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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Conceptualizing the difference between sigma, sigma "hat", and standard error for estimated beta coefficients

I've been struggling to comprehend the difference between σ (true standard deviation), σ"hat" (estimated standard deviation), and standard error of the estimated beta (for example, slope) ...
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Is it acceptable to create a dummy variable out of a quantitative variable?

I have a variable that takes the value of 5% or 10% throughout the data set. Is it okay to transform this variable into a dummy variable such that 10% (high) = 1 and 5% (low) = 0. I am running a ...
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Simulated data for logistic regression

I used the code below to create the random variable x1 and binary variable y, and fit the regression with y and x1. My questions are: Why regression coefficient estimates are not close to 2 and 10 (...
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Estimating heritability from twin studies--How to get it?

I was learning the concept of heritability, and come to the Falconer's formula: $h^2=2(r_{MZ}-r_{DZ})$                               (1) Where $r_{MZ}$ and $r_{DZ}$ are correlation coefficients of ...
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Ridge and Lasso regression coefficient change when we change the scales of the variables

I am interested in the following question: suppose we run a ridge of a lasso model on a bunch of variables. Now if we multiple one of the variables $x_1$ by 2, what happens to the coefficients. Some ...
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Coefficient from Regressing the OLS Residual on X

Say we have an OLS residual $\hat{ϵ}$ from regressing $y$ on $X$. If we were to regress $\hat{ϵ}$ on the same $X$, what would the OLS coefficient be? If we rearrange the first regression equation for $...
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Should I use standardised or unstandardised beta coefficient in this scenario?

I am running a regression on Tax payment and investment. Tax payment is numerical and investment is categorical like, number of projects carried out. When I run the regression the a unstandardised ...
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What is the 'right' slope formula of a regression? deltas or Pearson?

this may be a silly question, but still: I've been told that the slope formula equals the rise/run ratio, like this: $$ m = \frac{rise}{run} = \frac{y_2 - y_1}{x_2 - x_1} $$ in which rise equals ...
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Change versus level regression

I tried running a panel regression of y on contemporaneous x variables, and again using the change in y from year t-1 to year t. I am getting the opposite sign on my variable of interest (VOI) if I ...
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Standard error of estimated coefficient

In a book Intepretable Machine Learning by Christoph Molnar there is a following passage: I don’t understand how can we talk about a standard error of the estimated coefficient. I understand standard ...
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determining the effect of the change in an independent variable using regression

I'm creating a regression model that predicts a customer's spending based on their income, while adjusting for age, gender , and region. The model looks as follows: ...
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Intuition behind the formula for multiple linear regression coefficients from Econometric Analysis Greene

I was looking into the maths why coefficients change with the addition of new variables and so looked up the formula for multiple linear regression coefficients. This is what I found from section 3.2....
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Absolute effect of one dummy in a linear regression with multiple dummies

I am regressing meat consumption (a continuous variable) on several socio-demographic characteristics (all categorical variables) converted into dummies : sex (1/2), age category (1/2/3), level of ...
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partial correlation for effect modification

I am trying to answer a question of variable importance, but some of the variables of interest are assumed to be effect modifiers -- i.e. not having independent effects, while some others are assumed ...
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Linear regression with interaction variables need all interacted variables as independent variables? [duplicate]

Say we have a dependent variable $Y$ and two independent variables $X_1$ and $X_2$. If we are doing the linear regression with interacted variables, do we need to include both $X_1$ and $X_2$ as ...
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Regression coefficient of y~x_1, y~x_2 and y~x_1+x_2

If we regress $y$ on $x_1$ and get $y = b_1 x_1$, regress $y$ on $x_2$ and get $y = b_2x_2$, regress $y$ on $x_1$ and $x_2$ and get $y = b_1'x_1 + b_2' x_2$, what's the relationship between $b_1b_2$ ...
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How should I interpret the results of the OLS regression I did for 2 cointegrated variables?

