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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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Intercept increases in regression when adding explanatory variables

I am conducting an analysis, where I examine the size of the intercepts of three regression models (time-series). The models look something like this: $y_1=\alpha+\beta_1x_1+\varepsilon$ $y_2=\alpha+...
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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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Estimation of quantile regression by hand

Let us suppose we have following data x y 1 5 2 4 3 5 4 4 5 7 I would like to do Quantile regression in excel, I have found following information ...
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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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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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Interpreting GAM Coefficients

I could use some advice interpreting GAM (Generalized Additive Model) coefficients. I get the following results when I call coef on my model: ...
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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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Compare coefficients from two separate panel regressions in Stata

I am trying to compare the coefficients of two panel data regressions with the same dependent variable. What I am aiming at is the following: ...
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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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Differences-in-Differences coefficients meaning (from Mostly Harmless Econometics)

In Mostly Harmless Econometrics, section 5.2.1 (Regression DD), pages 233-234, equation (5.2.3) defines $Y_{ist}=\alpha + \gamma NJ_{s}+\lambda d_{t}+\delta (NJ_{s}.d_{t})+\epsilon_{ist}$, where $NJ_{...
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What is the impact of low predictor variance on logistic regression coefficient estimates?

Let's say I am using a logistic model to predict whether it rains (yes or no) based on the high temperature and have collected data for the past 100 days. Let's say that it rains 30/100 days. ...
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Is there a R command for testing the difference in coefficients of two linear regression​s? [closed]

I am looking for a R command to test the difference of two linear regressoon betas. Lets say I have data $x_1, x_2...x_{n+1}$. $\beta_1$ is obtained from regressing $x_1$ to $x_n$ onto $1$ to $n$. $\...
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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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ARMA - coefficient interpretation

I would like to interpret my ARMA model. I would like to tell about all those numbers as much as possible. I tried to study it but there as still some issues I am not sure about. I will start by ...
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Co-variance of beta coefficients for Dummy Variable regression with intercept

If I have a dummy variable regression output with intercept included (base category as omitted category), and I have to do a hypothesis test for difference of means between two categories other than ...
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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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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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Linear regression with error dispersion dependent on the independent variable

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 $0$ ...
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Mixed Effects Model - Some groups have a single value of x

I am working on sales of a B2B company and I have sales volumes of different customers at different price points. Some customers, however, purchased at only a single price point. I'm trying to ...
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Interpreting non-significant regression coefficients

Out of seven, six of the independent variables (predictors) are not significant ($p>0.05$), but their correlation values are small to moderate. Moreover, the $p$-value of the regression itself is ...
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Regression: Is it problematic to include a predictor when the outcome variable is based on it?

My question is based on the following discussion we often see when people try to model citation counts for research articles. The outcome variable is citation counts for an article and some typical ...
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How can a variable have a positive association through logistic regression, yet a negative association through Cox regression?

I am undertaking some medical research using R. My outcome of interest is mortality in the intensive care unit. Data My data looks like this (there are ~15,000 rows). ...
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Converting a Continuous variable to categorical for Cox regression

In a Cox regression model where our variable of interest is continuous (e.g., a lab measurement); If we want to obtain something other than a unit risk ratio for that variable (e.g., the hazard ratio ...
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Magnitude and direction of relationship between predictors and dependent in regression

I'm doing partial least squares regression (PLSR), using the df below, to investigate how to predictors (catchment characteristics) influence the dependent (nitrogen in the river). In this data.frame, ...
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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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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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297 views

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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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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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 $\tilde{X}$ ...
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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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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 ...