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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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Inclusion of standard error in regression equation

I often see that standard errors are displayed under the regression equation but I don't really understand the purpose of it. Are those the standard errors of the estimated slope coefficient? And how ...
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25 views

Coefficient Interpretation when dependent and independent variables are percentages

I have built a linear mixed regression model with fund returns (measured in percentage ie. 0.01 denotes one percent) as the dependent variable. For the independent variables I have percentage level of ...
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What is the effect of balanced class weights on logistic regression coefficients?

I'm specifically using sklearn's LogisticRegression on my unbalanced dataset, which has around 97% negative responses and 3% ...
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correlation coefficient [on hold]

Based on the data in the table above: I just need someone to confirm my answers. I did the question in MATLAB. a) Find the correlation coefficient between hydrocarbon levels and oxygen purity The ...
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How to test whether individual fits to regression line or not

I have a defined regression model for the healthy control (HC) group, with corresponding CIs of coefficients and of E(Y). I would like to test whether individuals belonging to another population (...
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Interpretation of removed continuous variables in regression due to linear dependence

I have created a standard OLS regression model to estimate the House Price and one group of variables describe the age group percentage of population in a particular neighborhood (ranging 0 to 100). ...
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Obtaining Mean Differences from DESeq2 Output

I have conducted some analyses using DESeq2 and obtained the output. However, instead of interpreting the effect sizes as log2FoldChanges, we would prefer to obtain a model-based mean difference. I ...
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Is the Coefficient of Variation valid for data which does not follow a normal distribution?

I am trying to compare the dispersion of several data vectors. As an example I have that via two methods produces one vector of data that fits a normal distribution and other one that follows an ...
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How to calculate the coefficient of a dummy variable reference category?

I am currently building a regression model with numerous continuous, categorical (employing dummies) and interaction variables. I understand we must use k-1 dummies with one variable becoming the ...
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interpretation of coefficients of independent variables in fractions

I am a bachelor student finishing my thesis and desperately need some help with the interpretation of regression coefficients. I am currently quite confused and my deadline is three days away. I have ...
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Interpretation of standardized (z-score rescaled) linear model coefficients

I have analyzed some data on vegetation change as a function of change in soil parameters. I compared a dataset from 2001 with a dataset from 2018 (fully balanced). To investigate the change in ...
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ANOVA is significant but coefficients aren't

My master thesis investigates the relation between stock raw returns and sentiment scores. To make a conclusion there is a multiple linear regression with the mean sentiment, the variance of the ...
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Multiple regression and multiple comparisons 3 groups

I'm trying to compare the effect of an IV on my DV, where my data are separated into 3 groups. Specifically, in one group there is a significant correlation between IV and DV, but in the other two ...
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regression with very low R2, metric coefficient interpretation

my regression model give extremely low R2. In this case can i still interpret my X variables with significant p-value in the way that x goes up by 1 unit, y goes up by coefficient unit (with others ...
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Log-linear difference-in-differences

I am estimating several linear models using a difference-in-differences (DiD) framework. The model interacts a treatment indicator (i.e., 1 for the treatment group, 0 for the control group) and a "...
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Elastic Net - number of non-zero variables

I have a question regarding the interpretation of the trace of coefficients when running Elastic net with the package glmnet in R. This is the plot I obtain with alpha = 0.5 My understanding is that ...
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Updating regression solutions for a new regressor without the original dependent variable

Note: This question is analagous to the question I asked here except instead of a removing column, I am adding it. I am interested in a linear regression on the model; $Y= X\beta + \epsilon$ And I ...
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how to report paired comparisons in linear basis function model?

I am struggling with correctly reporting the results of a linear (mixed) basis function model I ran. The model is specified in R as ...
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Ceteris Paribus interpretation if it isn't possible in reality

Does it make sense to include both respondent's age (in years) and respondent's partner's age (in years) in a simple linear regression with cross-sectional data? The outcome variable, for example, ...
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OLS loss function 3-d surface plot

I was trying to plot the OLS loss function as a function of coefficients $\beta_0$, $\beta_1$. As far as I know it should be a convex function with one local minimum which is also a global minimum. I'...
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Will LASSO choose variables that are highly correlated with the outcome variable?

Suppose we have access to an outcome variable $Y_i$ and a $p$-dimensional vector $X_i$ for $i=1,\ldots,N$. We run a LASSO regression of $Y$ on $X$ for every penalty/shrinkage parameter $\lambda$ in an ...
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Error estimates for coefficients of a non-negative quantile regression

I am looking for a way to provide an error estimate for coefficients obtained from a non-negative quantile regression. The complicated part aside from positivity constraints is that my observations ...
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1answer
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Corroborating a differnce in differences identification strategy

I read in Mostly harmless econometrics that a good way of testing whether a difference in differences is a good identification strategy is running this equation: where the first sums are post-...
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Validity assessment of multiple regression marketing mix model

My employer has engaged a consultancy firm to carry out marketing mix modeling in order to quantify the impact of various marketing activities and promotional campaigns on overall sales and also for ...
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Intercept in demeaned and rescaled regression model

Suppose I have a linear model; $Y=X\beta+\epsilon$ Where $X$ is $(n \times p)$, with the first column of $X$ being an intercept column (consisting only of ones). Now suppose I construct $\tilde{X}$ ...
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Coefficient of variation and residual standard deviation

From my knowledge, coefficient of variation and residual standard deviation are highly correlated. Such that if we find a significant change in one, we will find a significant change in the other. In ...
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Interpretation of regression coefficients: second-order differencing

Main Question: How are the coefficients of the second-order differenced explanatory variables to be interpreted? (See the attached screenshot of my result.) Analysis framework: I examine the ...
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Estimating effect of linear regression coefficients with multicollinearity

As I didn't find a satisfying for that questions I try it here: I have a multivariate Lineare Regression model with some correlated predictor variables. The "simple" question I want to answer is: "If ...
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How to determine predictor importance at each level of an HLM model

I am working with a Hierarchical Linear Model (HLM). I want to determine which predictors are important at each level of the data. Across different hierarchical levels the fixed effects along with the ...
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2answers
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Interpreting regression coefficients when the dependent variable is in percentages?

