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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14 views

Interpreting Logistic Regression Categorical Coefficients

So I have this question: If we fit a logistic regression with categorical predictor X with categories A, B and C, and have the estimated coefficients β0=−2.5 and βB=0.5 and βA=−0.2. (a) Interprete ...
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Converting coefficient of slope to autoregressive factor

I realize this is very fundamental. I apologize. Is there any way to convert the coefficients from a linear model into the decay factor if i want to express it as an autoregressive model? For a ...
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Interpretation of a quadratic term on a log transformed target variable

I've done some searching and found several posts related to this, e.g.: In linear regression, when is it appropriate to use the log of an independent variable instead of the actual values? Suppose I ...
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Interaction term and main effect multicollinearity [duplicate]

If I have the predictors $X$, $Y$, and $XY$ to fit a linear regression model. Won't I be increasing the standard error of the regression coefficients? This is because $XY$ is collinear with $X$ and $...
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In Simple Linear Regression $\hat \beta_1$ and $\bar Y$ are independent [duplicate]

I want to show that, in simple linear regression $\hat\beta_1 $ and $\bar Y$ are independent. My attempt: I have calculated the $\mathcal Cov(\hat \beta_1,\bar Y)$ and it turns out to be $0$.I also ...
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How to perform a multiple non linear regression without knowing the functions for each variable and the constraints for their coeffcients?

I have a data for number of cars and its causal variables are identified as GDP, population, urban fraction and fuel price but they have non-linear positive correlation but I don't know what that is. ...
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compare coefficients from different regression

I estimate the following models using the Hausman-Taylor estimator: $$y_{i,t} = a_{0} + B_1 controls_{i,t} + \beta_1x_{i,t=2000} + B_2 Year_t + B_3 x_{i,t=2000}*Year_t + e_{i,t}, (1) $$ $$y_{i,...
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Linear Regression with Changes

Consider two variables with levels over two time periods $\{y^i_t,x^i_t\},\{y^i_{t+1},x^i_{t+1}\}$. For example, it could be profit and cost data of various firms over two quarters. Suppose I take ...
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45 views

Spatial Lag or spatial Error Model? Deciding by using the Lagrange multiplier diagnostics

Honestly, my knowledge of geostatistics is limited. My assumptions are as follows: If I want to choose between a Spatial Lag Model (SLM) and a Spatial Error Model (SEM), I can use the Lagrange ...
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Capturing effects / Controlling for variables [duplicate]

I understand the idea behind regressions and know how to interpret them, however, when I hear the term "capturing the effect of.." or "controlling for.." so far I've just accepted it without ...
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Selected variables varies depending on whether or not standardization is in lasso regression (glmnet)

The paper often suggests both standardized and unstandardized coefficients in the lasso model (glmnet in R). However, when I run glmnet, the selected variable is different depending on standardized =...
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SVM as linear equations

I'm using SVM for a regression problem (sklearn.svm.SVR). After I train my model I use these 2 attributes svr.coef_ and ...
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How to compare LME regression coefficients across models with same variables but different sample sizes/trial numbers?

I have a quite specific situation that does not seem to be covered by other, similar posts: I ran a study where a task (Task A) was periodically interrupted by a probe that asked participants what ...
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Using a subset of parameters in joint confidence region of a linear model

For a standard linear model of the form $y = X\beta + \epsilon$, where $\beta$ is a vector of parameters. we can calculate an individual confidence interval for each parameter (of 1-$\alpha$ quartile)....
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How to interpret the resulting negative regression coefficient? [duplicate]

How to interpret the resulting negative Poisson's regression coefficient? I am investigating the effects of environmental factors on mortality. A negative regression coefficient means feedback (proves ...
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39 views

Dynamic regression, models with coefficients = 0 chosen as top models

I am running auto.arima on part of a time series (training data) using all possible combinations for several external regressors. I then choose the top 5 models according to fit to testing data using ...
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Incorporating rank-ordered logit results from different samples

I would like to create rank-ordered logit models to predict the outcome (winner in this case) of variants of a multi-player game. For the most part, the predictors for each variant differ. However, in ...
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How to calculate coverage rates for 95% confidence intervals for estimands (like regression coefficients)?

I'm working on a Synthetic Data Generation model, and I'm confused about a metric mentioned in a seminal paper (details of paper added below) Context: Synthetic Data Generation involves sampling from ...
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OLS reinterpretation (?)

I have read on a book written by a professor something similar to the following and want to check this statement on the forum, since it is the first time I have heard it. I have read that the OLS ...
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Determining Intercept for Regularized Logistic Regression

Going off of the standard set up, we have $N$ observations and $P$ predictors stored in the data matrix $\mathbf{X} = \{ x_{i,j} \}$ for $i = 1, \ldots, N$ and $j = 1, \ldots, P$. The response is ...
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How do I compute a Cohen's d from b weight and standard error?

From Table 3 and the paragraph below, you have a good deal of the information I have available. N's for taser and non-taser conditions are 339 each. My initial inclination is to take the raw B weight ...
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Understanding subgroups and covariates in linear regression

I'm trying to better understand how adding covariates, especially possible confounders, to a linear regression affect the regression results. I also want to better understand the relationship between ...
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Logistic regression vs segmentized logistic regression

This might be a very rookie question. I need help interpreting the results of my logistic regression. Assume I have the following model: y ~ categorical + numerical...
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Interpreting Multiple Regression [duplicate]

I am working on my thesis and I had to do a multiple regression. I have only 45 samples and I checked that there were not problems of multicollinearity (VIF < 3) and the residuals are normally ...
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Are correlated errorbars useful for regression fitting?

