# Questions tagged [multiple-regression]

Regression that includes two or more non-constant independent variables.

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### Partial derivative of a linear regression with correlated predictors

Let's set up the situation of having some $Y$ that I think depends on a linear combination of $X_1$ and $X_2$. I could fit a regression model: $$y_i = \beta_0 + \beta_1x_{i1} + \beta_2x_{i2}$$ We ...
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### Logistic regression model for the probability of a don’t know response and a separate ordinal model for the ordered categories

Questions: A response scale has the categories (strongly agree, mildly agree, mildly disagree, strongly disagree, do not know). A two-part model uses a logistic regression model for the probability ...
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### Gaussian Process Regression for High Dimensional Data: Vanishing predicted y values

I am working on a dataset with roughly 196 dimensions. I have been trying to fit Gaussian Process Regression into this dataset but it does not perform well. Mathematically speaking, I found out that ...
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### Is it valid to use company/year combinations for (financial) data analysis?

I want do to a multiple regression analysis on some financial data. Sadly I only have 30 observations (the 30 different companies) and I would like to have more. My friend asked me why I don't add the ...
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### Statistical illusion? What's statistically happening, when regression analysis results get significant only with all predictors and interaction term?

I got a research question, where the hypothesis (derived from theory) postulates, that the relationship between predictor X and outcome Y is moderated by W (X+W+X*W -> Y). All variables are sums of ...
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### Drivers that should be positively correlated to Y have a negative correlation with the residuals?

In my data set it's clear that X,Y, and Z are positively correlated with A, since they have a strong correlation (close to 1) when I test the correlation in Excel. However, I took the regression of ...
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### Lagged (in)dependent variables: 2 time periods

Summary I have a dataset with observations regarding an industrial process in two time periods. My goal is to find predictors of future performance, and I am wondering whether panel data regressions ...
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### Comparing two logistic regressions

I am working on creating a predictive model using logistic regressions. I am hoping to compare two different populations, using the same set of variables but different data sets with different sample ...
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### IHME Model Chris Murray [closed]

For Coronavirus death projections, does anyone know of any documentation on how Chris Murray produced the model?
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### Liklihood ratio test and linear mixed effects regression

I have a data set which includes sex, age, and 5 polygenic scores as independent variables, with 16 dependent variables. I have constructed univariate linear mixed effects regression models and ...
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### Why should $n$ be greater than $k$ for multiple linear regression?

For multiple linear regression we have $n$ observations of the $k+1$ variables, $$y_i = \beta_0 + \beta_1x_{i1}+ ... + \beta_kx_{ik} + \epsilon_i \text{ for i in 1,...n }$$ $n$ should be ...
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### ANCOVA, Covariates, & Variable Selection

I just want to preface this question by saying: I've searched extensively for answer elsewhere without luck. If, however, you think this question has been answered elsewhere please point me in the ...
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### Model specification through machine learning (neural network)

Assumptions: I observe the entire population N, so in my setting there is no overfitting, a model that fits perfectly with my data is a "perfect" model I know that the variables at play are the only ...
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### How to fix heteroscedasticity (funnel shape)?

I am running a mlr in python on a dataset with 2D feature vectors, X1 and X2 on a single response, Y. The data ends up being funnel-shaped, as below: X1 v Y, with the colors being X2. It was ...
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### In a linear regression, how can I test whether a given variable is driving the regression's predictive power?

Let's say I have at linear regression of income per capita (PPP) and other variables on food-prices I suspect that the variable that is driving most, if not all, the prediction power of the ...
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### Maximum likelihood estimation using R [closed]

I have a multiple linear regression, that I want to estimate using a MLE approach. I would like to make the fit using a Beta distribution, with parameters u and v. How can I do this using R?
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### Comparing highly correlated predictors in log-binomial regression

I'm trying to figure out the best way to assess which of my highly correlated independent variables best predicts my dependent variable (y), a binary variable coded ...
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### R utility for pulling out parameters for individual variable in lm when there are effect modifiers (interactions with categorical variables)

NOTE: I think the emmeans package may be what I'm looking for. Still welcome any input! Suppose I have a regression model $y = \beta_0 + \beta_1 x_1 + \beta_2 x_2 + \beta_3 x_1 x_2$, where $x_1$ is ...
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### Determining the distribution of fitted values and residuals [duplicate]

For exam prep, we're supposed to answer this question (which we are supposed to be able to find the answer to in the course literature) For the model specified in a) and proper normality ...
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### Multiple linear Autoregression

i'm new at statistics and can't be sure with my equation, which model it is. I have a dependent variable Y (from 1.Jan. 2020 to 20.March., every 10 seconds.) and independent variables in the same ...
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### Can someone provide the intuition as to why least squares and MLE lead to the same coefficient estimates for linear regression?

In books, I am seeing that the estimates for a linear regression are the same whether you do least squares estimation or maximum likelihood estimation (with certain assumptions). I am not ...
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### Multiple Regression - How to find the case that worsens my model the most?

The big picture problem I am missing participants for a Multiple Regression (MR) (as judged by a-priori power analysis). I want to be able to say: "Not enough participants, but even in the worst-case ...
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### Longitudinal data modeling with lmer

In a longitudinal dataset, each subject is tested every x period of time. I need to find the correlation coefficients between the score, age, and experience in years. The age and experience increase ...
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### Interpreting regression with log transformed outcome + 1 control variable

I have checked the numerous posts on interpreting regressions with log-transformed outcome variables, but none that describe if this interpretation is impacted at all by the inclusion of a log-...
### Why is it that $M_{X_2} M_X = M_X$ for two different residual makers?
I can't seem to figure this out algebraically, or intuitively. Same with a result like $M_X M_X = M_X$ which I know is the idempotent property for a residual maker. If I think of $M_X X = 0$, this ...