Questions tagged [multivariate-regression]
Regression with more than one response (dependent) variable.
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Can I use a variable from Principal Component Analysis (PCA) as outcome Y in a linear regression [closed]
(1) I have a set of 3 predictors which predict an outcome Y (BF10 = 10). Each predictor alone does not predict Y (BFincl < 1)
(2) I would like to assess if another predictor can predict those 3 ...
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Effect of Variable Disaggregation on Other Coefficients
Suppose that I do a multivariate regression of variable $Y$ on variables $X_1, X_2, \ldots X_k$ and find coefficients $\beta_1, \beta_2, \ldots \beta_k$.
Consider that variable $X_n$ can be dis-...
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Bayesian multivariate regression with repeated measures
I am trying to estimate variance components (specifically, genetic correlations) using mixed-effects models. My random effect is subject id and my dependent variables y1 and y2 are categorical scores ...
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Predicting continuous variable based on curve
I have a dataset of a set of curves measured at different frequencies, so it is composed of curves as the figure below for example. My dataset has many more curves of course. A curve is associated ...
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Deriving orthogonality of residuals without normal equation?
In my reading I stumbled across this page which seems to prove the expression for the OLS estimator using the fact that $X^T\hat{\varepsilon} = 0$. However I cannot seem to find a proof of this former ...
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Target encoding in linear regression
I have a dataset with the loss rates of each contract as dependent variable. As independent variables I have country (four values), profession (5 values) and income (continous variable). I apply ...
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Understanding the significance of a few results derived in the course of linear regression
I am reading up on linear regression from 18.650 MIT. In the way of explaining it, the professor derives a few results and I have attached them in the image
The first result gets used along with the ...
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A question about linear regression results
This is from the lecture slides of mit 18.650
Here $\sigma^2$ is the variance of the error term ($\epsilon$) in the true model $Y = \beta X + \epsilon$ and $\hat{\beta}$ is the model's estimate of $\...
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Multivariate statistical criterion to select key variables
I have a complex dataset with several predictor variables $X_i$ ($i=1,...,m$) and several outcome variables $Y_j$ $(j=1,...,n$). The problem is that many of the predictor variables are correlated ...
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Terminology: multivariable when multiple levels of categorical variable?
Oftentimes, one sees people use terms such as univariate and multivariate logistic regression, where they clearly refer to number of predictors rather than number of response variables. I know it ...
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Univariate approach to a Bivariate logistic regression
Consider a situation where two independent agents (out of a set of many agents) look at the same problem and attempt to solve it with a yes/no response, obtaining $(Y_{i1},Y_{i2})$ for $i \in \{1,\...
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Multivariate Regression - Categorical and Continuous Outputs?
I am performing process characterization of a welder and want to put together a model of the inputs vs outputs of the system.
Currently I am performing individual multiple regressions with 4 inputs (...
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Logistic regression - When to include or exclude a confounding variable from the model?
I am working on determining if there is an association between a medication (yes/no) and a health outcome (yes/no).
However, the lines between what is a confounding variable to include in the model, ...
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How can I quantify uncertainty for a least squares estimator in a multivariate linear regression with covariance structure?
Suppose that we have
$$\mathbf{y}\sim\text{N}(\mathbf{X}\boldsymbol{\beta},\sigma^2\mathbf{M}\mathbf{M}'),$$ and let $\boldsymbol{\hat{\beta}}$ be the least squares estimator for $\boldsymbol{\beta}$. ...
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How do I find all the independent variables for a time series regression model?
Suppose I have a single time-dependent variable $y_{t}$ (e.g. stock price) and a few hundred independent variables $X_{it}$ with data available for the same time frame as $y_{t}$ (e.g. company revenue,...
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