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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Multiple regression, full and restricted model

So I have a data set that looks like this. I want to write a full and restricted model which would evaluate the null hypothesis that latitude - controlling for continent and sex - has a significant ...
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Regression Interpretation conundrum

I am running an OLS regression of the form $$\log\left(Y\right)=x_0 + \left(\frac{x_1}{Y}\right)\beta_1+\log (x_2)\beta_2 + \epsilon$$ I have one covariate as $\left(\frac{x_1}{Y}\right)$ which is a ...
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How to interpret my coefficients?

I have the following model: $$ Gini_{it} = \alpha_i + \beta_1\ln(BNP_{it}) + \beta_2trade_{it} + \epsilon_{it}, $$ where $Gini_{it}$ is the Gini-index from 0 to 100, $\ln(BNP_{it})$ is $\ln$ of the ...
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Standard error for the sum of regression coefficients when the covariance is negative

I have a question about appropriately calculation the standard error for the sum of two coefficients in a linear regression model. My question is similar to this and this, but I can't seem to solve ...
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Interpret interaction effect of 2 continuous variables

My dependent variable is house prices. And my interaction term contains two continuous variables 1) log of employment at the nearest firm 2) log of distance to the nearest firm. House price = b0 + b1 ...
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Estimate $\beta^{2}$ in linear regression $y_{i}=\beta_{1}+\beta_{2}x_{2,i}+\beta_{3}x_{3,i}+\varepsilon_{i}$

I have the following standard linear regression model: $y_{i}=\beta_{1}+\beta_{2}x_{2,i}+\beta_{3}x_{3,i}+\varepsilon_{i}$ where $\varepsilon_{i}$ is normally distributed with mean 0 and variance $\...
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How to interpret meaning of regressors in this logistic regression model?

I'm trying to understand the model in this paper where they treat the item response theory model as a form of logistic regression. In the model the probability of getting an item (question) correct ...
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Backtransforming the vertex of a quadratic function

I have created a model for which it was necessary to scale my predictor values by subtracting by the mean and dividing by the standard deviation of the X values. This resulted in variables centered ...
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Confusion over interpreting regression coefficients

My lecturer's regression: ...
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Adjusted R squared on a holdout set

The formula for adjusted $R^2$ is: $$ 1 - \frac{(n-1)}{(n-p-1)}(1-R^2) $$ where $r^2$ is the coefficient of determination, $n$ is the number of points, and $p$ is the number of parameters the model ...
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How to interpret a regression coefficient for the reciprocal of an independent variable?

Does anyone know how to interpret a coefficient when the variable in the model is the reciprocal of the original variable? I have an inverse equation, where $\text{time} = \beta_0 + \beta_1(1/\text{...
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Average effect of coefficients across multiple linear models?

I have several OLS models with robust s.e.'s that predict an outcome variable Y. For instance: Model 1: $Y=B_0 +B_1X_1$ Model 2: $Y=B_0 + B_1X_1 + B_2X_2$ Model 3: $Y=B_0 +B_1X_1 + B_2X_2 +...
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Do I need a validation set if I am doing 10-fold cross validation?

I am looking at a dataset with ~120 observations and I am investigating it using two sets of explanatory variables, one has about 12 features, the other about 8. This is for a regression analysis. ...
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Controlling for a variable in OLS - Stratification and Reaggregation. Simple Example

In his engrossing book "Naked Statistics" Charles Wheelan begins to explain how controlling for variables works by stratifying the sample. However, he stops short of explaining the reaggregation, ...
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Proving that $ (\hat{\beta} - \beta)' (X' X) (\hat{\beta} - \beta)$ is independent with SSE

Exercise: Prove that $ \mathbf{(\hat{\beta} - \beta)' (X' X) (\hat{\beta} - \beta)}$ and SSE are independent for a Least Squares Regression Model. Attempt: Note that by $'$ I denote the transpose ...
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Standardization and explanatory variables of different domains in Multiple Regression

There's many questions on related topics but I have been unable to find one that precisely answers my question. Let's say I'm performing a regression on multiple predictor variables $x_1...x_n$ for ...
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How to deal with various sample sizes in the calculation of a predictor variable?

Let's say one of the predictor variables in a regression model is 3-point shooting percentage. However, some of the observations (players) only have one or two attempts while others have several more. ...
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What is the interpretation of the coefficient of a covariate control variable in a multiple linear regression

I was reading the Rubin: Causal inference and Angrist, J.D. and Pischke: most harmless econometrics. Both of them are great textbooks. During my reading, I have the following question: what is the ...
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How to compare coefficients within the same multiple regression model?

As the titles states, I would like to compare two coefficients in my multiple regression model but I'm not quite sure how. ...
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Regression coefficients tests before or after model selection

I have a set of data containing 4 predictors (environmental conditions and animal size) and one predicted variable (animal growth rate). I want to fit a regression model to this data. I have two ...
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719 views

standard error of transformed regression coefficient

I have the regression $y= \beta_0 + \beta_1 \,x + e$, along with the standard error of $\beta_1$ I would like to find the standard error of the elasticity at $\bar{x},\bar{y}$, which is given by $\...
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How to interpret regression coefficients when outcome variable was transformed by Box-Cox

I try to do a linear regression of a positive continuous dependent variable (outcome) with several independent variables (all of them are categorical / binary). I had many troubles to get Gaussian ...
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Beta coefficients from stratified analysis when there are covariates?

