# Questions tagged [regression-coefficients]

The parameters of a regression model. Most commonly, the values by which the independent variables will be multiplied to get the predicted value of the dependent variable.

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### linear regression, symmetry of model does not lead to symmetry of coefficients

Experiment: You are given a large population of real numbers. For simplicity take the whole numbers from -n to n. Take two independent random samples x and y of size k and sort them (each one ...
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### Poisson Regression and Negative Binomial regression results interpretation

I'm using Poisson Regression and Negative Binomial regression to estimate temporal trends. My understanding is that the coefficients are in log scale and they have to be translated to data-unit (count ...
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### What is a “high” standard error (in logistic regression)?

I can't find in any statistics book what would start to be considered a large standard error of a regression coefficient. In my research, I have a group of a categorical variable with a small number ...
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### Linear SVM feature weights interpretation. Binary classification, only positive feature values

I'm using clf = svm.SVC(kernel='linear') on a data set with only two classes $y \in \{-1, +1\}$ and the feature values of all samples are normalized between 0 and 1....
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### Multivariate Bayesian Testing with an F-test

In Bayesian statistics a standard way to perform a Lindley significance test for the hypothesis $\theta=\theta_0$, where $\theta_0$ is the suggested value for $\theta$ at the $\alpha$ level of ...
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### Adjusting regression coefficient for predictor error

I saw a famous review paper about intelligence, and the authors introduced a way to adjust the regression coefficient for predictor error. As many of you might know, if the predictor has a ...
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### regression - does R2 only apply to measure linear regression performance?

Background According to Wiki: https://en.wikipedia.org/wiki/Coefficient_of_determination, $R^2$ is coefficient of determinant. The definition is $$R^2 = 1 - \dfrac{SSE}{SST}$$ Since $SSE$ is ...
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### Are these negative binomial regression results reasonable?

I did a negative binomial regression on a data set with 4 covariables. The count outcome has values up to 600. I did a mixture model with 2 components, also called a latent class model. However, I am ...
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### R bayesglm: Estimates depends on order of variable

I did a logistic regression with bayesglm from package arm. I got different results depending on the order of the variables in the model: ...
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### Confidence interval for the increase in P(Y=1) from moving between 2 levels of a factor in logistic regression

I have a logistic regression model fit with one categorical variable $x$ that takes value in $\{1,2,3,4,5\}$. In R I have obtained the estimate and standard error for $\beta_0$ and $\beta_1$. The ...
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### Efficient ways to partition rows of augmented design matrix $[X|y]$ into subsets with similar regression results?

Imagine I have $n$ observations on a regression model; are there any reasonably efficient methods for partitioning that into two (or more) roughly equally sized groups which almost reproduce the ...
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### SARIMA, coefficients check

I would appreciate if someone could check the mathematical equation for the seasonal ARIMA (4,1,4) x (1,1,1) period 12 that I wrote. I have done it this way, but I am not really sure if it correct is. ...
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### Aggregating Standard Errors for Predicted Probability Estimates

I obtain predicted values from a logistic regression for a certain outcome (e.g., mortality) at the hospital level – the data is at the patient level – and need to compute the average across hospitals....
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### Backing out the standard deviation from information on baseline mean/s.d., and coefficient mean/s.d

I am trying to run a power calculation for a randomized control trial. For this I need a mean and standard deviation for our 'baseline'. There are papers out there which would have a mean and standard ...
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### Is there a difference between $\beta$ and $\theta$?

I've seen both $\beta$ and $\theta$ used to indicate model parameters in different publications. For example, Andrew Ng uses $\theta$ in his ML course and Gareth James et al use $\beta$ in ISLR. My ...
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### Should the logistic regression equation always result in a value between 0 and 1?

I am a medical scientist but an amateur statistician (not even amateur). I have a simple question. Here is the output from a logistic regression examining a number of variables which may predict if a ...
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### Can I make a better linear model than this?

I am getting the below plot for my data, and relevant summary is as below:- ...
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### How does one interpret regression coefficients when no dummy variables nor intercept are dropped?

I am familiar with how to interpret linear regression coefficients when the independent variables are dummy coded and one of them is dropped. And this question helped me understand how to interpret ...
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### Sample Size for Poisson Regression

Recently, I was tasked with a sample size calculation for a study in which the outcome is to be modeled using a Poisson regression (i.e. a generalized linear model). For quick and simple calculations ...
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### How to decide whether a variable belongs to a linear model?

I have a set of inputs $x$ and noisy outputs $y$. I think that either $$y = a_0 + a_1 x$$ or $$y = a_0 + a_1 x + a_2 x^2.$$ How can I determine which model was more likely to have generated the data? ...
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### How to interpret p value of regression coefficient which is nearly 0?

