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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Interpretation of coefficients and their confidence intervals in a regression analysis

Note: apologies in advance if this is a duplicate, I didn't find a similar q in my search Can you compare two independent variables and their confidence intervals in a regression model? I am running a ...
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Testing for regression coefficient equal to 0

I usually take a look at the diagonal elements of the matrix $(X'X)^{-1}$ and the $MSE$ in order to determine the standard deviation of the regression coefficients. I encountered a problem from a ...
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varying coefficient models parameters and estimation first principles

Please could someone explain in lay terms how the varying coefficient model works? The generalised form looks like eigenvectors. I am unsure why there is Xb(U-u) and K(U - u) and what these are used ...
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Interpretation of multiple regression coefficients

I want to analyse the causal effect of the attendance of an event on the attitude of inviting other people to any event in the future. I have data from individuals from around the world with data on ...
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1answer
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Adjust 95% CI and P value if I scale up predictors in the logistic regression?

I am conducting a logistic regression in R and trying to understand whether to adjust the p-value and 95% CI, in the same way, I did for the coefficient/odds ratio if I want to report "every 5-...
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Compare regression coefficients across two (or more) svyglm() models

The question I have is related to this one, but slightly more specific. Suppose I use data from a large-scale educational assessment to investigate how students' proficiency in math depends on their ...
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Interpretation of coefficients when multiplied OLS [duplicate]

Suppose I have a Ordinary Least Squares model of this form: $Y = \beta_0 + \beta_1 X_1 + \beta_2 X_2 + \beta_3 X_1*X_2$ What would be an interpretation for the coefficient $\beta_3$? (Suppose that $...
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Interpreting regression coefficients with log percentage as dependent variable and first difference of share as independent one

I estimate a model where the dependent variable is log-transformed percentage (0-100) and the independent variable are the first differences of a variable that is simply given as a share (0-1) whereas ...
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How many significant figures to report in the coefficients of a regression equation?

I'm given a table of experimental data, wherein a known functional relationship exists between its two columns $x/y$. I then perform regression to determine a quadratic fit equation ($y = ax^2 + bx + ...
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Converting unstandardised regression coefficients to Cohen's d for meta-analysis

I am conducting a meta-analysis of Cohen's d and some raw effect sizes are unstandardised regression coefficients. Of these unstandardised regression coefficients: Some are based on a binary ...
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calculate untransformed OLS coefficient

I used OLS model to understand the effect of promotion on units sold. I have transformed the dependent variable( square root) as well as the independent variables(standard scaler).The coefficients ...
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How are the penalized splines defined here?

Based on 'Semiparametric Regression with R' (https://link.springer.com/chapter/10.1007%2F978-1-4939-8853-2_1), a penalized spline $$ f(x)=\beta_{0}+\beta_{1} x+\sum_{k=1}^{K} u_{k}\left(x-\kappa_{k}\...
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Derivation of pair-wise relationships expression of βyx.z and σyx.z

I'm reading Linear Models: A Useful “Microscope” for Causal Analysis. In the article, when discussing the beta coefficient and standard error of partial correlation, the auther mentioned "express ...
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How to deal with error "Coefficients: 2 not defined because of singularities" in R for factor variables? [duplicate]

I ran multiple linear regression in R. The coefficients for 2 levels of factor variables give me NA values and the message: Coefficients: (2 not defined because of singularities) Please find the ...
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Coefficient testing for linear regression: multiple categorical variables

Assume that I am interested in performing a between group comparison for a given variable but I know that this $y$ variable is confounded by at least a couple of other variables. Say, $y = Device_1 + ...
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Interpreting regression results w/ disproportionate populations

I'm working with a dataset that has a binary outcome but has multiple groups (race, language, etc.) in the dataset in which I'm attempting to find statistical significance. After doing some research ...
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1answer
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Change of value of coefficient when including a new variable in multiple regression

