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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11
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4answers
16k views

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 ...
10
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1answer
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) <...
11
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1answer
10k views

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 ...
10
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3answers
16k views

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 ...
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4answers
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 ...
9
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1answer
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): ...
7
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1answer
3k 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 ...
6
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2answers
4k views

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, ...
6
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1answer
565 views

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 ...
6
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3answers
4k views

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,...
3
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1answer
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 ...
3
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1answer
7k views

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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1answer
3k views

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 ...
8
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1answer
6k views

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: ...
6
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2answers
16k views

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,...
5
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1answer
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 ...
5
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1answer
16k views

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 ...
4
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2answers
4k views

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 ...
4
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2answers
678 views

How to interpret logistic regression coefficient

How do I interpret a regression coefficient in a logistic regression with two predictors? $\hat{L} = -14.27+3.32(3)+0.88(7)$ My understanding is to take the anti-log of the coefficient, like $e^{3....
3
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1answer
1k views

Coefficients for regression in levels from estimated first difference coefficients

I would like to know if there a simple way to compute coefficients for a regression in levels after having estimated a regression in first differences. Having estimated $$ y_t - y_{t-1} = a + b(...
3
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2answers
4k views

How to perform a meta-analysis of regression coefficients?

I want to perform a meta-analysis but the included studies use different models to analyze the data. There are Pearson correlation (3 studies), Spearman correlation (1 study) and several studies (~7-...
6
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2answers
403 views

Positive Poisson regression: what is the effect on the model of shifting vs truncating?

Let's say that you were wanting to model how many times someone had to take a certain test before passing (depending on a range of predictors like practice, mock tests taken, classes attended, etc.). ...
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0answers
892 views

SARIMA, coefficients check

I would appreciate if someone could check the mathematical equation for the seasonal ARIMA (4,1,4) x (1,1,1) period 12 that I wrote. I have done it this way, but I am not really sure if it correct is. ...
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0answers
636 views

Why signs of coefficients change when doing multivariate vs. univariate logit regression? [duplicate]

Excuse my dumb question, but I did an univariate logistic regression where the sign of the coefficient of my variable was negative (and it was significant). Once I have input it into a multivariate ...
3
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1answer
298 views

Regression when response variable is a function

I have a set of data $(X_i,Y_i)$, $i=1,\ldots,n$ where $X$ and $Y$ are supposed to satisfy the following equation $$ y = \beta_0(1+x^2)^{\beta_1},\quad x>0, \quad\quad (1) $$ I am interested in ...
3
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2answers
6k views

Should the final R glm include only significant levels of factors

I am running a glm in R on data with quite many predictors (~50), both initially continuous and factors. The response is binary and the volume of the data is OK (~100K rows), in order to model non-...
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2answers
7k views

How to interpret regression coefficients for a variable with takes positive and negative values?

I am running a GEE negative binomial regression to see how predictors affect the onset of violence through time. I have an $X$ variable (vegetation cover) which is calculated as whether an ...
2
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1answer
9k views

Changing units of measurement in a simple regression model

Assume a simple regression model, $y = \beta_0 + x\beta_1 + u$. I decide to change the units of measurement for the explanatory variable and the response variable. Do the $\beta_0$ and $\beta_1$ ...
2
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2answers
2k views

If a variable is found with p-value greater than 0.05, why is it also taken for calculation in the regression equation Y=a+b1*X1+b2*X2?

Suppose, I have performed multiple regression analysis on the following data set where X1 and X2 are independent variables and Y is the dependent variable. And achieved the following multiple ...
2
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2answers
1k views

Large coefficients and std. errors

I run a fixed effect model with Stata and because my dependent variable is a large number (max of 12 million and min of - 4 million), I got large coefficients for ...
2
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1answer
903 views

Interpreting the change in two logs in a regression

If I have a log-log regression, like: $\ln(\text {Price}) = b_0 + b_1 \times (\Delta \ln (\text{emp}))$ Where $\Delta(\ln (\text{emp})) = \ln(\text{employment growth_year2}) - \ln(\text{employment ...
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1answer
214 views

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 ...
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2answers
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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1answer
2k views

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 ...
0
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0answers
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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0answers
16 views

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 ...
0
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1answer
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, ...
20
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1answer
6k views

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 ...
20
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3answers
25k views

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' ...
22
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1answer
15k views

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: ...
5
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1answer
1k views

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 ...
6
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2answers
45k views

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 ...
6
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1answer
14k views

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 ...
5
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1answer
12k views

How to interpret the significance code?

I'm studying for some time and I´m trying to do a logistic regression (using GLM in R) and now it´s extremely difficult to know what to do. I have a binary dependant variable and 15 independent ...
14
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1answer
21k views

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 ...
9
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1answer
2k views

Can standardized $\beta$ coefficients in linear regression be used to estimate the $R^2$?

I am trying to interpret the results of an article, where they applied multiple regression to predict various outcomes. However the $\beta$'s (standardized B coefficients defined as $\beta_{x_1} = B_{...
6
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2answers
5k views

Feature Importance for Breast Cancer: Random Forests vs Logistic Regression

Assume I'm a doctor and I want to know which variables are most important to predict breast cancer (binary classification). Two different scientists each present me with a different feature importance ...
5
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1answer
6k views

Using the normal equations to calculate coefficients in multiple linear regression

I am trying to understand how to get the coefficient of a multiple linear regression. The formula is: $b = (X'X)^{-1}(X')Y$ I try to calculate $b$ without package and with the ...
7
votes
3answers
4k views

In linear regression, what does $\beta_1 = 0$ really mean?

If granted omniscience and we know that $\beta_1$ in a multiple linear regression model is truly 0, what does that mean in words (and math notation)? The model is: $Y = \beta_0 + \beta_1X_1 + \...
6
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4answers
4k views

Modeling prices with the Hedonic regression

I'm using the concept of Hedonic regression in order to model the prices for real estates. I'm having some trouble with my approach. What I have and what I do my data consists out of real estates ...