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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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Directly Comparing Regression Beta-Weights [on hold]

I have a model where my dependent variable and 3 independent variables are standardized so that they are beta-coefficients. I would like to use these coefficients to predict a new point WITHOUT the ...
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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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Correlation coefficients, many realizations [closed]

I'm doing an experiment to see the level of correlation between two variables $x$ and $y$. I simulated under the same conditions the set of data $x$ and $y$, and repeat it many times. After each ...
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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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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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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 ...
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1answer
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Interpreting regression results with decimal percentage variables

I have a regression where both my Y and X variables are measured in percent (so they are decimals values, mostly less than 0). The coefficient from the regression is 0.43. Is it correct to say that a ...
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Is there a formula to convert t-value from a regression parameter to an effect size (d)?

I've seen formulas to convert independent or dependent samples t-tests into effect sizes, but what about converting the t-value from a regression parameter to an effect size?
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Interpreting GAM Coefficients

I could use some advice interpreting GAM (Generalized Additive Model) coefficients. I get the following results when I call coef on my model: ...
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Comparing coefficients of survival analysis with Gompertz distribution in R

I am performing Gompertz analysis of survival to calculate initial mortality rate (IMR) and Gompertz coefficient (rate of ageing) of different strains of worm. I am doing this by using the package ...
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1answer
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asymptotic behavior of OLS estimators

Conceptually when do estimated regression coefficients converge with the true values; is it a) when the sample size of observations tends to infinity or b) when the regression with the same predictors ...
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How to back-transform glmer() cbind() proportion data

I have fit a binomial GLMM (glmer) to a response variable that is a proportion. How my data looks: ...
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Interpreting the coefficients on age categories in Panel Regression

I am running a panel regression for 20 quarters of 311 local authorities. I am regressing their recycling rate on a series of variables (log income, log household size, log population density). I ...
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Interpretation of Conway Maxwell Poisson regression coefficients

For a simple Poisson regression, I would interpret the coefficient as (1-exp(coef))*100 for percentage change in y given a unit change in x So for a Conway-Maxwell Poisson regression, Sellers and ...
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interpreting HLM coefficients

I have created the following model of longitudinal observations in HLM7: ...
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1answer
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Multiple correlation coefficient of a simple linear regression

I'm having a bit of a hard time understanding why the 'multiple correlation' coefficient within a simple linear regression (i.e., 1 predictor) isn't identical to the coefficient of determination. I ...
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Do I need a validation set if I am doing 10-fold cross validation?

I am looking at a dataset with ~120 observations and I am investigating it using two sets of explanatory variables, one has about 12 features, the other about 8. This is for a regression analysis. ...
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1answer
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Interpreting regression coefficients when the outcome variable is an inverse hyperbolic sine function

I just learned that when there are zero or negative values, a good alternative to using a logged function is the inverse hyperbolic sine function. When using log transformation on the dependent ...
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How to test if regression coefficient = 1 [duplicate]

I’m attempting to run a regression and test whether the slope is equal to 1. Most statistical packages only test of it's equal to zero. Is there a way to bypass this ? I’ve SPSS and minitab and can ...
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Least squares regression coefficient with minimal information

If I only have a correlation matrix of 4 variables and the sample size, is it possible to predict 1 variables from the other 3 while using information about sample size? I’m trying to use lm but my ...
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relation between OLS regressions using different data transformations

I have a $(n \times d)$ panel $y$ of $n$ different variables , and a $(n \times d)$ panel $x$ of their forecasts. $d=$ time length of data $n=$ cross section width/ no. of variables I run a pooled (...
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Removing coefficients from multiple regression analysis

0verview I am undertaking a study where we analysing the fine details of two multiple regression equations. Multiple regressions were carried out for the months of February and August 2017, with ET ...
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Rescaling model coefficients

I have the following model $y \sim b_0 + Z \theta_0 + X \beta + \sum((X_j \circ Z) \theta_j)$ Where... $Z$ is (n, k) $X$ is (n, p) $\beta$ is (p,) $\theta$ is (p, k) $\theta_0$ is (k,) $\circ$ is ...
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Including % Race/Ethnicity in Regression Model

I have been examining high school graduation rates, and wanted to include race/ethnicity as a control. The only data available is % of students identifying as one of 7 race/ethnicity categories. My ...
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1answer
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Coefficient of multiple correlation for multiple linear regression with degree > 2 and interaction terms

I want to calculate the Coefficient of Multiple Correlation $R^2$ for a multiple linear regression with polynomial features of degree >= 2 (with interaction terms). Let's say I want to obtain the ...
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Interpreting coefficients when variables are % of GDP and an index value (0 to 1)

My dep variable is investment (% of GDP) and my independent variables are saving (% of GDP), Terror (which is an index I have created, where a value of 0 is the lowest level of terrorism and 1 is the ...
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2answers
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Why does the OLS-intercept not just “de-mean” the residuals of the same model without intercept?

The answer here explains, why the residuals of an OLS-regression have mean zero if an intercept is included. Problem: Intuitively, i would assume that including an intercept just "de-means" the ...
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Difference between regression p-values and t-test on residuals?

I'm interested in testing if a particular (binary) feature is significant in explaining a target variable, after other factors have been considered. Naively, I can do this by including the test ...
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How to obtain regression coefficients of a multiple linear regression model from simple linear regression models? [duplicate]

Suppose I have a multiple linear regression model $$ Y=\beta_0+\beta_1X_1+\cdots+\beta_pX_p+\epsilon$$ How can I obtain the regression coefficients $\hat{\beta_i}$ by fitting just a series of simple ...