So I've been doing cointegration between two variables that are both I(1). I run the OLS regression between the variables to possibly check the stationary of the residuals. However when I checked the ...
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cv.glmnet vs glmnet

I'm using glmnet to fit a ridge regression model on some data and evaluate the model's test MSE. The lambda value I select is derived from cross-validation. I'm ...
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How to interpret the sign of Helmert contrasts regression coefficients?

Helmert1 is the the contrast encoded in the vector (-1 0.333 0.333 0.333). Suppose the groups in order are control, No-Show, Treatment One, Treatment Two. Suppose the dependent variable is the log(...
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How to interpret the coefficient of a limited independent Variable (Index)?

I assume this is a very simple question, however I am not sure about it. I have a regression table in front of me that contains the coefficients of a linear regression. The dependent variable is ...
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Combining/updating parameters from multiple estimations

Take a simple example of performing two independent linear regressions on a set of x-y data, in the form of y = mx + b, each using half of the data. I will obtain two separate estimates for m1, b1, m2,...
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How do I interpret a regression model when there are impossible additive effects?

Let's say I have a model of count data as a function of the month of the year along with an additive effect of season (factor with 2 levels Wet and Dry which correspond to Jan - June and July to Dec ...
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In Lasso regression, why is the intercept equal to $\bar{Y}$ when we center the columns of $X$

I am currently learning Lasso regression, and I am confused about a lecture slide that I am looking at: https://www.stat.cmu.edu/~ryantibs/datamining/lectures/17-modr2.pdf (Page 9). I attached a ...
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Alternative interpretation of multiple regression coefficients?

If we have a linear regression of the form $$ Y = \beta_0 + \beta_1X_1 + \beta_2X_2 $$ is it valid to interpret the coefficient $\beta_1$ as the associated change in $Y$ when $X_1$ increases by a unit ...
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Interpreting the time series linear regression - differences before and after collapsing data

Consider the following time series: The coefficient on the linear regression makes sense: each additional year, the variable Y increases by 3 percentage points. Now, the problem occurs when I'm ...
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robust::glmRob (method 'mallows') vs robustbase::glmrob (method 'Mqle') - very different estimates

I want to apply a robust logistic regression in R and I tried the functions robust::glmRob (using the method mallows) and ...
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Regression coefficients with different signs (one positive, one negative) in a mediation analysis

I ran a mediation analysis following this article (which goes over the Baron & Kenny method). Step 1. lm(Y ~ X, data); My X (independent) variable has a significant relationship with my Y (...
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Sign change of coefficient in logistic regression when change from binomial to continuous predictor

I am looking at the association between the application of animal control and population reduction. Population reduction is my outcome variable; it is a binomial variable where 1 = population ...
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Is the magnitude coefficient vector in Ridge regression monotonic in lambda?

recently an interesting question came up and while I would have intuitively said it is not, other students have now made a compelling case (while not being sure themselves). For ridge (or l2 ...
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Univariate Regression Coefficients and Multivariate Regression Coefficients

I got the following question: Suppose I have three variables, $x_1$, $x_2$ and $y$. We run univariate regression of $y$ on $x_1$ ($x_2$) with intercept and get the regression coefficients $\beta_1$ ($\...
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felm R function doesn't kick out time-invariant variable despite fixed effect

I noticed that the felm-function doesn't kick out time-invariant variables, despite controlling for fixed effects. My data: I am using individual-level data with a monthly panel over four years. In ...
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R: Multiple regression continuous independent variable interpretation [closed]

I have mental health score as my dependent variable, the relationship with people as one of my independent variables, which has 7 scores representing the mood from the most happy to the most bad. ...
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means of centered variables not exactly 0 (and negative) and then product interaction term is negative, messing with beta coefficients in regression?

When centering continuous predictor variables for a hierarchical multiple regression, the means of the centered variables come out near zero but as a negative number. As a result, the product ...
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Best way of modelling date of month seasonality/cyclical patterns in daily timeseries data, an bayesian approach is proposed!

