# 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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### Including the interaction but not the main effects in a model

Is it ever valid to include a two-way interaction in a model without including the main effects? What if your hypothesis is only about the interaction, do you still need to include the main effects?
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### How to interpret coefficients in a Poisson regression?

How can I interpret the main effects (coefficients for dummy-coded factor) in a Poisson regression? Assume the following example: ...
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### Interpretation of log transformed predictor and/or response

I'm wondering if it makes a difference in interpretation whether only the dependent, both the dependent and independent, or only the independent variables are log transformed. Consider the case of <...
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### How to interpret coefficients from a polynomial model fit?

I'm trying to create a second order polynomial fit to some data I have. Let's say I plot this fit with ggplot(): ...
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### Does the order of explanatory variables matter when calculating their regression coefficients?

At first I thought the order didn’t matter, but then I read about the gram-schmidt orthogonalization process for calculating multiple regression coefficients, and now I’m having second thoughts. ...
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### How does bootstrapping in R actually work?

I've been looking into the boot package in R and while I have found a number of good primers on how to use it, I have yet to find anything that describes exactly what is happening "behind the scenes". ...
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### What does “all else equal” mean in multiple regression?

When we do multiple regressions and say we are looking at the average change in the $y$ variable for a change in an $x$ variable, holding all other variables constant, what values are we holding the ...
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### How to interpret main effects when the interaction effect is not significant?

I ran a Generalized Linear Mixed Model in R and included an interaction effect between two predictors. The interaction was not significant, but the main effects (the two predictors) both were. Now ...
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### interpreting estimates of cloglog logistic regression

Could someone advise me on how to interpret the estimates from a logistic regression using a cloglog link? I have fitted the following model in lme4: ...
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### Importance of predictors in multiple regression: Partial $R^2$ vs. standardized coefficients

I am wondering what the exact relationship between partial $R^2$ and coefficients in a linear model is and whether I should use only one or both to illustrate the importance and influence of factors. ...
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### Calculate coefficients in a logistic regression with R

In a multiple linear regression it is possible to find out the coeffient with the following formula. $b = (X'X)^{-1}(X')Y$ ...
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### How to compute the standard errors of a logistic regression's coefficients

I am using Python's scikit-learn to train and test a logistic regression. scikit-learn returns the regression's coefficients of the independent variables, but it does not provide the coefficients' ...
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### Interpretation of betas when there are multiple categorical variables

I understand the concept that $\hat\beta_0$ is the mean for when the categorical variable is equal to 0 (or is the reference group), giving the end interpretation that the regression coefficient is ...
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### Standard errors for multiple regression coefficients?

I realize that this is a very basic question, but I can't find an answer anywhere. I'm computing regression coefficients using either the normal equations or QR decomposition. How can I compute ...
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### How to deal with an error such as “Coefficients: 14 not defined because of singularities” in R?

When doing a GLM and you get the "not defined because of singularities" error in the anova output, how does one counteract this error from happening? Some have suggested that it is due to ...
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### How to treat categorical predictors in LASSO

I am running a LASSO that has some categorical variable predictors and some continuous ones. I have a question about the categorical variables. The first step I understand is to break each of them ...
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### Question on how to normalize regression coefficient

Not sure if normalize is the correct word to use here, but I will try my best to illustrate what I am trying to ask. The estimator used here is least squares. Suppose you have $y=\beta_0+\beta_1x_1$, ...
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### Can I ignore coefficients for non-significant levels of factors in a linear model?

After seeking clarification about linear model coefficients over here I have a follow up question concerning non-signficant (high p value) for coefficients of factor levels. Example: If my linear ...
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### How to interpret the coefficients from a beta regression?

I have some data that is bounded between 0 and 1. I have used the betareg package in R to fit a regression model with the bounded data as the dependent variable. My ...
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### An unbiased estimator of the ratio of two regression coefficients?

Suppose you fit a linear/logistic regression $g(y) = a_0 + a_1\cdot x_1 + a_2\cdot x_2$, with the aim of an unbiased estimate of $\frac{a_1}{a_2}$. You are very confident that both $a_1$ and $a_2$ ...
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### “Moderation” versus “interaction”?

I have come across these two terms which are used interchangeably in many contexts. Basically, a moderator (M) is a factor that impacts on the relationship between X and Y. Moderation analysis is ...
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### Do coefficients of logistic regression have a meaning?

I have a binary classification problem from several features. Do the coefficients of a (regularized) logistic regression have an interpretable meaning? I thought they could indicate the size of ...
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### Sparsity by discarding least squares' coefficient

Suppose I wish to regress $Y$ against a normalized $X$, but I would like a sparse solution. After regression, why is discarding the coefficients with smallest magnitude not allowed? For the record, ...
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### What's the difference between regression coefficients and partial regression coefficients?

I've read in Abdi (2003) that When the independent variables are pairwise orthogonal, the effect of each of them in the regression is assessed by computing the slope of the regression between ...
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### Regression to the mean in “Thinking, Fast and Slow”

In Thinking, Fast and Slow, Daniel Kahneman poses the following hypothetical question: (P. 186) Julie is currently a senior in a state university. She read fluently when she was four years old. ...
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### Recovering raw coefficients and variances from orthogonal polynomial regression

It seems that if I have a regression model such as $y_i \sim \beta_0 + \beta_1 x_i+\beta_2 x_i^2 +\beta_3 x_i^3$ I can either fit a raw polynomial and get unreliable results or fit an orthogonal ...
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### Ridge regression coefficients that are larger than OLS coefficients or that change sign depending on $\lambda$

When running ridge regression, how do you interpret coefficients that end up larger than their corresponding coefficients under least squares (for certain values of $\lambda$)? Isn't ridge regression ...
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### Interpretation of incidence-rate ratios

So, I want to fit a random effects negativ-binomial model. For such a model STATA can produce exponentiated coefficients. According to the help file such coefficients can be interpreted as incidence-...
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### Joint model with interaction terms vs. separate regressions for a group comparison

After gathering valuable feedback from previous questions and discussions, I have came up with the following question: Suppose that the goal is to detect effect differences across two groups, male vs. ...
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### What does r, r squared and residual standard deviation tell us about a linear relationship?

Little background I'm working on the interpretation of regression analysis but I get really confused about the meaning of r, r squared and residual standard deviation. I know the definitions: ...
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### Positive correlation and negative regressor coefficient sign

Is it possible to obtain a positive correlation between a regressor and a response (+0,43) and, after that, obtain a negative coefficient in the fitted regression ...
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### Acceptable r-square value for multiple linear regression model [duplicate]

I'm currently working on my thesis, more specifically I'm analyzing some data collected from researchers about the project's they're working on. In the end, I have performed a multiple linear ...
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### Comparing regression coefficients of same model across different data sets

I'm evaluating two (2) refrigerants (gases) that were used in the same refrigeration system. I have saturated suction temperature ($S$), condensing temperature ($D$), and amperage ($Y$) data for the ...
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### Difference between marginal and conditional models

A marginal model accounts for the correlation within each cluster. A conditional model also takes into account the correlation within each cluster. My questions are: Does a marginal model models ...