I have a quite stupid question. It seems quite obvious that when a new variable was included into a multiple regression, the coefficients of independent variables already in the regression could ...
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Finding confounder in multiple regression

I want to identify confounding factors with multiple regression. I have two models. ...
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Correlation formula between slope and intercept of linear regression

I'm studying the example H.3 from this Standard, regarding the expression of the uncertainty in measurement, but I cannot understand from where the formula (H.13e) comes. My problem is to find the ...
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Effect of including a confunder or a mediator in a multiple regression

I have two questions regarding the change of coefficient when including a confunder or a mediator as a independent variable in a multiple regression. When I include a mediator in a multiple regression,...
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1answer
34 views

Fixed-effects with dummy variable interaction

I am currently thinking about a theoretic problem I cannot get my head around, so I am here hoping to find a statistical mastermind, which can help me in this regard. A classical thing to do in ...
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How to derive sales contribution in a log-log regression media mix model?

I am working on a media mix model to determine how different media channels impact sales. Since there is a non-linear relationship between sales and media spend, I needed to apply a log transformation ...
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Doubt about Lagrange Multiplier Statistics for q exclusions restrictions

For obtaining the Lagrange Multiplier Statistics I follow this steps (Wooldridge 2019, Introductory Econometrics): Regress $y$ on the restricted set of independent variables and consider the ...
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Triple difference-in-difference with continuous treatment

I am struggling to understand how to interpret a triple DiD with one continuous treatment. I found Olden and Møen (2020) useful, but it only considers the case of two binary treatment variables. ...
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Inferring the coefficients of two datasets by analyzing the coefficients of the combined dataset

I have two datasets, but for some reason, and in each of them I need to do a regression analysis of Y = aX + bZ +e. Assume for some reason I cannot do the regression analysis for each dataset, but ...
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Is it possible to conduct a coefficient test within a multiple regression?

In an analysis of employment, a difference in means test shows that gender is important. Multiple logistic regression using several specifications robustly identifies a positive coefficient on gender, ...
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Test Dummy Variables Linear Regression

I have the following model: relacc_t= β_0+β_1*D2+β_2*D3+β_3*D4+β_5*D5+e_t in which relacc=relative forecast accuracy, D2 = 1 for the second forecast of the day (...
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Testing difference in coefficients for two treatment conditions in separate models with shared control group

Subjects were randomized into treatment and control groups. Within the treatment group, subjects were randomized to receive the treatment under condition A or B (mutually exclusive groups). For all ...
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Multivariable Regression: t vs. z to determine relative significance

I have a multivariable regression model that includes 4 independent variables. I would like to determine relative significance between the variables. The 't stat' is given by the software. Can I ...
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How to produce to standardised regression coefficients in R for multivariable logistic regression

I am very new to R and epidemiology and am trying to create a model of how metabolic syndrome is associated with disease 'Y'. I have been asked to calculate a standardised odds ratio for the effect of ...
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How do I find coefficients for logistic regression manually-user defined function?

I got data from wikipedia. Hours show the number of hours each student spent studying, and Pass shows passed (1) or failed (0). Hours=...
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Why is coefficient of determination found using Pearson's Correlation Coefficient, and not the Regression Coefficient? [duplicate]

This is almost certainly an extremely novice question, but it is one that I am struggling to wrap my head around. I am enrolled in a Master's Statistics course, and we just recently covered ...
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Power analysis without a prior and for observational data

I am trying to develop the design for an observational study, but I am struggling with the number of observations that would allow us to estimate our model and generalize its results. As a dependent ...
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Interpretation of ratio variable in a log - linear model

I have a log-linear model which can be represented as bellow. log(revenue) = beta_0 + 1.14 Promotion_Depth + etr Since Promotion depth is a ratio which took value between 0 and 1 (not 0 and 100) and ...
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Regression with linear (equality) constraint on coefficients (MATLAB): least-squares vs. RLS estimator?