Let's say I have a dataset that roughly fits a 2nd order polynomial but I trying to fit it using a linear regression (see image). The error in my y measurement depends on y, but the coefficient of ...
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How Do I Summarize To a Single Estimate After Bootstrap Resampling For Various Statistics?

It is relatively straightforward when I want to know about the coefficients, fitted values, residuals and residual standard error of my (ordinary least squares) regression models, especially if you ...
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How to average 1000+ regression coefficients?

I am doing OLS regression on 1000's of stocks forward returns against a factor score. All the factor scores are the same model results for each stock at some point in time and vary between 1-5. My ...
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Creating a risk score from Cox Regression

I have two datasets with palliative cancer patients including 106 and 60 patients, respectively. I have biomarkers of inflammation and coagulation, as well as clinical characteristics for all patients....
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Non-linear regression where dependent variables are dependent on different independent variables in R

I would like to know how to proceed with the following non linear regression analysis, which is a simplified version of my real problem. 5 Participants where asked to observe the speed of three ...
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Closed-form solutions for constrained multiple linear regression

Normally a multiple linear regression is unconstrained $$y=X\beta+\epsilon$$ so that closed-form solutions in the case of data orthogonality ($X^\top X=I$) are $$\beta=(X^\top X)^{-1} X^\top y$$ ...
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How to convert orthogonal polynomials from MULTIVARIATE regression to basic polynomial equation [duplicate]

I believe the link below converts the coefficients of one x from orthogonal to monomial form, but does someone know an edit to that code that can convert the coefficients of many x's in one regression ...
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Chow test results interpretation

I am analysing time series data right now using gretl, and want to test for a structural break, but I am not quite sure how I have to interpret the results. Let's say I have a wheat price and flour ...
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How to interpret the ratio between a coefficient on a dummy and the coefficient of a log income variable?

I was reading this paper by Kahneman & Deaton: Kahneman, D., & Deaton, A. (2010). High income improves evaluation of life but not emotional well-being. Proceedings of the national academy of ...
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Correlation coefficient of x and y

If we have $$ X\sim Poisson(\lambda), Y|X = x\sim Binomial(x+1,p) $$ What is the correlation coefficient of X and Y? So I used $$\rho=\frac{Cov(X,Y)}{\sqrt{Var(x)Var(Y)}} = \frac{E[X[E[Y|X]]-E[X]E[...
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Intuition for nonmonotonicity of coefficient paths in ridge regression

Intuitively, why may some of the slope coefficients in ridge regression increase in magnitude when the penalty parameter $\lambda$ is increased? Or in other words, why are the coefficient paths ...
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Identifying important variables in a PLSDA model using caret in R: are coefficients standardized?

I am doing a PLSDA using the caret package in R. My objective is to predict a status of a cow (0 vs 1) using spectral data. I want to compare the coefficients to know which spectral points contribute ...
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155 views

Interpret GLM log link coefficients

I am currently doing a college assignment in which I have a GLM model in the gaussian family with a log link. I would like to know what the impact per variable is. I know how to calculate the ...
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Error variable correlated with explanatory variables

We know that sometimes the error variable in a regression framework may be correlated with explanatory variables; this happens e.g. when we omit an important predictor from our study, getting the well ...
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Diagnostic test to test for change in regressor

In the previous part of this question, I worked out there is a structural change in the Chow test as 5.04> 2.1 (Fc) hence H0 is rejected and the restriction does not hold. In the next part of the ...
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How to interpret coefficient if the independent variable has negative values?

I have a simple OLS regression: Y=a+B*X+epsilon X is the percentage change in house prices and has negative values (except in the 99th percentile). If the sign of 'B" coefficient is positive, how ...
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79 views

comparison of coefficients (they are not Standardized Beta ones)

I estimated a model with three-stage least squares (3SLS) and have two main explanatory variables (the model also includes a set of control variables but they not important at the moment). I want to ...
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Correlation between external variables and model coefficients over time

Are there any techniques which can allow me to test for correlations between a set of variables (e.g. population, disposable income) and the time-varying coefficients of a model? I would like to ...
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Obtaining Mean Differences from DESeq2 Output

I have conducted some analyses using DESeq2 and obtained the output. However, instead of interpreting the effect sizes as log2FoldChanges, we would prefer to obtain a model-based mean difference. I ...
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interpretation of coefficients of independent variables in fractions

I am a bachelor student finishing my thesis and desperately need some help with the interpretation of regression coefficients. I am currently quite confused and my deadline is three days away. I have ...
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21 views

Multiple regression and multiple comparisons 3 groups

I'm trying to compare the effect of an IV on my DV, where my data are separated into 3 groups. Specifically, in one group there is a significant correlation between IV and DV, but in the other two ...
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Elastic Net - number of non-zero variables

I have a question regarding the interpretation of the trace of coefficients when running Elastic net with the package glmnet in R. This is the plot I obtain with alpha = 0.5 My understanding is that ...
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26 views

how to report paired comparisons in linear basis function model?

I am struggling with correctly reporting the results of a linear (mixed) basis function model I ran. The model is specified in R as ...
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Will LASSO choose variables that are highly correlated with the outcome variable?

Suppose we have access to an outcome variable $Y_i$ and a $p$-dimensional vector $X_i$ for $i=1,\ldots,N$. We run a LASSO regression of $Y$ on $X$ for every penalty/shrinkage parameter $\lambda$ in an ...
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Error estimates for coefficients of a non-negative quantile regression

I am looking for a way to provide an error estimate for coefficients obtained from a non-negative quantile regression. The complicated part aside from positivity constraints is that my observations ...