# 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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3answers
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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
67k 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?
1answer
7k 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 $y=\beta_0+\beta_1x_1$, ...
1answer
17k 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
9k views

### 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 ...
2answers
41k 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, ...
5answers
10k 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 ...
1answer
67k 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
5k 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 $b_2$: ...
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 ...
3answers
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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
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 ...
1answer
2k views

### 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
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 ...
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. ...
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 ...
2answers
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### 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
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 ...
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)...
2answers
2k views

### 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 ...
1answer
4k views

### 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
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. $b = (X'X)^{-1}(X')Y$ ...
3answers
48k 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 ...
3answers
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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. ...
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 ...
1answer
12k views

### 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
9k views

### 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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2answers
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### Testing for coefficients significance in Lasso logistic regression

[A similar question was asked here with no answers] I have fit a logistic regression model with L1 regularization (Lasso logistic regression) and I would like to test the fitted coefficients for ...