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 views

Comparing Groups in a linear regression with an interaction term

I have the below equation: $$ y_{ij} = b_0 + b_1X_{ij} + b_2Z_{ij} + b_3XZ_{ij} + \gamma H_{ij} + \delta S_{ij} + \mu_{ij} + e_{ij}, $$ where $b_1X_{ij}$ is a dichotomous variable, indicating whether ...
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standardizing(scaling) Linear Regression with continuous and categorical independent variables

I have a dataframe with a ctm, dependent continuous var, ctp, independent continuous var and day, factor with 10 levels. And I'm trying to run the linear model below in R. ...
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Trying to show $E[\hat \beta_1 | \mathbf{X}] = \beta_1$ directly from the definition of $\hat \beta_1$?

Suppose we have the standard simple linear regression model: $$ Y_i = \beta_0 + \beta_1 X_i + \varepsilon_i, $$ with $E[\varepsilon_i|X_i] = 0$ and $\text{Var}[\varepsilon_i|X_i] = \sigma^2$. I'm ...
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Interview question: patterns in residuals in “handmade” regression model

I was asked this during an interview, I am not sure my answers make sense. Q: You have got $n$ features $x_1,..,x_n$ for each observation $y$. You build a linear regression model by estimating the ...
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What methods can I use to quantify the impact of multiple variables on a response variable?

Suppose I have observations for both the predictors ${x_1,x_2,...,x_p}$ and the response $y$, what I am interested in is the controls of these predictors on the response $y$. There are several cases ...
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Market Mix Modeling using Random Forest

I am trying to build a random forest-based market mix model, wherein I want to calculate the contribution of each of my X variables towards the target. Typical MMM problem statement, but here am not ...
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How to choose initial $\theta$ (intercept and $\beta$s) in simple linear regression? [closed]

I have the sales of items from January 2013 to October 2015. I just want to predict the total sales for the next month. Just for the sake of learning, I would like to transform it into a multiple ...
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Can I conduct a paired t-test to compare regression coefficients?

I want to compare the regression coefficients for two variables from the same sample. My models may look like this: $$ \hat{Y}_1 = \alpha + \beta_1 * V_1 + \beta_2 * V_2\\ \hat{Y}_2 = \alpha + \beta_3 ...
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Finding Marginal Effects of Logistic Regression Coefficents

I used a logistic regression model to predict the probability of a fruit being a pomegranate or not with the explanatory variables as the number of seeds and the ounces it weights. My coefficients ...
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Including data errors in error estimates for linear regression coefficients

I would like to model a set of data that have been measured with a certain random experimental error. Suppose $X_i,Y_i~,~i=1,...,N$ are, respectively, $\mathcal{N}(\mu_i,\sigma_x)$ and $\mathcal{N}(\...
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Alternatives of dealing with perfect collinearity in OLS Regression

I am running an OLS regression with hundreds of dummy variables. Some columns of the X matrix (design matrix) are linearly dependent on others. My question is, is the value of the fitted values (Y ...
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$t$-test and likelihood ratio test for testing the regression coefficient

I am studying hypothesis testing for the regression coefficient, it is given that The hypotheses for testing the significance of any individual regression coefficient, such as $\beta_{j},$ are $$ H_{0}...
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Determine what equation is being modelled with linear regression?

I am performing linear regression using the equation $x^{*}=(A^TA)^{-1}A^Tb$, from: $Ax=b$ → $A^TAx^{*}=A^Tb$ → $(A^TA)^{-1}A^TAx^{*}=(A^TA)^{-1}A^Tb$ → $x^{*}=(A^TA)^{-1}A^Tb$ I am trying to model an ...
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In logistic regression, is there an official term for the value you get when you multiply feature values with coefficients?

