I need to do is turn an Elastic-net problem: argmin_\omega \Vert y-\Phi(x)^T \omega \Vert_2^2 + ...
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### From Ng video: Using feature normalization with polynomial regression

In this video on machine learning by Andrew Ng, called "Features and Polynomial Regression", at time 4:34, he mentions the possibility of feature normalization in polynomial regression. By which he ...
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### Linear regression with feature representation confusion - is design matrix column space the feature space?

I am trying to visualise the geometry of linear regression with feature representation. I have a regression problem with $n$ data pairs $\mathcal{D}:=\{(\mathbf{x},y)_{i}\}_{i=1}^{n}$, independent ...
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### Integration by parts with empirical measure

I'm currently reading through the paper Asymptotic normality of nearest neighbor regression function estimates and am struggling to understand the asymptotic equalities that were shown in the proof of ...
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### Minimization problem with latent function and splines

I have a dataset consisting of pairs $(x_i, y_i)$. I want to determine the function $f$, so $$f(x)f(y) = 1$$ with the constraint that $f(x) \leq x$, $f'(x) \geq 0$ and $f''(x) \geq 0$. I was ...
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### Finding an interval by curve fitting

Suppose I have a function like the one in this graph: I have samples $x_i,y_i$ from this function, with some Gaussian noise (like the black points). The function behaves, in some interval $[a,b]$, ...
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### Statistical limitations of conducting nonlinear regression of $x$ vs.$f(y)$ as opposed to $y$ vs. $f(x)$

I derived a solution to a physics problem using a method of analysis that gives me an inversed relation, the independent variable $t$ expressed explicitly in terms of a nontrivial algebraic set of ...
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### What are tolerance intervals for linear regression?

What are tolerance intervals for linear regression. I am trying to break down this paper into general terms, not a specific problem. What are they used for? What is the basic principles behind this ...
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### Linear regression where the error is modified

I have a set of coordinates $\{(x_1,y_1),(x_2,y_2),\ldots,(x_n,y_n)\}$ , where for every $i<n$, $$x_i \ll x_{i\space+\space1}\space\space\text{and}\space\space y_i\ll y_{i\space+\space1}$$ I know ...
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### Linear regression with integer function

I have a dataset, that only takes integer values ($x$ and $y$ coordiantes). E.g. my data is the following: $x = (1,2,2,3,3), y = (1,2,3,3,4)$. I want to make a linear regression through the data, i.e....