# Questions tagged [multivariate-regression]

Regression with more than one response (dependent) variable.

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### How do we know adding an uncorrelated variable to a regression will not change existing coefficients?

Say I have a regression with 3 independent variables and I decide to introduce a 4th variable and rerun the regression. A previous post states that the coefficient on an original variable will change ...
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### Running a multivariate multiple regression with different numbers of observations of the outcomes

Say I have two dependent variables, y1 and y2, and two predictors, x1 and x2. I want to test whether y1 is affected by x1, and whether y2 is affected by x1 or x2. I have less observations of y2 and x2 ...
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### Is single-output regression the same as univariate?

Similarly, is multi-output regression the same as multivariate regression?
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### Whither multivariate regression?

I've been handed someone else's data (again). It's measurements of six proteins' levels from 20 human brain samples, 5 each of different stages of a disorder. I'd like to run a multivariate regression,...
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### What to do with statistically insignificant dummy/categorical variables? [duplicate]

From the research I've done the common answer is that you can not remove insignificant dummy variables from a regression. I'm having a hard time finding academic papers or books that back up this ...
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### Correlation in the residuals of a multivariate linear regression

I'm using a multivariate multiple linear regression model to predict 4 scalars out of multiple regressors. I'm not sure if this model is a good one and now I'm trying to asses the validity of the ...
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### Multivariate zero_one_inflated_beta regression

