# 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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### Is converting stationary regression output back to non-stationary format valid?

Say I want to do some regression. The thing I am interested in modelling is non-stationary. To have a well behaved noise term I differentiate my dependent and independent variables to something ...
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### Solving an overdetermined system of linear equations, $Ax = b$, using least squares regression.

I'm trying to solve a particularly challenging linear algebra problem. However, unfortunately I have little linear algebra background. The problem is as follows: These linear system of equation [*...
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### Does quadratic risk of MLE for multivariate linear regression go to zero with more and more data?

For the simple multivariate linear regression with Gaussian noise: $\mathbf{Y} = \mathbf{X} \boldsymbol{\beta} + \boldsymbol{\epsilon}$, where $\mathbf{Y} \in \mathbb{R}^n$: the vector of dependent ...
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### Logistic Log-Loss Function with Shrinkage

I have a loss function for optimizing the beta parameters in a logistic regression model. The professor doesn't label $s$ (constant shrinkage factor?) and doesn't explain why we're transposing the ...
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### Regression/forecast with an added linear constraint

I am not sure if I am asking on the right place. But given a set of independent variables $X_i$ and the dependent variable $Y_i = f(X_i, b) +c$, how can I estimate the regression equation given a set ...
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### Understanding and implementing a multilateration localization algorithm.

I’m trying to implement a Time Delay of Arrival Multilateration algorithm. However, I’m struggling to understand the concept on the level necessary to produce an actual implementation. For reference, ...
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### A log-regression in an Economic problem

I have this problem: I have the regression model (that satisfies MLR.1–5): $$log(taxrev_m)=\delta_0+\delta_1 taxrate_m+\epsilon_m$$ for $m=1...98$. What is the interpretation of $\delta_1$ in ...
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### Can we estimate $y = \beta_1\exp(x) + \beta_2\exp(-x) + \beta_3$ using Linear Regression

Can we estimate the following relationship using linear regression. Here, $\beta_1, \beta_2$ and $\beta_3$ are parameters. $$y = \beta_1\exp(x) + \beta_2\exp(-x) + \beta_3$$
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### How to account for increasing probability in odds of winning a competition when each round there is a random single decrease in the non-winner pool?

My Example: Players 1 through n are playing a game and in each round there is one winner and after the winner is determined, one of the non-winners gets randomly taken out of the total players pool (i....
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### Nearest Neighbor regression for non iid data (for instance for stationary ergodic Markov)

For part of my work I am using k-NN regression for $\{X,Y\}$ be jointly stationary and ergodic Markov. I am looking for some results on the consistency of NN regression for estimating $E[Y|X=x]$, i.e.,...
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### Least square with a logarithm of determinant regularization

I am trying to fit a quadratic function to 2D data. Namely, I want to find the solution to a problem similar to: $$\arg \min_A \sum_{i=1}^N (\mathbf{x}_i A \mathbf{x}_i - b_i)^2,$$ with $A$ a ...
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### Coefficient of Determination and Standard Error of the Model

Background explaining standard concepts and standard terminology used in linear regression and analysis of variance: It will be supposed that one has data points $(X_i,Y_i),\, i = 1,\ldots,n.$ The ...
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### asymptotic equivalence for nonparametric Regression

I would like to find some good literatur for asymptotic equivalence between the nonparametric multivariate regression model (with equidistant design points and non gausian errors) and the ...
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### Closed form solution for Restricted Weighted Least Squares

From Greene, we know that the closed-form solution of a restricted least squares is: $\beta_{Constrained} = \beta_{Uncon} - (X'X)^{-1}R'[R(X'X)^{-1}R']^{-1}(R\beta_{Uncon}-r)$. Is there any similar ...
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### Is there a way to “estimate” an indefinite integral?

I'm working with empirical data and have estimated the non-linear marginal effects of my independent variable in my dependent variable. Let's call these marginal effects $\frac{dy}{dx}(x)$. Is there ...
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### Fit curve to points

I have set of (approx. 1500) points from the measurement that begins with peak and than slowly decreases to zero (blue). I would like to define the formula of the curve that fits the trend of the ...
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