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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Interpreting regression coefficients based on Andrew Gelman's re-scaling method

I have two predictors in a binary logistic regression model: One binary and one continuous. My primary goal is to compare the coefficients of the two predictors within the same model. I have come ...
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655 views

Can I calculate Cohen's $d$ from multiple regression coefficient?

Question: Is it appropriate to calculate Cohen's $d$ (effect size) from the regression coefficient of an independent categorical variable? Background: My regression coefficient represents ...
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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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Cross model comparison of quantile regression coefficients

I am looking for a way to compare coefficients obtained from quantile regression. The two surveyed models are nested, estimated on the same sample and for the same quantile. $$ Y = \beta_1X+\epsilon_2\...
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709 views

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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Interpreting difference in difference event study regressions

Lets say I have a model: $$ y_{i,t}= \sum_{k \neq -1} \beta_k \times treat_i \times \mathbf{1}_{K = k} + \lambda_t + \mu_i + e_{i,t}, $$ where $k$ indicates event time, and treatment takes place at ...
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Can autoregressive coefficient values be greater than 1?

I am using multivariate autoregressive (MAR) models to fit my long-term dataset of species abundances and environmental variables but when I use only the data from a specific period of the year (e.g.,...
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318 views

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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327 views

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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49 views

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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669 views

What explains the correlation between the slope and intercept?

If $R^2$ explains the variation explained by a model, what explains the correlation between the coefficients given for a slope parameter and an intercept? I have been thinking of it in two ways: If ...
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892 views

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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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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Regression with coefficients having a multiplicative relationship

Assume I need to calibrate a linear model of the form shown here: $$Y\sim\beta_0+\beta_1X_1+\beta_2X_2$$ where the $\beta$ terms are the coefficients and the $X$ terms are the independent variables. ...
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How to interpret coefficients from rank based regression (Rfit package in R)?

I need to examine the relationship between an outcome variable (continuous) and a number of predictors. Since my data is non-normally distributed (i.e. the residuals from the multiple linear ...
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estimation of polynomial regression: bootstrap approach

Assume, one deals with polynomial regression, i.e. $$ y_{i} = \beta_{0} + \beta_{1}x_{i} + \beta_{2}x_{i}^{2}+ \dots + \beta_{m}x_{i}^{m} + \varepsilon_{i}, $$ where $i = 1, \dots, n$, with $m < n$...
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Marginal means vs. marginal effects. What is the difference?

In R, there are two packages: emmeans and margins. The first implements the LS-means known from SAS, here called estimated marginal means, the second implements the margin command from Stata. I ...
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121 views

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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70 views

R - Interpretation of coefficients and written form of fitted model in lm() linear regression when using poly()

I've tried reading several resources on poly(), I'm not able to see an answer to my question. My question pertains how I might present my fitted linear model in a way that the coefficients are ...
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1answer
49 views

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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1answer
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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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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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225 views

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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83 views

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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582 views

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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601 views

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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R2 SCORE. Scikit Learn vs StatsModels

I have the next code (and question): ...
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Obtaining significance for variables in a linear discriminant function analysis

I have run a linear discriminant function analysis using the lda() function in the MASS library to determine which of 6 ...
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Is it appropriate to conclude the relationship “does not matter” because the regression coefficient is not significant?

Many papers (e.g. apps.washingtonpost.com/g/documents/national/does-the-amount-of-time-mothers-spend-with-children-or-adolescents-matter/1490/) try to claim an insignificant regression coefficient ...
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3k views

How to determine the significance of an interaction?

My question is simple: How do you determine the overall significance of an interaction (i.e. the marginal effect of $X$ on $Y$ for different values of $Z$)? But the background is a bit long-winded,...
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511 views

Finding standard error of beta coefficients in ridge regression using lambda

I need to get the standard errors of coefficients with Ridge Regression, by calculating the SE of the beta estimates after I choose the right lambda. ...
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559 views

Normality violations in multiple regression - report bootstrapped CIs, p values & t values?

