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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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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In R, test whether coefficients in lm are different each to a given value (other than zero)

In R, is there a way to use the lm function to test for the hypothesis that the coefficients are different from a value other than zero? For instance, if the model ...
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How to interpret regression equations with logarithms, based on log difference being approximate to percentage change?

$y = 4 + 2.5\,x + u$ For an increase of 1 unit of $X$ (that is, $X$ to $X+1$), we expect an increase $2.5$ units of $Y$ (that is, $Y$ to $Y+2.5$). Is that right? What if there's a/an $\ln$? $\ln(y)...
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296 views

Regression when response variable is a function

I have a set of data $(X_i,Y_i)$, $i=1,\ldots,n$ where $X$ and $Y$ are supposed to satisfy the following equation $$ y = \beta_0(1+x^2)^{\beta_1},\quad x>0, \quad\quad (1) $$ I am interested in ...
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166 views

Does the “divide by 4 rule” give the upper bound marginal effect?

In the logisitic regression chapter of "Data Analysis Using Regression and Multilevel/Hierarchical Models" by Gelman and Hill, The "Divide by 4" rule is presented to approximate average marginal ...
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Analyzing the results from a logistic regression

I'm new to logistic regression. Can you help me understand how to read this? Here's what I understand - For every +1 of continous_variable, the probability of ...
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377 views

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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1answer
597 views

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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421 views

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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1answer
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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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166 views

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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1answer
119 views

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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1answer
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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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1answer
9k views

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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3answers
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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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1answer
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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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1answer
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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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28 views

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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1answer
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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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1answer
231 views

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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2answers
143 views

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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2answers
602 views

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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2answers
72 views

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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2answers
2k views

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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1answer
489 views

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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1answer
71 views

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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1answer
98 views

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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1answer
91 views

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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1answer
108 views

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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1answer
37 views

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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1answer
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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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1answer
48 views

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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1answer
69 views

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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1answer
420 views

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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1answer
628 views

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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2answers
86 views

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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1answer
2k views

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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1answer
94 views

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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1answer
232 views

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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1answer
310 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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1answer
439 views

Confusion over interpreting regression coefficients

My lecturer's regression: ...