When regression coefficient is nearly 0 (in fact in the real model it's exactly 0), what's the meaning of p value (<0.05) of the coefficient? For example, I did a multiple variable regression ...
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### Why is odds ratio used when interpreting logistic regression?

I am fairly certain when interpreting logistic regression output, the odds ratio should be used instead of the estimated coefficients; however, I am unable to figure out why this is the case. So my ...
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### Simple regression, switching X and Y, t-test stays the same? (edited)

I did a simple regression where the independent variable was the educational background of the mother. The dependent variable was the language skills score of the child. I switched them around and ...
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### Categorical variables in LASSO regression

I just built a logistic regression model via Lasso Penalization. Now I'm trying to interpret the coefficients. One is "days". I have a coefficient for "days". when I do a normal logistic regression ...
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### Backtransform coefficients of a Gamma-log GLMM

I am analysing data from an exclosure experiment, this means for several years, goats were kept outside a fence and inside the fence, plants could grow without being grazed. Outside the fence, grazing ...
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### When to divide data into training & test set in logistic regression?

I am using Logistic Regression in a low event rate situation. Overall universe: 46,000 Events: 420 Conventional logistic regression models divide the data into ...
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### Do Beta weights from regression have error terms?

I am looking at standardized regression weights (i.e., Beta weights). I was thinking of reporting the errors next to the weights in a figure, but upon some thought I was debating whether such errors ...
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### How to measure the “Impact/influence” of a feature y on Logistic regression model based on the coefficients?

I have a dataset X which contains probabilities returned for classification 4 different classification models, say M1, M2, M3, M4 those probabilities are use to feed a fourth model M4 and that model ...
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### Interpretation of standardized (z-score rescaled) linear model coefficients

I have analyzed some data on vegetation change as a function of change in soil parameters. I compared a dataset from 2001 with a dataset from 2018 (fully balanced). To investigate the change in ...
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### Which random effects to include in this GLMM?

In my study growth of plants was measured in different years on different plots (all plants were measured in all years). The question I'd like to answer with my model is: Which factors influence ...
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### regression coefficient in the poisson model [closed]

When we are dealing with count variables we are told not to log transform our data but to instead use a poisson regression. I was wondering.. when it comes Poisson regression, the common formulae is :...
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### Why do coefficients in a binary logistic regression model differ according to the number of predictor variables?

I fit a binary logistic regression model with a single categorical variable, for which I received a coefficient. When I added further categorical predictor variables, the coefficient of the original ...
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### Incident rate ratios with log-transformed variables in Poisson regression

I'm in a bit of a mess with interpreting the output of a Poisson regression model with log-transformed predictors. The predictors are counts, and the log transforms them for the linear part of model. ...
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### Linear regression with $n<p$: Solution of $Ax=b$ that minimizes the $2$-norm of $x$

Consider a full-rank $n\times p$ matrix $A$ and $b\in\mathbb{R}^p$. If $n<p$, I want to minimize the norm $||x||^2=x_1^2+\dots+x_p^2$ over $x\in\mathbb{R}^p$, subject to the condition $Ax=b$. So, ...
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### How to perform a meta-analysis of regression coefficients?

I want to perform a meta-analysis but the included studies use different models to analyze the data. There are Pearson correlation (3 studies), Spearman correlation (1 study) and several studies (~7-...
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### How do you interpret a percent variable with a log-transformed outcome?

It doesn't make sense to log transform my x-variable (for a more intuitive elasticity interpretation), since it is already in a % format, but with a log transformed outcome: ln(y) = B0 + B1X1 where ...
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### Generate predictions from a logistic regression model reflecting the uncertainty of the model

I want to generate predictions from a fitted logistic regression model that reflect the uncertainty of the model (within a classic frequentist framework). To clarify, my objective is not to ...
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### Problem related to OLS estimators

The problem is: Suppose we fit a model Y = XA βA + ε. However, the true model is Y = XA βA + XB βB + ε. A is kA x 1 and B is kB x 1. Show that the OLS estimates of βA will still be equal if XTAXB ...
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### Reconstructing a logistic regression model from literature using published coefficients

I have a logistic regression model with the form: logit(p) = alpha + X*beta Where alpha is the intercept, X is the covariate matrix, and beta the corresponding coeffiecient. I want to be able to ...
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### Intercept in demeaned and rescaled regression model

Suppose I have a linear model; $Y=X\beta+\epsilon$ Where $X$ is $(n \times p)$, with the first column of $X$ being an intercept column (consisting only of ones). Now suppose I construct $\tilde{X}$ ...
Suppose $y=ax+z$ where $x, y, z$ are random variables with range in $\mathbf R$, $\mathbf E[x]=0$, the probability distribution $p(z|x)$ is 1) normal distribution $N(0,\sigma(x)^2)$ with mean $0$ ...