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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regression coefficient on sum of regressors

Say I have the true linear model with normal errors: $y = \beta_1 X_1 + \beta_2 X_2 + \epsilon$ However, I only observe $Z = X_1 + X_2$, so I estimate instead: $y = \delta (X_1 + X_2) + e$, can I ...
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How to do permutation test on model coefficients when including an interaction term?

Given the following model as an example: $$Y=\beta_0+\beta_A\cdot A+\beta_B\cdot B+\beta_{AB}\cdot A \cdot B+\epsilon$$ In alternative notation: $$Y\sim A + B + A: B$$ The main question: When ...
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What is the probability regression coefficient is larger than its OLS estimate

Consider a sample of 34 pairs of values $(x,y)$ for the regression equation $$y_{i}=\alpha + \beta x_{i} + \epsilon_i .$$ Using linear regression (OLS), I got the estimate $\hat{\beta}=2.3$. What ...
638 views

Standardized and unstandardized variables yield different results for mixed regression model

I have created two mixed regression models, one with raw unstandardized variables and the same model with standardized variables. When I convert the coefficients from the standardized variables I get ...
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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 ...
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Time varying coefficient in Cox model

I have a model for survival after an injury that is borderline passing the Schoenfeld test for the proportional hazards assumption (cox.zph() in R). However, ...
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Prior for the coefficients of a linear regression model

I have a linear regression model $\bf Y=\bf{X}\bf{\beta}+\epsilon$. I want to assign a prior on $\bf\beta$ in order to derive the posterior predictive model $p(y_{predictive}|\bf{y},\bf{X},\beta)$. ...
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Comparing coefficients of time series models

How do I test if two time series' coefficients differ significantly from one another? I feel like this should be pretty simple... should I just use the estimates/standard errors and calculate a Z-...
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How to interpret coefficients in a vector autoregressive model?

Can I interpret the coefficients in a VAR model in the same way as I do in a normal OLS regression?
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Will larger correlation coefficient values result in greater slopes between x and y?

For example, if there are two data sets, and the first has a larger correlation between x and y than the second, does this mean the first data set has a greater slope than the second?
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Comparing coefficients in logistic regression

I have some problems I need help with. I am running a binary logistic regression. ...
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Should a predictor, significant on its own but not with other predictors, be included in an overall multinomial logistic regression?

I constructed a model via multinominal logistic regression analysis. The final model contains three predictors. All predictors are significant when they are the only predictors. However, the ...
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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,...
966 views

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 ...
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Population parameters of a regression

So this has really been bothering me and I was hoping for a (simple!) explanation if possible. Suppose I've specified a linear regression model: $$Y = \beta_0 + \beta_1 X + \epsilon$$ And an ...
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Interpretation of coefficients in polynomial regression for predictive modeling

I am building a predictive model (binary target variable) in the financial services industry. One of the (many) potential predictors I am adding to the model is related to the customers checking ...
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Testing a regression coefficient against 1 rather than 0

Brief caveat- I haven't dusted off my stats knowledge since some university courses a few years ago, and I'm struggling with cobwebs. I have a model where a linear 1 to 1 relationship has been ...
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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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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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How to read the Interaction effect in multiple linear regression with continuous regressors?

If the interaction happens between a continuous and a discrete variable it is (if I'm not mistaken) relatively straightforward. ...
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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 ...
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Variance of slope

I have a bunch of data that I fit a linear regression to, and now I need to find the variance of my slope. Is there an analytical way to get this? If an example is necessary, consider this my data in ...
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Correctness of regression with ARIMA errors model and coefficient interpretation issues

I am trying to forecast electricity consumption in GWh for 2 years ahead (from June 2013 ahead), using R (the forecast package). For that purpose, I tried regression with ARIMA errors. I fitted the ...
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Zero regression coefficient when correlations are not zero

I don't really have a motivation for this - but I was thinking about this and couldn't work it out. Suppose I have a random variables $X$ and $Y$ which are correlated. Is it possible that the ...
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Combining regression estimates by summing

I want to know if one can combine regression estimates from panel regressions when the new dependent variable is a sum of the dependent variables from previously estimated regressions. To be ...
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Regularized parameter overfitting the data (example)

Possible duplicate of (Why) do overfitted models tend to have large coefficients? How does regularization reduce overfitting? In the Coursera's machine learning course by Andrew Ng, I came across ...
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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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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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Can the bias introduced by lasso change the sign of a coefficient?

L1 penalized regression introduces a bias on your regression model but decreases the variance. When this bias is introduced, is it possible that the coefficient of $B$ changes sign? This would ...
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Interpretation of coefficients in logistic regression output

I am doing logistic regression in R on a binary dependent variable with only one independent variable. I found the odd ratio as 0.99 for an outcomes. This can be shown in following. Odds ratio is ...
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Regression slope that increases persistently as my sample size increases

I found a peculiar feature in some data that I am analyzing and was wondering whether there was a technical term for this type of phenomenon and whether anyone has come across it before. I am doing a ...
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Can I calculate Cohen's $d$ from multiple regression coefficient?

Question: Is it appropriate to calculate Cohen's $d$ (effect size) from the regression coefficient of an independent categorical variable? Background: My regression coefficient represents ...
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Regression coefficients by group in R?

I have a dataframe with a group variable GRP (ranging from 1-100) and an X and Y for each one. I'd like to get a list of the regression intercepts and slopes for lm(Y~X) within each group. The ...