# 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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### Standardized beta weights for a multilevel regression

How can one obtain standardized (fixed effect) regression weights from a multilevel regression? And, as an "add-on": What is the easiest way to obtain these standardized weights from a ...
8k views

### R linear regression categorical variable “hidden” value

This is just an example that I have come across several times, so I don't have any sample data. Running a linear regression model in R: a.lm = lm(Y ~ x1 + x2) <...
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### How to interpret a negative linear regression coefficient for a logged outcome variable?

I have a linear regression model where the dependent variable is logged and an independent variable is linear. The slope coefficient for a key independent variable is negative: $-.0564$. Not sure how ...
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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 ...
26k views

### 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 ...
10k views

### 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): ...
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### 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 ...
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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, ...
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### Is there something called “mean coding” (like dummy coding & effect coding) in regression models?

When we perform a regression analysis with categorical predictors, we can use (1, 0), called "dummy coding". The coefficients in this case represent the deviation of the groups' means from the mean of ...
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### How to interpret coefficients of $x$ and $x^2$ in same regression

If I have the below functional form for an OLS regression, how do I interpret the $x$ and $x^2$? I cannot interpret them separately, correct? Do I interpret them as a summation of the two coefficients,...
314 views

### Which random effects to include in this GLMM?

In my study growth of plants was measured in different years on different plots (all plants were measured in all years). The question I'd like to answer with my model is: Which factors influence ...
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### There are low variations in the explanatory variables

I am running a regression and find coefficients of my explanatory variables very interesting (they are dummy variables). When I informed that to my lecturer, he told me that there are not much ...
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### Why is functional form so important when specifying models? [duplicate]

Variables: lprice = log(price of house) ldist = log(distance from incinerator) lintst = log(distance from interstate) 1st regression 2nd regression: In the 2nd ...
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### How to manually calculate dfbetas

I am trying to replicate what the function dfbetas() does in R. dfbeta() is not an issue... Here is a set of vectors: ...
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### Relationship between regressing Y on X, and X on Y in logistic regression

Correlation and linear regression are sometimes distinguished in statistics books by saying that the former is symmetric and the latter is asymmetric in the following sense: in the case of correlation,...
462 views

### Why don't the results of testing $H_0 : \beta = 0$ and $H_0 : {\rm cor}(X,Y)=0$ agree?

I have 4 IVs in my model that directly effect the DV. The results of the correlation & regression analyses showed that: IV1&DV: Pearson Correlation Coefficient: insignificant Regression ...
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### Clarification: The covariance of intercept and slope in simple linear regression?

Help me understand this relatively simple (I think) concept: The covariance of the intercept ($\beta_0$) and the slope ($\beta_1$) in simple linear regression. Furthermore, what range of values ...
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### Standard deviation of the sum of regression coefficients

I'm doing OLS estimation with an independent variable lagged as t-1, t-2, t-3, and t-4 (four beta coefficients). I would like to have the sum of these coefficients for interpreting the net impact of ...
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### Interpretation of different logistic regression models to test hypotheses

I would like to test two hypotheses, but I am a little bit confused. I have a binary dependent variable z, my key variable a is ...
337 views

### Closed form solution for slope coefficients in bivariate regression

In a univariate regression, $Y=a+bX+e$, the solution for slope b is given by $COV(X,Y)/VAR(X)$. Is there a similar expression for a bivariate regression $Y=a+bX+cZ+e$. What is the closed form ...
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### Calculate expected values using logistic regression coefficients [duplicate]

The outcome of the logistic model is binary (0;1) - intervention that occurs in hospital (3838 interventions in 51096 cases). I am modeling the effect of age groups (60 to 74; 75 to 89 and 90+) and ...
102 views

### Simultaneous estimation of a group of linear model (regression) parameters

Suppose $y=ax+z$ where $x, y, z$ are random variables with range in $\mathbf R$, $\mathbf E[x]=\mathbf E[z|x]=0$ and $a$ is a constant. Note the distribution of $z$ conditioned on $x$ depends on $x$. ...
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### Least squares fit of a bivariate quadratic-linear product to an oriented point set

As explained in this question, a bivariate quadratic has 6 DoF (coefficients), and a bivariate cubic has 10 DoF, while a bivariate quadratic-linear product has 8 DoF. The quadratic or the cubic models ...
273 views

### Calculating group mean and confidence interval from single-subject means and confidence intervals

I have a sample of 20 subjects. I have two continuous variables, X and Y which are linearly related. I use linear regression to estimate the regression coefficient relating X and Y. For each subject, ...
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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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### 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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### 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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### Relationship between least-squares regression and information theory

Is there a well-known relationship between least-squares regression and information theory? I've just started reading about information theory. It seems almost trivial to say that the regression ...
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### How to interpret Quadratic Terms

I'm answering a practice exam questions, and having trouble with one on quadratic terms. Could someone give me a quick summery of 1) why they are sometimes included? 2) How to interpret them? In ...
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### Interpreting Principal Component Analysis output

If I have 50 variables in my PCA, I get a matrix of eigenvectors and eigenvalues out (I am using the MATLAB function eig). I have normalised the eigenvalues to sum ...
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### How to interpret the significance code?

I'm studying for some time and IĀ“m trying to do a logistic regression (using GLM in R) and now itĀ“s extremely difficult to know what to do. I have a binary dependant variable and 15 independent ...
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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 ...