I am currently calling it the effect, so I can report on the impact of the feature values for each observation. But is there an official term for it? That is, to understand why someone is getting a ...
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Regression coefficient for a logged dependent variable

I am running into a puzzling econometric issue. Here is my data set-up and the model: I am using a two way fixed effects model on a panel data of states. For regression results, I take natural log of ...
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How to prove the following linear regression properties? [duplicate]

Why is it that the below are true? $\sum_{i=1}^n \hat{y}_ie_i= 0$ so far, I have, for the above: $\sum_{i=1}^n (\hat{y_i})(y_i-\hat{y_i})=0$ = $\sum_{i=1}^n \hat{y_i} y_i- \hat{y_i}^2$ so does the ...
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How do we use linear regression in which response variable is related to the regressors in a nonlinear fashion? [duplicate]

"This is called a multiple linear regression model because more than one regressor is involved. The adjective linear is employed to indicate that the model is linear in the parameters β 0 , β 1 , ...
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Compare two effect sizes

I want to ask whether two effect sizes (B1 and B2) are different than one another. Both B1 and B2 are derived from a Spearman correlation, and I can extract the SE and confidence intervals. I ...
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Coefficient of $Y$ on $X$ and Coefficient of $X$ on $Y$ [duplicate]

Under what circumstances the coefficients from simple linear regression of $Y$ on $X$ is equal to that of $X$ on $Y$? Will it hold when the standard deviations of $X$ and $Y$ are the same? I would ...
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Appropriate way to report multiple linear regression in APA

I have a significant result for linear regression: When I control for age and sex, the main coefficient of interest is no longer significant: What is the appropriate way to write in APA format the ...
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How to interpret normalized coefficients in logistic regression?

I trained a logistic regression model with 5 features per sample. Before training, I normalized the range of my features into [0,1] (MinMax scaler). After training, I received the following ...
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Least square estimator for regression with errors depending on observed values

Consider the following model: $y_i = \beta x_i + \epsilon_i x_i$ where $y_i$, i = 1,2,3...n are observed; $x_i$, i = 1,2...n are known positive constants and $\beta$ is an unknown parameter. There ...
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Should the treatment effect coefficient in a difference-in-difference model be consistent with graph trend?

I am running a difference-in-difference regression and the coefficient of the interaction term (treat*post) is negative, so I concluded that the effect of the treatment was negative on the outcome ...
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Does the variance in the estimates of the coefficients for standard linear regression decrease as $O\bigg(\frac{1}{n}\bigg)$?

I am interested in how the estimate of the regression $\beta_1$ decreases with respect to sample size $n$. Does this look ok or am I missing something? $$ \begin{align} \text{Var}(\hat \beta_1) & =...
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Shouldn't the variance of the vector of regression coefficients decrease when we have larger sample sizes?

In the first answer to this post, it is shown that the variance of the estimated regression coefficient $\hat \beta_1$ in simple linear regression is $$ \text{Var}(\hat \beta_1) = \frac{\sigma^2}{\...
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Response variable (a percentile) is uniform and identically distributed but not independent?

Imagine the following problem: $(X,U,Y)$ is drawn from one of $n$ groups where X are the explanatory variables and $U$ is some quantity (a ratio if that’s relevant). The response variable $Y$ is the ...
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Multiply beta coefficients from two different models

I have a count outcome with a heavy right skew that is modeled with a negative binomial. I have a continuous mediator that is modeled with OLS. We're attempting a method of causal mediation analyses ...
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ARCH coefficient in GARCH models

Is anyone knows to interpret ARCH Coefficient in GARCH Models ? I tried to find what is ARCH Coefficient means. Some says it's for detecting Spillover effect, Some says Volatility Clustering or ...
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Testing equality of coefficients from two different regressions / distribution of test statistic

There was a question posed on how to test for differences between regression parameters from two different regressions. If $\beta_1 $ and $\beta_2$ are the two coefficients from two respective ...
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What to report in cross validated elastic net regression?

Let's assume I want to construct a regression model to predict a specific outcome variable but I don't have enough data to do a proper train-test set split (n = 200). I have 7 predictor variables (...
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How do you check whether heteroscedastic-consistent estimators fix your error variance problem?

I am running an OLS regression, and have non-constant error variance (residuals vs fitted looks like a fan opening up to the right). I have tried a number of power transformation but they seem to make ...
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Finding Variance for Simple Linear Regression Coefficients

Suppose we have the simple linear model $$\mathbf{y} = \beta_0 \mathbf{1} + \beta_1 \mathbf{x} + \boldsymbol{\epsilon},$$ with $\mathrm{E}[\boldsymbol{\epsilon}] = \mathbf{0}$ and $\mathrm{Var}[\...
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R: Reconstructing a logistic regression model with splines using published coefficients and spline knots

What I would like to do I would like to reconstruct a logistic regression model with splines (Lymph Node Involvement (Cores)) using published coefficients and spline knots. All sources that I posted ...
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How to visualize result of cumulative link model using the ordinal package in Rstudio?