I want to estimate a cost function $y = f(A,B,C,D)$ in MATLAB. The model is the following: $log(y) = \beta_1 + \beta_2 log(A) + \beta_3 log(B) + \beta_4 log(D) + \beta_5 log(C) + u_i$ How do I ...
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Is there a way to write Elastic Net in expanded matrix form?

I am working through a regression problem for a matrix of data that isn't full rank and has more features than observations. For these reasons, I'd like to use elastic net because of its $L1$ and $L2$ ...
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1answer
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Omnibus test significant but no individual factors are significant [duplicate]

I'm running a multiple logistic regression in R. Im predicting whether or not a stimulus was seen from the number of dots in the stimulus (sample_numerosity; 4 ...
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1answer
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Interpret regression coefficients when dependent variable is standardized

Let's say we have the following regression model: $$z_i = \beta_0 + \beta_1 X_{1,i} + \beta_2 X_{2,1} + u_i$$ Where $z_i = \frac{y_i - \bar{y}}{\sigma_y}$ is the (standardized) dependent variable. How ...
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1answer
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Interpreting coefficients when dependent variable is a fraction/proportion?

I'm a little confused about how to interpret coefficients when the dependent variable is a proportion/fraction and the independent variables are absolute numbers. For example, let's say I have a ...
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If I have one non-significant factor level in a glm, is that entire variable now considered non significant?

I have a question similar to this one, but I just wanted to follow on and ask if the entire variable is now insignificant? I have a factor with 3 levels. When doing the model simplification, it showed ...
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1answer
128 views

Adjusting weight for best linear regression

I have test scores for theoretical ($T_i$) and practical ($P_j$) exams of students ($s$), and the aim is to calculate the dependence of theoretical and practical success. I calculated the sums for ...
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Linear Regression Goodness of Fit Test & Partitioning a Data Set to Approximate Linearity

I have a stochastic mapping from vectors $X$ to $Y$ with a great deal of variance and a linear regression model $Y = a+bX$. Is there a simple statistical test which can tell me whether or not this ...
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Can linear regression be effectively used to fit these forms of functions?

a) If our training data x in all reals is of the form y = beta* x^4 I know that y (labels) are not linearly related to our examples, but can linear regression still be used here? b) how about the same ...
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1answer
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How to interpret results of logistic regression?

I am struggling with interpreting the output of logistic regression correctly. The dependent variable is leaving the university (=1) and I have 7 significant independent variables. The coefficient for ...
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Interpreting OLS coefficients with (absolute) changes in dependent variable

Could someone suggest how to interpret beta coefficients in regressions like below Y1 - Y0 = intercept + beta*X0 abs(Y1-Y0) = intercept + beta*X0 (Y1-Y0)/Y0 = intercept + beta*X0
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Modify a variable such as to get a particular correlation coefficient value with the other variable

I am working on a problem where i have to change a column to make it 0.75 correlated to some other column. suppose i have two columns X1 and X2. The current Pearson correlation coefficient between ...
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Does it make sense to group variables together in a regression model?

Would it make sense to use a variable that consists of two features when estimating the effect on a dependent variable? For example, when estimating admission into a college - would having the ...
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Level-Log Regression Interpretation [duplicate]

So, I have this regression that expresses the relationship between the compensation of the senior executives of a firm and the revenues of the same: The regression displays the following coefficient ...
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Random effects covariance parameters: Participants ID

so I have a very basic question which really confuses me. I'm comparing the acceptance rate (yes vs. no) of two independent groups, participating in a task where they have to decide if they either ...
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How to prove that the posterior of the regression coefficients $\mathbf{w}$ is roughly gaussian in MAP regularized logistic regression?

The logistic regression model is $$ p(y=\pm 1 \mid \mathbf{x}, \mathbf{w})=\sigma\left(y \mathbf{w}^{\mathrm{T}} \mathbf{x}\right)=\frac{1}{1+\exp \left(-y \mathbf{w}^{\mathrm{T}} \mathbf{x}\right)} $$...

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