# 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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### Multiplying coefficients of logistic regression to get per 10 unit increase?

I'm working on a project in R where I'm looking at California's census tract-level demographic data in an explanatory logistic regression model. I have 6 demographic variables of interest and am ...
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### Standardized dependent variable, effect size interpretation

I have the following model: RT ~ condition + (1|participant) RT is a continuous variable. Condition has three levels and is coded using Helmert contrasts. I ...
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### Standardize linear regression with single contrast coded predictor

I am trying to fully standardize a linear model which I am running in R using "lme4". However, I am not really sure if I am doing it correctly. The model consists of a continuous outcome ...
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### Only observing sign of the output of a linear model under Gaussian assumption

Suppose the linear model is $y = \beta x + \epsilon$, where $X \sim \mathcal{N}(0, 1), \epsilon \sim \mathcal{N}(0, s^2)$. If we only observe the sign of the output $y_i$, and the number of ...
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### Regression analysis with constant dependent variable

Can someone explain to me what's going on in the following? Suppose we have data with constant dependent variable: ...
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### Interpreting coefficients of beta regression

I have implemented a beta regression and am a little confused on how I should interpret the coefficients of my model. For context, both my independent variables and dependent variable are expressed in ...
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### Ordinal regression in sas [closed]

I want to build an ordinal regression model in SAS for workplace satisfaction as the dependent variable (rating 1-10), and several other ordinal independent variables (rated from 1-5 and 1-9). I know ...
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### What does it mean for $\hat\beta_1$ and $\hat\beta_0$ to have a variance?

With regarding to OLS estimators why $\hat\beta_1$ and $\hat\beta_0$ have a variance?
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### Standardizing coefficients in gamma distributed model - piecewiseSEM

I am running a sem using piecewiseSEM package. One of my three models is gamma distributed. I wanted to calculate scale standardized coefficients as it would be ...
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### R squared for a regression plane without observations

Assuming we have three random variables $X$, $Y$, and $Z$, and we want to estimate a least squares regression plane of the form $Z = a + bX + cY$. We do not know the individual observations, but we ...
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### regression coefficients: changing the scale of the independent variables?

I'm running a weighted regression model, but I have no idea how to deal with some variable that I need to put inside My dependent variable has values with a scale of thousands, while my independent ...
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### Dropping a hierarchical linear model intercept when centering the outcome at 0?

Suppose a hierarchical linear model with "random intercepts" $\mu_i$ fit to some raw (unscaled) data: $$y_i \sim N(\mu_0 + \mu_i, \sigma) \\ \mu_i \sim N(0,\sigma)$$ If I rescale $y_i$ to ...
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### ANOVA is significant but coefficients are not? [duplicate]

I was wondering how I would report this? My ANOVA is significant but when I look at the model and the different predictors, there is no significance?
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### Compare full set and subsets of response variable in poisson regression?

I want to compare three versions of the same count response variable using Poisson regression. Can I make comparisons based on how significant the predictor coefficient is, and can I put the results ...
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### Interpreting Output Statistics of a Regression Model: Seeking Guidance

I recently estimated a regression model using statistical software, but I'm having trouble interpreting the output statistics like estimated coefficients and R-squared. Can you help me understand the ...
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### How to conduct a statistical analysis for a regression model when different independent variables have ordinal or continuous relation

I have a question about analyzing a regression model with a count type, 1 dependent and 10 independent variables that are in ordered fashion. For example, I have a dataset containing information on ...
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### What would it take for the omitted-variable bias from multiple omitted variables to cancel out?

Let's stick to ordinary least squares linear regression for now, and assume the typical conditions for the Gauss-Markov theorem. If it is helpful to assume Gaussian errors, that's fine. In such a ...
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### How can I set a multiple regression model to find out the correlation between store position and sales?

I need to calculate the inherent quality for every sales position inside a retail store. A sales position is a piece of furniture that holds multiple products on display for customers. Given that ...
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### Conducting a regression model with beta coefficients dependent to each other in a nonlinear way (My different independent variables are ordered)

I have a dataset of 1000 previous contests in a giveaway show where the contestant earns a random number of boxes named from "one" to "ten". The boxes contain either 1 or no gift. ...
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### Marginal effects in a Probit Model

The exact problem I am trying to solve is as follows. I have a Probit specification: $$P_t = \Phi(\beta^T x_t)$$ where $\Phi$ is a standard normal CDF and $x$ is a matrix of independent variables ...
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### In my DiD regression, I have % change as dependent variable and log(x) as a regressor. How do I interpret the beta coefficient?

I am trying to study how rent changes has evolved over distance to the city center between the pre- and post-COVID time periods. So I devote particular focus on comparing the relative rental and house ...
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### Same SE for all coefficients of a linear model

I am trying to find shellfish densities for a field-based aquaculture program and wanted to understand the impact of reef structure and site on the response. This experiment only has a sample size of ...
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### coefficient magnitude interpretation [duplicate]

I have a question regarding the interpretation of coefficient magnitude (not coefficient) in linear regression when the dependent variable is log-transformed. When the y is not log-transformed the ...
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### coefficient magnitude

"An interpretation based on coefficient magnitude also suggests that an increase of x (independent variable) by one standard deviation is associated with the increase of y (dependent variable by ...
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### Solving for the relationship between two regression coefficients

Is it possible to write $\beta$ as a function of $\gamma$ given the following definitions: $$\beta = \frac{cov(\log(W+X),\log(Y))}{var(\log(W+X))}$$ \gamma = \frac{cov(\log(W),\log(Y))}{var(\log(W))}...
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### OLS - The relationship between "minimizing SSR" and "the ration between cov(X,Y) and Var(X)" [closed]

Question What would be the intuitive explanation for the slope of Ordinary Least Squares(OLS), which is $\frac{cov(X,Y)}{var(X)}$ contributes minimizing the sum of squared residuals? In the same ...
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### Is it okay to sum logistic regression coefficients of multiple models to find an "average" model?