I used ordinal GLM with cumulative link model using dependent variables with 5 levels. The objectives are to examine people's attitudes towards pet cat in two countries and to also find out if people ...
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Bayesian Regression Model

I am new to Bayesian modeling. I am running Bayesian regression model in R using brm function from brms library, which is powered by STAN. I have a data with 10 million records. I took 10% sample out ...
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How does the Zeiger-McEwin & Kung algorithm work for fitting a sum of exponentials?

I am trying to understand this paper fit sum of exponentials but am having a bit of difficulty. Let me go through what I have understood so far. One has a certain time-series data set and want's to ...
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If $\beta$ can be expressed $\frac{\text{cov}(Y, \widetilde X) }{\text{var}(\widetilde X)}$… So where does the shared component of the variance go? [duplicate]

I think this is a fairly technical, conceptual question so I'm going to do my best to explain what I'm thinking. For the regression $\widetilde Y = \hat \beta_0 + \hat \beta_1 X_1 + \hat \beta_2 X_2$, ...
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How to test the influence of conditional probabilities in a regression?

I would like to test how people weight different levels of probabilities. Assume that there is an action $A$ which might lead to a consequence $C$ with value $W(C)$ with a probability of $p_C$. A ...
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covariance in multiple linear regression

This is a general question Im trying to understand. Say for example you have two timeseries, ts1 and ts2, and the correlation between ts1 and ts2 is 0.5 (corr(ts1,ts2) = 0.5). If the MLR model is of ...
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Does L1 regularization (Lasso) always leads to feature reduction? [duplicate]

This is a basic question about regularization term but I have searched for a while and cannot find the answer. My question is: does Lasso regularization always make some coefficients zero? A famous ...
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Does it make sense for correlation coefficients to be vastly different from regression coefficients?

I'm working on a project where I'm analyzing how improvements in players' skills are associated with changes in their values. Specifically to see if there is a correlation between point changes in ...
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How to interpret standardized continuous coefficients marginal effects at the mean in logit regression

In R I am attempting to run a logit regression model which can predict an individual's probability of developing hypertension. But I am struggling in how to properly interpret the continuous ...
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Why can I interpret a log transformed dependent variable in terms of percent change in linear regression?

Looking at resources such as this one and this one, you see claims like "Exponentiate the coefficient, subtract one from this number, and multiply by 100. This gives the percent increase (or ...
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Why is $Y=\beta_0 x^{\beta_1} e$ a linear model?

Why is $Y=\beta_0 x^{\beta_1} e$ a linear model? When we apply the transform, it becomes $lnY = ln\beta_0+\beta_1 lnx +lne$, and why is it still linear when the $\beta_0$ part is under ln?
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Why do the coefficients of cross-sectional fixed effects and time fixed effects become zero?

I currently have a panel data set that contains the quarterly increment of loans initiated from more than 300 cities in China over the period from 2011Q1 to 2020Q2. I want to examine the impact of ...
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How to model the regression coefficient of a sum as a function of the sum elements?

I wonder if it is somehow possible to model the regression coefficient of a sum as a function of the sum's elements by any transformation of the model/the regressors. If you ask yourself what the idea ...
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Coefficient of 0.001 with p < 0.005 [duplicate]

This should be a simple inquiry. Doing a regression analysis I found that the coefficient of a predictor has a(n) (infinitesimal) positive effect of 0.001 that is significant at the 0.005 level. I ...
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Term for exp(beta) from a Gamma-GLM

I have read a lot about interpretation of coefficients from Gamma-GLMs (using a log-link function), e. g. from this thread How to interpret parameters in GLM with family=Gamma , and found this to be ...
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Explanation for regression coefficient $\beta= 0$ and standard error $\sigma(\beta) = 0$

one of the coefficients in an OLS regression turned out zero and its Standard error is zero as well. Would you be suspicious of this result? Is there any possible explanation for this?
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Should I only select two Principal components for a regression analysis?

Why are two principal components usually selected for principle regression analysis? I read somewhere that since it is 2 dimensional data, there should only be 2 principal components extracted from ...

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