I have a dependent variable that is % of students graduating, but the explanatory variables are all absolute numbers, such as number of applicants and college fees. How would I interpret a coefficient ...
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Logistic Regression with categorical predictors - how to report?

Hello Stack Exchange. I need to run a logistic regression to determine the significance of the effect of 5 categories of one variable on my dependent variable. I just can't find online anywhere how ...
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Calculating standard error of coefficients in segmented regression

I know this is kinda stupid question to ask here but just to make sure that I am doing this correctly, here it is anyway: Consider the following equation resulted from segmented regression: $$\hat ...
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Comparing independent MRDM models (multiple regression on distance matrices)

I am conducting Multiple Regressions on Distance Matrices (MRM or MRDM) to estimate the influence of 3 independent variables (IVs) on intraspecific $\beta$-diversity (my response variable DV) between ...
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1answer
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REGRESSION :A log-linear interaction term

How do I interpret a log-linear interaction term, is it possible? My model: $Y= B_1 + B_2\log X_1 + B_3X_2 + B_4(\log X_1 X_2) + u $
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Interpreting coefficients and understanding logistic lasso

In lasso regression, increasing the regularisation strength/shrinkage penalty eventually forces all of the regression coefficients to zero. In this instance the regression is logistic. The plot shows ...
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Does dummy code a variable affect the intercept in a linear regression model

My colleague and I were both using R to fit a linear regression with the same dataset and same variables. The outcome variable is test grade while the independent variables are gender, age, and times ...
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Interpretation of coefficients for DV in shares

I very ensure about following interpretations, hence I would be very thankful for any advice. Let's say that my dependent variable is a percentage of managers in total employment ((managers employed ...
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1answer
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the constant coefficients are penalized in the ridge logit conditional model?

I am estimating a conditional ridge logit model, there is very little bibliography about it, and I do not know if the constant coefficients are penalized. My model has 2 variables and 3 alternatives, ...
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Decomposing R^2 into independent variables

Consider a linear regression model: $$y = β_0 + β_1X_1 + β_2X_2 + ... + β_kX_k + ε$$ where $R^2 = 1 - (SSR/SST)$. I would like to determine the contribution of a factor $i$ (call it $R^2_i$) into ...
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Correlation formula for a Quadratic

I have used quadratic regression on a dataset to find the graph of best fit, that is, finding the coefficients a, b and c in the general formula of y = ax^2 + bx + c. Having done that I would now ...
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Invariance of results when scaling explanatory variables in logistic regression, is there a proof?

There is a standard result for linear regression that the regression coefficients are given by $$\mathbf{\beta}=(\mathbf{X^T X})^{-1}\mathbf{X^T y}$$ or $(\mathbf{X^T X})\mathbf{\beta}=\mathbf{X^T ...
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Regression coefficient signs different for log/asinh and level versions of same variable

I ran two regressions. First, say, y=βx, and the second one, asinh(y)=βx, which I read is asymptotically equivalent to log(y)=βx, where x and y are the same variables with same data set for these two ...
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How to account for incrementation in a log-linear model

I want to perform a mixed regression analysis with random intercept and uncorrelated random slope after multiple imputation. The dependent variable is continuous, namely a duration as number of days ...
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Standarized coefficients of a general additive model GAM

I am using a GAM model to study the effects of time (in weeks) and quality parameters (qp1, qp2, qp3 and qp4) on a response variable. Since the effect of time is modelled best by a spline, I am using ...
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Pairwise comparisons of regression coefficients [duplicate]

I would like to know how to make quickly pairwise comparisons of regressions coefficients across three or more groups in R. Here is a small example: ...
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1answer
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Interpreting ridge coefficients as a function of regularization

Data consists of 40 observations with 4 dimensions and a response-variable. When doing a ridge regression on my data and plotting the coefficients and coefficient errors (MSE of the ridge ...
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How to prove that conditional distribution for Y given OLS for simple linear regression do not depends on original parameters? [duplicate]

How to prove that for a simple linear regression model: $$y_i=\beta_0+\beta_1 x_i+\varepsilon_i,$$ the conditional distribution $$Y|\hat{\beta}_0,\hat{\beta}_1$$ do not depends on $\beta_0$ and $\...
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Interpreting log coefficients in differences model (time series/panel)

I am struggling with the interpretation of coefficients in $\delta(\log y)=\alpha+\beta\delta(\log x)$ Usually in a $y=\alpha+\beta x$ model, $\beta$ represents change in $y$ corresponding to unit ...
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Interpreting log transformations in a logistic regression

This stats.stackexchange post contains explanation of how to interpret transformed variables in linear regression. In particular, I found this snippet in Graham Cookson's answer (2nd answer): Y ...