I have analysed some data for a research project using multiple linear regression. However, normality assumptions for this method were not met in my data (and could not be resolved using ...
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Comparing nonlinear regression coefficients from independent datasets

I performed enzyme kinetics experiments on a three independent preparations of an enzyme and produced the following three datasets which I separately fit to the Michaelis-Menten equation: $$ V= \frac{...
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241 views

Test regression parameter against a constant in SPSS

This is a pretty basic question, but I can't find an answer by searching for different statements of the same problem. Is there a straightforward way to test if a regression parameter is different ...
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2k views

Getting spline coefficients in R

I'm fitting a natural basis spline on a data set of the form: splineModel=lm(dist~bs(speed, df=3), data=cars) using bs ...
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How to pool regression coefficients

I have a question in the area of meta research. I have a dataset that consists of regression data of several economics papers. More explicitly, I have the values of the regression coefficients, the ...
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24 views

Random coefficients and fixed effects

In a nonlinear model, for each time $t\in\{1,..,T\}$ and product $ j\in \{1,..,J_t\} $ individual $i \in \{1,...,I_{t}\} $ chooses an amount $y_{i,j,t}$ modeled as $ q_{i,j,t} = \frac{1}{\tau_j k_{j,t}...
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How can I compare coefficients in a Cox regression analysis from PCA features to the coefficients of categorical variables?

I am running an analysis on a Cox model where I used PCA features extracted from medical images to predict survival. However, when I examine the coefficients on these features they are very small. (...
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1answer
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How to interpret change in main effect odds ratio with continuous by continuous interaction term?

I am running a logistic regression model to evaluate how age and another measured variable (endo_thickness) associate with clinical pregnancy as an outcome. Both associate at a univariate level with ...
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112 views

Creating a plot for twoway fixed effects regression on how estimator changes over time

I am running a twoways (individual and time) fixed effects within model. Is there an econometrically sensible way to plot how the within effect of the independent variable changes over time? Or ...
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Linear predictive model: how to attribute performance to individual features?

Here is my use case: I am running some data analysis for a large retail chain who has thousands of outlets across the country. I am using a linear predictive model to predict whether we should start ...
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How do you use the context of a problem to determine what your error values mean in linear regression?

I have been told that you must consider the context of a problem in order to determine what your error metrics are telling you. Question: What thought process would you go through to determine how ...
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154 views

Equivalence of ANCOVA and repeated measures model

Consider an RCT with individuals i in 2 arms (group, with 0 = control and 1 = treatment) in which one metric outcome (score) is collected at baseline (pre) and after some treatment (post). In an ...
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Test for difference of coefficients in two logit regressions

I have the following problem. I have a sample of $n$ observations and divide it into two non-overlapping subsamples with size $n_1$ and $n_2$ correspondingly. Then I run logit regression for both ...
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1answer
38 views

Comparing Regression Coefficients from a “log-log” to an Alternative De-meaning Procedure

Consider two regression models: $log(y_i) = \log(x_i)\alpha + \epsilon_i \,\,\,\,\,$ (Model 1), $log(y_i) = (\frac{x_i}{\overline{x}})\beta + \varepsilon_i \,\,\,\,\,\,\,\,$ (Model 2), ...
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1answer
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Can I partition the only independent variable in the regression into two groups and compare the slopes between the partitioned groups?

I have a regression model of y = a + b * x and both variables are continuous. I've found that the coefficient of x, which is b, is statistically significant in the regression y = a + b*x. Now I want ...
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137 views

Log level model - do I exponentiate all coefficients for interpretation?

I'm working with a regression model where I have a log transformed target variable due to the distribution of the log transformation being more normal. I have some numeric variables and also some ...
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222 views

Shapley value vs ridge regression

My goal is to get the feature importance for multiple regression. I have a data set with some multicollinearity. I found two methods to solve this problem. The first one is the Shapley value. ...
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1answer
58 views

Intuition of second order differencing dependent variable on non-differencing independent regressor regression?

I have two time series sequences. One is $y_t$, which is non-stationary, and the other is $x_t$, which is stationary. Suppose I would like to do a regression of $y_t$ on $x_t$ to forecast $y_t$. The ...

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