# 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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71k views

### 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?
50k views

### 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 <...
8k views

### 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 ...
18k 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, ...
44k views

### 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, ...
11k views

### 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 ...
71k 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: ...
6k views

### 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 $b_2$: ...
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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 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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### 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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### 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 ...
8k views

### How to apply coefficient term for factors and interactive terms in a linear equation?

Using R, I have fitted a linear model for a single response variable from a mix of continuous and discrete predictors. This is uber-basic, but I'm having trouble grasping how a coefficient for a ...
18k views

### 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 ...
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### Distribution of linear combination of OLS regression coefficients

I have a simple linear OLS regression $Y_i = \alpha+ \beta_1 X_{1i} + \beta_2 X_{2i} + e_i$ where $e_i \sim N(0,\sigma)$. I have estimated the regression from the data and obtained estimates for my ...
21k 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 ...
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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 ...
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 ...
9k 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. ...
51k 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 ...
16k 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 ...
4k views

### Linear regression with log transformed data - large error [duplicate]

I have a set of data which is has a very large positive skew, and has been transformed using a logarithm. I wish to predict one variable from another using the lm ...
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### 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)...
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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 ...
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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 ...
11k 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. $b = (X'X)^{-1}(X')Y$ ...
49k views

### 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 ...
10k views

### 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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### 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 ...
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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 ...