Suppose I have a regression model shown below Model 1: $$ Y = \beta_0^\ + \beta_1SEX\ + \beta_2ALCOHOL\ + \beta_3SEX*ALCOHOL\ $$ The predictors I am interested in are SEX (binary: 0 female, 1 male) ...
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Interpreting regression coefficients and economic significance

I am having a difficult time understanding how to discern whether the regression coefficients I am getting are large or small relative to the data. I have one regression that is cross-sectional. For ...
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Forcing smoothness of regression coefficients

I'm building regression models on spectral datasets: the predictors are the intensites of signal at the different frequencies. In this case the intensities at close frequency values are highly ...
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290 views

Perfect Multicollinearity

If 2 independent variables $x_1$ and $x_2$ in a hypothetical linear regression model $y = \beta_0+\beta_1 x_1 + \beta_2 x_2 + \varepsilon$ are perfectly multicollinear, which of the 2 independent ...
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Is Square Root of the Variance of a Regression Coefficient the Standard Error?

Quick question, in the textbook "Introductory Econometrics", the variance of a Regression Coefficient is given as: $var(\hat\beta_j) = \frac{\sigma^2}{SST_j(1-R_j^2)}$ where, $SST_j$= $\sum_{i=1}^n (...
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Clustering data based on regression coefficients

Context: In my master thesis, I am examining the evolution of maintainability issues over time on a set of around 2000 Android applications. For every application in the dataset, I have the counts of ...
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Boostrap Confidence Intervals for biased estimators in R?

So, this is a two part question. I have made a multilinear regression model in R. The model has been ridged with lm.ridge() with the $\lambda$ that minimizes the GCV prediction error. This was done by ...
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double feature value in ridge regression, coefficients change?

In ridge regression using unnormalized features, if you double the value of a given feature A (i.e., a specific column of the feature matrix), what happens to the estimated coefficients for every ...
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Binary logistic regression: interpretation of explanatory variables

I have performed a binary logistic regression in R using the glm command and family=binomial. The dependent variable (DV) is not re-contracted = 0 or re-contracted =...
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Binary Logistic regression results

Is it correct to find that an explanatory variable was found to be statistically significant with the chi-square test but insignificant with the logistic regression analysis model?
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Regression: centered vs. uncentered predictors [duplicate]

I'm trying to understand how/why centering predictors in a 2 predictor regression model would change the coefficients Lets say I have 2 centered predictors and an interaction term, predicting a ...
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Confidence intervals of coefficients of multiple regression

With following model of mpg vs other variables in mtcars dataset: ...
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How to decide which main variable is modified by the interaction term?

Given the following linear model $Y=int+aX1+bX2+c(X1*X2)+e$, where $X1$ and $X2$ are the main variables, ($X1*X2$) is the interaction term, and $a$, $b$, and $c$ are the corresponding coefficients. ...
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Performance of regression models

If we have to choose between two regression models, one has a correlation coefficient of 0.95 and the other has a correlation coefficient of 0.75. Is it always the case that the first model is to be ...
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Logistic regression weights of uncorrelated predictors

I am a bit puzzled about the behavior of uncorrelated predictors in logistic regression. As in OLS, I thought that if two predictors (rv1 and ...
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What rules should guide scaling variables to maximise interpretation, particularly within a regression context?

Context: In this previous question @adhesh asked about the benefits of coding a binary variable zero-one rather than one-two. I realised when I wrote this answer that I had quite a lot to say about ...
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In linear regression, any intuitive explanation why duplicating samples will reduce coefficients' std-dev? [duplicate]

I read the explanation by Ocram here about how to calculate the stddev of coefficients in linear regression. I also run experiment with my sample data. I have test1 which contains 1000 samples; I ...
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Quantile regression and linear regression coefficient comparison

I am trying to understand the concept of quantile regression by modelling the monthly expenditure on insurance on several variables. The R package ...
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Interpretation of functional regression models for scalar response

I have an application scenario in which I want to determine a single outcome from the course of a series of measurements. I decided to give functional regression a try, so I read and ran the example ...
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How to test whether individual fits to regression line or not

I have a defined regression model for the healthy control (HC) group, with corresponding CIs of coefficients and of E(Y). I would like to test whether individuals belonging to another population (...
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Importance of regressors in time series data

Could anyone recommend bibliography or name some useful methods to analyze which (exogenous) variables are most important in determining the value of a time series? For context, I have a random time ...
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Interpreting glmnet Lasso coefficients on dummy variables (multiple levels) [duplicate]

I am trying to apply glmnet's lasso to a set of features in which there are multiple categorical variables with multiple levels. My intention is to let lasso reduce ...
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Interpretation of Elastic Net Regression Coefficients

I would like to interprete the coefficients of a elastic net regression (i'm using function glmnet()$beta in R). The coefficients of the elastic net regularized ...
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Is Omitted Variable Bias Always Bad? What are the implications of omitting variables from a regression that aren't easily obtained in the real-world?

Say I'm using multiple logistic regression to help caterers in a large city predict the probability invited adults will come to a wedding. Say I have a proprietary dataset of likely relevant predictor ...
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Find Feature Weighting in Deep Learning

If I train a deep neural network on standard tabular data (csv file etc. with labeled features) is there a good way to gauge how important each feature is in a particular new instance's prediction ...
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Multinomial Logistic Regreesion with Lasso penalty in R

I am applying regularized logistic regression (in R) to the handwritten digits data set. I have fitted a logistic multinomial model with lasso penalty to the training data. I am asked to obtain the ...
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What is the covariance between estimated coefficient of a regression model?

Consider the simple linear regression model: \begin{align} Y_i &= \beta_1 + \beta_2X_i + u_i \\ \hat{Y}_i &= b_1 + b_2X_i \end{align} (a) Show that the regression line always passes ...
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Reported Coefficients for Glmnet using Caret

I understand GLMnet standardizes the predictor variables by default before fitting the model. After fitting, the computed regression coefficients are then destandardized to allow reporting in their ...