I want to run a zero_one_inflated_beta regression with brms on the following multivariate formula: ...
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I'd like to simulate data from a bivariate normal distribution to a regression problem. In other words, let $X = (X_1, X_2)$, where $X_1$ and $X_2$ be two matrices $n \times 1$. $X_1\sim N(3, 2)$ and $... 0answers 53 views ### calculating log likelihood for multivariate linear regression using R I want to calculate a loglikelihood for multivariate linear regression. I’ve been calculated the log likelihood using multiple linear regression. ... 0answers 37 views ### Variance-covariance matrix of multivariate response, with censored values: MCMCglmm alternatives? I have a dataset I need to analyze in which I'm interested in the relationships among several variables, after accounting for covariates that may affect some of those variables. More specifically, I ... 1answer 79 views ### Linear regression with stochastic gradient descent p-values Is there any way to get summary statistics (p-value specifically) for the results of a multivariate linear regression ($y = X\beta + \epsilon)$using gradient descent? Most online library ... 0answers 18 views ### intervention analysis with multivariate regression Does intervention analysis make sense when one has multiple external regressors? How would one know if say, a level shift, is caused by a combination of external regressors or by a change in a law ... 0answers 16 views ### multivariate multiple regression - predicting vectors with different lengths Obviously, multivariate multiple regression is the method of modeling multiple responses, or dependent variables (aka a vector), with a single set of predictor variables. Which techniques can I use ... 0answers 22 views ### Multivariate sparse regression - selective predictors What do I do to find predictors that are ONLY/mostly related to one of several continuous response variables ? E.g., if you have (continuous) outcomes y1,y2,y3 and predictors a,b,c,... and a is ... 1answer 106 views ### Binary logistic regression with two dependent variables I have a continuous independent variable, X, and two binary dependent variables, Y and Z. I'm trying to run a binary logistic regression that models the correlation between Y and Z. X = age, while Y ... 0answers 28 views ### multivariate multiple regression with probabilities as the dependant variable I have a problem that involves multiple dependant variables, where each dependant variable is a probability and for each observation the probabilities sum to 1.0. I also have a range of independent ... 0answers 29 views ### Estimating parameters of multivariate regression using the maximum likelihood method with a uniform distribution of residuals? Representation of regression in a matrix form: $$Y = XA + E,$$ where:$X$- independent variables,$Y$- dependent variables (observations),$E$- errors, which have a uniform distribution,$A$- ... 0answers 37 views ### OLS regression with multiple dependent variables that are correlated with each other Suppose I want to see the impact of an explanatory variable$X$on two different dependent variables:$Y_1$and$Y_2$. Suppose also that I find that$Y_1$and$Y_2$are correlated. Assuming that all ... 2answers 163 views ### Predict a vector of values with constraints? [duplicate] I am aware of a variety of methods for simultaneously predicting multiple outcomes known sometimes as multivariate regression/analysis. However, my situation is a little more special. I am trying to ... 0answers 47 views ### What is the correct way to follow up a multivariate multiple regression? I recently conducted a study in which I used a series of multiple linear regressions to predict different outcomes (y1-y6) using the same set of predictor variables (x1-x8). My hypotheses were that ... 1answer 196 views ### Multivariate (Multi-responce) for negative binomial (GLM) in R I developed a multivariate linear regression using lm() function in R. However, I am having trouble coding a Multivariate model in R for glm(), especially for the negative binomial. Can anyone point ... 1answer 42 views ### Hypothesis testing: significance i conducted a survey that aims to find out if Australians prefer Australian phones over Chinese phones. My hypothesis states: Australians prefer Australian phones over Chinese phones This was ... 0answers 25 views ### Question about the correlation between residual/error and regressors [duplicate] In multivariate regression: Why can the sample correlation between the error term and a regressor be ≠ 0, but the sample correlation between the residual and a regressor has to be = 0? 0answers 58 views ### Write Lack-of-fit Sum of Squares in Quadratic Form Let \begin{equation} SSLF = \sum_{i=1}^{m}n_{i}(\bar{y_{i}} - \hat{y_{i}})^{2} \end{equation} then \begin{equation} \sum_{i=1}^{m}n_{i}(\bar{y_{i}} - \hat{y_{i}})^{2} = n(\bar{\overrightarrow{y}} -... 0answers 29 views ### Integrated mixed model testing correlation and difference in correlation across factors I'm currently performing the following analysis : Computing$r_j(Y_{ij}, X_{ij})$for each design cell (factor with level 1 or 0 for each unit) Estimating effect of factor on$r(Y,X)$with a linear ... 1answer 26 views ### Null hypothesis for individual coefficient's p-value in multivariate logistic regression When calculating$p$-values for individual coefficient$a_i$(for variable$X_i$) in a multivariate logistic regression, is the null hypothesis that all$a$'s are zero? that$a_i$is zero and others ... 0answers 42 views ### Testing for Heteroscedasticity of Multivariate Multiple Regression [closed] I want to test for heteroscedasticity on a regression model with multiple dependent variables using R. I want to see if the indenpendent variable has an effect on the variance of all of the dependent ... 1answer 77 views ### Linear regresson with four values as input and two values as output I have the following problem for a personal project of mine: I am solving a system of two differential equations that has 4 changing parameters. The output are two vectors of numbers. Let's say I am ... 1answer 147 views ### Multivariate regression vs. multiple univariate regression models This is a naive question, but I am a little confused over the term "multivariate" regression. And note this question does not (to my knowledge) pertain to "multiple" regression. When people use the ... 0answers 31 views ### multivariate linear regression without b_0 [duplicate] I created a multivariate regression following the scheme $$y = \beta_0 + \sum^n_{i=1}\beta_i*x_i$$ and got an average deviation ofaround 5%. When I tried the regression without the$\beta_0$I got a ... 0answers 54 views ### multi-response outcome: multivariate or univariate regression? I have a dependent variable which represents participants' responses on 20 words, coded as 1 = correct , 0 = incorrect Question: I am keeping the regression as univariate for now (as far as dependent ... 0answers 229 views ### multivariate normal distribution with mean vector 0 and covariance matrix Σ I am newby in statistics and I have huge data with "p" variables and "n" samples. My data is a two dimensional matrix with "n" columns (each column is a sample) and "p" rows (each row is a variable). ... 1answer 67 views ###$R^2$and p-value for multivariate linear regression with confounders I am working on a project where I am interested in the following variables: Dependent variables:$y_1,\, y_2,\, y_3,\, y_4,\, y_5$(continuous) Independent variables:$x_1,\, x_2, \ldots,\, x_{18}$... 1answer 92 views ### Conjugate priors for dynamic model$x_{t+1}=Ax_{t}+\eta_t$What conjugate priors do we have for the model(multivariate)$x_{t+1}=Ax_{t}+\eta_t$, where$\eta_t\overset{iid}\sim N(0,\Sigma)$? I was thinking of using$\tilde{x}=Diag[x_1,...,x_{n-1}]$,$\tilde{y}...
Say I do principal component analysis on $n$ variables, and I sort the fractions of variance explained to find the largest. What is the probability distribution for this figure? For context I just ...