# 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.

176 questions
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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 <...
17answers
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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?
1answer
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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 $y=\beta_0+\beta_1x_1$, ...
2answers
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### Multiple regression or partial correlation coefficient? And relations between the two

I don't even know if this question makes sense, but what is the difference between multiple regression and partial correlation (apart from the obvious differences between correlation and regression, ...
1answer
16k views

### Is there a way to use the covariance matrix to find coefficients for multiple regression?

For simple linear regression, the regression coefficient is calculable directly from the variance-covariance matrix $C$, by $$C_{d, e}\over C_{e,e}$$ where $d$ is the dependent variable's index, ...
5answers
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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 ...
5answers
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### Coefficient changes sign when adding a variable in logistic regression

In my logistic regression the sign of coefficients of a variable (location distance of an amenity) changes based on other variables (with time -ve, with travel distance +ve) in the model. When the ...
1answer
64k views

### 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: ...
1answer
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### Interpretation of interaction term

I have a model: $$\ln({\rm earnings}) = a+b_1{\rm female}+b_2{\rm white}+b_3{\rm female}\times{\rm white}$$ ${\rm female}$ and ${\rm white}$ are dummy variables. I have interpreted $b_1$ and $b_2$: ...
2answers
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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 ...
3answers
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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 ...
2answers
21k views

### 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 ...
3answers
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### How to interpret logarithmically transformed coefficients in linear regression?

My situation is: I have 1 continuous dependent and 1 continuous predictor variable that I've logarithmically transformed to normalise their residuals for simple linear regression. I would ...
1answer
10k views

### How to compare two regression slopes for one predictor on two different outcomes?

I need to compare two regression slopes where: $y_1 ~ a + b_1x y_2 ~ a + b_2x$ How can I compare b1 and b2? Or in the language of my specific example in ...
2answers
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### Compare the statistical significance of the difference between two polynomial regressions in R

So first of all I did some research on this forum, and I know extremely similar questions have been asked but they usually haven't been answered properly or sometimes the answer are simply not ...
4answers
19k views

### “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 ...
3answers
8k views

### 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. ...
2answers
15k views

### How to convert standardized coefficients to unstandardized coefficients?

My goal is to use the coefficients derived by previous research on the subject to predict actual outcomes given a set of independent variables. However, the research paper lists the Beta coefficients ...
2answers
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### How can $R^2$ have two different values for the same regression (without an intercept) [duplicate]

My question is multifaceted. So I'll start by asking my question and then explain what has caused me to ask this question. How can I calculate the coefficient of determination for a linear ...
2answers
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### Efficiency of beta estimates with heteroscedasticity

I need something clarified and that is when you have non-constant variance, estimates won't be biased but will be a problem when it comes to the S.E. formulas and efficiency. Therefore OLS estimates ...
2answers
2k views

### Is the model wrong if a coefficient changes from minus in correlation table to plus in OLS?

Perhaps a very basic question but one that has me confused. Say, in a correlation table the relationship between A and the DV (B)...
1answer
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### R: linear regression: very small coefficient and R-squared but significant P values

I've got a very small coefficient (-0.04) and R-squared (0.028) but a significant P value (<0.0001). My question is: Is my result still meaningful? How to interpret it? The result is from a ...
2answers
10k views

### 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. $b = (X'X)^{-1}(X')Y$ ...
3answers
47k views

### 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 ...
1answer
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### Interpretation of LASSO regression coefficients

I'm currently working on building a predictive model for a binary outcome on a dataset with ~300 variables and 800 observations. I've read much on this site about the problems associated with stepwise ...
1answer
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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 ...
1answer
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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 ...
3answers
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1answer
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### Cox proportional hazard model and interpretation of coefficients when higher case interaction is involved

Here is the summary-output of the Coxph-model I used (I used R and the output is based on the best final model i.e. all significant explanatory variables and their interactions are included): ...
3answers
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### Is it possible in R (or in general) to force regression coefficients to be a certain sign?

I'm working with some real world data and the regression models are yielding some counterintuitive results. Normally I trust the statistics but in reality some of these things can not be true. The ...
4answers
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### How to interpret standardized regression coefficients and p-values in multiple regression?

I've been using R to analyze my data (as shown in example below) and lm.beta from the QuantPsyc package to get the standardized ...
2answers
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### How are partial regression slopes calculated in multiple regression?

I'm trying to understand how multiple regression statistically controls for the effects of other predictor variables when calculating partial regression slopes. In a multiple regression of Y~X1+X2, ...
1answer
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### Significance of individual coefficients vs Significance of both

This was a question I read from google quantitative analyst interview on glassdoor: If each of the two coefficient estimates in a regression model is statistically significant, do you expect the test ...
1answer
2k views

### Cohen's d from regression coefficient?

Is it appropriate to calculate Cohen's d (effect size) from the regression coefficient of an independent categorical variable? My coefficient represents participation in an intervention (treatment ...