I have several datasets which exhibits clear seasonality/cyclical patterns w.r.t date of month. The days after the 25th seem to be clearly correlated between months suggesting that in this case ...
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R and Stata show different results when I run zero-inflated Poisson in each program. Why does this occur? [closed]

I ran zero-inflated Poisson in both R and Stata using the same dataset and the same variables and found out the coefficients of the results are different. I found out that Poisson is set as a default ...
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Ensuring the correct coefficient sign in the BACE method

My question is related to the Bayesian Averaging of Classical Estimates (BACE) method, introduced in Xavier Sala-i-Martin, Doppelhofer, G., & Miller, R. I. (2004). The gist of the article is that ...
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What does it say about the data if ridge regression is not reducing multicollinearity?

I am predicting the salary to be offered to a new candidate for which I am concentrating on just continuous (9 in number) variables. Variables are as attached. When I ran OLS the coefficient for total ...
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How can I estimate the sum of coefficients

I am trying to estimate the cumulative effect. When I have an ols regression with many dummies as explanatory variables, can I sum the coefficients to find the cumulative effect? If yes, how do I find ...
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Confidence bounds for coefficients of a fit of data set obtained with another fit

I fitted an equation to a set of data points. Then I substracted the fit previously obtained to another set of data points. After that, I fitted another equation to this new data (result of the ...
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On two-stage-least-squares regression

My professor has just covered the concept of two-stage-least-squares (TSLS) regression today. In particular, we explored the over-identified case where we have a single endogenous regressor, $X$, with ...
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How to understand the significance and effect of each term in a non-linear model with interaction terms?

Let's say we have a model as given below: $Y_1 = \beta_0 + \beta_1 X_1 + \beta_2 X_2+ \beta_3 \frac{X_2}{X_1} + \beta_4\frac{X_2^2}{X_1}$, $R^2= 0.98$ Here, $X_1$ & $X_2$ are positive integers. ...
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Help determining model and interpreting coefficients of log-linear relationship

I am trying to determine if the hospital I work at should open a new unit for admissions. I intend to do this by correlating patient assigned unit and length of stay in days. So far, I have determined ...
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How do I fit a constrained logistic regression model via quadratic programming in R?

I trying to find $\pi_{1}, \pi_{2}, \pi_{3}$ for model: $$ Y = \pi_{1}X_{1} + \pi_{2}X_{2} + \pi_{3}X_{3} + \epsilon, $$ with constraints: $\Sigma_{k}\pi_{k}=1$ and $\pi_{k}\geq0$. (All $\pi$ are ...
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What can OLS with a Box-Cox transformed dependent variable tell me?

Just to ellaborate: I’m doing an OLS-test to determine the following things: Do my independent variables have a significant effect on the dependent variable? What’s the direction of the effect of my ...
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Interpretation of coefficients in GLM: coefficients associated to continuous covariates interpreted as MD's or OR's

I was having a discussion with someone regarding OR’s estimated trough a logistic regression and then he claims that OR’s for continuous variables can only be estimated trough a logistic regression. ...
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understanding coefficients in negative binomial regression (glm.nb)

Hi CrossValidated Community, I have a very simple question about the interpretation of coefficients produced by fitting a negative binomial to some toy data. I generate the toy data by sampling from a ...
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Calculate variance of estimates in logistic regression

I was wondering if there exist formulas or reliable approximations (but not simulation or bootstrap based) to calculate the variance of the parameter estimates in logistic regression? If my model is $...
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Which coefficient is correct for assessing effect size of a regression interaction, standardized or unstandardized?

My team is conducting a healthcare regression analysis and is interested in both the p-value and the magnitude of an interaction coefficient (i.e., effect size). For our project we want p-value < ....
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How do we determine the variable of greatest impact in a multiple linear regression?

As a newbie, I'm not sure if this situation can be described more succinctly using better terminology, so kindly bear with me. The performance of a machine+human system is dependent on four ...
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How do I test whether coefficients in different models are statistically different when grouping off DV

I'm trying to see whether good players in chess (those with more than a 1250 Elo) are helped more by puzzles than bad players (those with less than a 750 Elo). Usually, the way I would do this is with ...

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