If I have N subsets of the data, each with the same variables, and run logistic regressions on each subset, could I then take an average of the coefficients found to find an "average" model? ...
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### Can I compare the coefficients of the ramp function between two groups in ARIMA model?

I analyzed the impact of a celebrity's disclosure of mental health condition in the monthly incidence of the diagnosis of the celebrity using an interrupted time series analysis (ITA) with the ARIMA ...
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### Interpretation of the coefficient of a dummy variable in a regression with log-transformed outcome

I want to interpret the models (2) Pool variable. It equals 1 if the house has a pool and 0 if not. The relation between the dependent variable and the Pool variable is a log-linear that means ∆y/y = ...
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### Split independent variables into two bigger categories

I am currently doing multiple linear regression and have around 8 independent variables x1....x8. I wanted to divide the 8 variables into two bigger categories named C1 and C2, containing the ...
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### Does one really need to normalize the features of a regression model when doing R^2 explained variance analysis if regression is convex?

TLDR; I want to know the percentage % of explained variance of the dependent variable given a list of D independent variables with crazy different scales -- but I believe that given convexity of ...
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### How to test H0 that two coefficients associated with dummy variables of same categorical variable are equal?

I have a variable $X$ which I predict with a nominal categorical variable $Y$ with category labels $\{0,1,\dots,m \}$ using a linear model. I use standard dummy coding which gives me the regression ...
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### Statistical test for significant change in regression parameter with new data?

Is there a statistical test that determines if there is a significant change in a regression coefficient parameter's value when more data is added? For example, you have 11 months of data, fit a ...
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### Log-log regression with log(1+x) and log(1+y)

I just read a paper where they used a log-log regression with log(1+x) as one of the independent variables and log(1+y) being the dependent variable. The only inference from this regression in the ...
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### How to estimate regression coefficients if the errors are t-distributed?

I estimated the linear regression using ols but the errors turned out to be t-distributed with df=3 according to q-q plot, I already know that gauss-markov theorem still assume the coefficients to be ...
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### Multi-collinearity

I have a binary response variable (presence/absence) and four independent variables (min.temp, max.temp, precipitation and elevation. My scatter matrix is showing collinearity between 3 of the ...
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### Sign of pearson correlation with negative regression coefficient

I want to obtain the pearson correlation of "experienced disfluency" and "narrative engagement" from the attached unstandardized coefficients for my meta-analysis. The paper is ...
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### Difference between controlling for other variables in additive models vs. interaction model

In a regression model with multiple predictors, the word "control" is used to refer to the inclusion of other variables than the one relevant to a specific question (e.g., the effect of ...
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### Understanding log odds ratio from quartiles in logistic regression

Data is found by running data(PimaIndiansDiabetes) from the mlbench package. ...
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### Is it allowed to compare coefficients in a discrete model WITHIN the same model?

I am conducting a discrete choice model (specifically, conditional logit). I would like to compare the strength of coefficients (log-odds) between four variables x1, x2, x3, and x4. I have heard ...
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### What does size of coefficients have to do with multicollinearity or overfitting?

In the section on Ridge Regression (source: Elements of Statistical Learning by Hastie, Tibshirani, Friedman) : When there are many correlated variables in a linear regression model, their ...
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### Estimating the parameter in a mixed population

I have different mixed populations where everyone as received a treatment among a list of treatment (let say Ta, Tb, Tc....). I know how many received each treatment. For each population, I know how ...
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### Build a model with Logistic Regression prediction and the same response

Probably a weird question, it's just something I am trying to understand. Say I have a binary classification problem (X,y) and y is in fact generated from X with some know coefficient (we can simulate ...
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### Find an estimator of linear regression when errors variance is correlated with one of the K regressors

I need to answer to the following problem: In an heteroschedasticity setting, let $n$ be the index of the n-th statistical unit with $n=1, \dots, N$. Suppose a multiple linear regression setting with ...
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### Multiple regressions and a coefficient being larger than the units of the dep.var

Can the coefficient of an independent variable in a multiple regression model be greater than the dependent variable units? E.g. if my dep. var. is categorical (10 scale), does it make sense if one of ...
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### What is the relation between the coefficients of linear models and the Jacobian matrix?

What is the relation between the coefficients of linear models and the Jacobian matrix? Should the matrix of coefficients of a (generalized) linear model be thought about as the Jacobian?
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### 3D Surface Fitting

I have a large empirical dataset which may be modelled via the following 3D surface formula: A*[X]+B*[Y]+C*[Z]+D*[X]*[Z] = 1 Where X & Z are the independent ...
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### meta-analysis: computing effect sizes for correlation coefficients, regression coefficients, and odd ratios

I'm conducting a meta-analysis examining the associations between two variables. I came across studies using different analyses including correlations (r), multiple regression, hierarchical linear ...