# Questions tagged [regression]

Techniques for analyzing the relationship between one (or more) "dependent" variables and "independent" variables.

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### Recommend a research-level book on econometrics, particularly for the theory of linear regression for random regressors X

Can anyone suggest a research monograph (with proofs or at least detailed references) for econometrics? Specifically, I'm looking to learn about the theory of linear regression and all the usual ...
1 vote
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### How does a 'basic' panel regression model with fixed effects looks like?

I have modeled a basic panel data regression model under fixed effects in Stata. Specifications and results are clear. But, now I want to write down the model in lets say general formation. I spent ...
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1 vote
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### Backend process of lmer function [closed]

I am trying to learn mixed models using lmer function and I am able to use it. But I am not able to understand what is going on in the backend like how it is taking care of fixed effects and random ...
1 vote
18 views

### Is maximal spectral entropy of residuals a poor loss function because phase information is lost?

Suppose I define a custom loss function SpectralEntropy as follows: ...
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### Should we scale the data if our response(Y) is numeric, a large number, and 99% of other variables are dummy variables?

Our response variable is something like Sales which should be very large(Mean at the million level), and one predictor is also numeric but with mean at ten thousand ...
• 309
1 vote
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### What is the hat matrix and why is it inappropriate for GLMM standardized residuals?

When I run this code to plot standardized residuals for a standard logistic regression: ...
18 views

### Two different answers when calculating MSEP

I would appreciate help with understanding why I get two different answers when I calculate MSEP (mean square error prediction) in two different ways using R, both for simple linear regression and ...
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### How does ridge regression reduce the variance of the estimates of $\beta$

In the scikit-learn library, Ridge class, there is a note that reads: "Regularization improves the conditioning of the problem and reduces the variance of the estimates." Given the ...
• 111
1 vote
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### Application of Maximum Likelihood estimation (MLE) to the step of Feasible Generalized Least Square (FGLS)

I have the following regression $$y = X\beta +u$$ where $y$ and $u$ are $(n\times 1)$ and $X$ is a fixed $(n \times k)$ matrix with full column rank and $\beta$ is an unknown $(k\times 1)$ vector of ...
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1 vote
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### Is standarization necessary for ridge regression?

Is variable normalization necessary in Ridge regression (for both X and y)? If so, what happens (mathematically) if we don't do it?
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### Showing the unbiased estimator of variance for GLS estimator

I have the following regression $$y = X\beta +u$$ where $y$ and $u$ are $(n\times 1)$ and $X$ is a fixed $(n \times k)$ matrix with full column rank and $\beta$ is an unknown $(k\times 1)$ vector of ...
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