Questions tagged [intercept]

The intercept in regression-type models is the value of the Y variable when all X variables are 0.

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What is the intercept in a regression model with demeaned dependent variable?

Suppose you have a regression model $\tilde{y}$ = $X\beta$ + $\varepsilon$, where $\tilde{y}$ = $y$ - $\bar{y}$ and $X$ contains a constant. If you estimate the model by OLS, does the estimated ...
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All variables are not significant, but intercept is

I am using SPSS for the first time and just trying to make sense of my findings. I had two IV (nationality, age group), each with 2 levels (English-non English; young-old), which is why I ran a 2x2 ...
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How to simulate data of a random intercept effect model in R?

I want to simulate data of the following random intercept effect model in R $$Y_{ij}=\alpha+\beta x_{ij}+u_{0,i}+\epsilon_{ij}$$ $$u_{0,i} \sim N(0,\tau^2)$$ $$\epsilon_{ij} \sim N(0,\sigma^2)$$ Here ...
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Why model expected value is computed using a model with input features?

This post is kind of related to these two posts here and here I learnt that model expected value (average prediction) is nothing but performance of the model when all input features are absent. But I ...
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What's the asymptotic variance for OLS estimates of intercept and slope of homoskedastic simple linear regression?

Suppose data is generated by $Y_i=\beta_0+\beta_1X_i+U_i$ satisfying $E(U_i|X_i)=0$ and $E(U_i^2|X_i)=\sigma^2$. Suppose I have a random sample $\{Y_i,X_i\}_{i=1}^{n}$, and obtained OLS estimates $\...
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Why does removing intercept not change predicition of linear model in the precence of factor predictors? [duplicate]

In a linear model that predicts birth rate (TFR) per country from per capita GDP, the country is encoded in "treatment coding", and there are several measurements (different years) per ...
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Intercept of logistic regression with contrast coding

Say I have a binary dependent variable (Choice) being either 0 or 1, and people answer this DV multiple times. I also evenly split people in two groups (Group, group A vs group B). I simulate data so ...
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Calculating Slope and Intercept From Multiple Linear Regression

Consider this linear equation: $$ Y \sim \beta_0 + \beta_1X_1 + \beta_2X_2 + \beta_3X_3 + \beta_4(X_2*X_3) + \epsilon $$ where $Y$ is what I'm trying to explain (it happens to be the evolved growth ...
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ICC in Random intercept model with a predictor variable

Are we able/ or is it correct to calculate ICC in random intercept model which has a preditor variable within? Does this value give us the variation of the outcome which is purely related to subject ...
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Adding predictors to an intercept-only model

I'm currently testing out a logistic regression model I plan to use to analyse the results of an experiment I'm yet to conduct. I'm running it in R. My experiment is going to measure whether animals ...
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Linear Mixed Models: how to interpret intercept from multiple fixed factors?

I am running this model using lme4: ...
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Regression without intercept when evaluating correlation

By default, a linear regression model minimizes the least squares function for inputs $X$ and outputs $Y$ by fitting the slope and intercept. If I'm only interested in the Pearson correlation ...
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Which one is intercept in linear mixed-effects model?

I have a repeated measures of depression as a dependent variable. I could not solve which one is intercept here. I was checking the graph but none of them reflects to the intercept. https://ibb.co/...
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Poisson Regression with both categorical and numerical variables: interpreting the outcomes and intercept

I have some difficulties in thoroughly interpreting all the outcomes of the Poisson Regression Model. I have a Poisson regression model with Observed deaths as dependent variable, A categorical ...
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Should residuals be equal (or unequal) in multigroup SEM when testing means?

What happens if I allow residual variances (and their correlations) to be freely estimated when testing multigroup differences in intercepts? I am comparing intercepts of my dependent variables (e.g., ...
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Linear regression withouth intercept R

I'm trying to implement a cost function for linear regression withouth intercept. I tried understanding what "no intercept" means, but not found anything which could reassure me. I have a ...
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Questions about the constant value of a fixed effects model in Python’s PanelOLS

I have a question about the constant value of a fixed effects model. I am currently conducting research using a fixed effects model that controls for the effects of companies using Python's ...
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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 wgls output coefficients to construct equation of a line

I have the following model which looks at the relationship between number of boats (continuous) and frequency (factor) on recorded sound pressure level (continuous). ...
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Is this intercept-free regression line really correct?

I know there are many arguments against intercept-free regression but we are very interested in the convex or concave shape of these lines. Because I got suspicious real results, I switched my ...
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Chisq test for significance of intercept in R

I have a logistic mixed-effects model with both fixed and random effects. Imagine something like: ...
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Multiple Regression, R output how to interpret the intercept

In the example linear regression below, how do I interpret the (Intercept) with this R output? A) Does the (Intercept) line represent pop1? B) Does the Estimate column indicate the slope or the ...
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Logistic Regression, ''Intercept'' instead of a Category [duplicate]

I am currently trying to analyse the effect of an ilness (0= no infection, 1= infection) on 9 different Genotypes in plants. My Dataframe consist of 2 colums Genotyp and Infection. I have 459 rows for ...
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Understanding fixef() output of fixed effects coefficients

I have a panel data set with several ID's and each has a certain number of year observations. When I fit a fixed effects ...
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When you are running an analysis with only an intercept, does it make sense to include random subject and item intercepts?

Lets image a study where people get two shapes and are told to pick one. They each get 40 trials, each with a different shape/colour. There are 40 different pairs of shapes. There are 100 participants....
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Is computing the average of a ratio the correct approach, and how to do it with nested data?

In general, is computing the average of a ratio appropriate? And secondly, is the nested model below appropriate for doing this? Here is a data set created from the Iris data that resembles my ...
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How to decide if I should fit SARIMAx with or without intercept

I am trying to find the best SARIMAX model for my data, I am using auto_arima to find the order(ARMA and Seasonal) of the model. How do I decide whether or not I ...
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Compare intercept of logistics (mixed-effects) model to value other than 0

Is it possible to compare the intercept of a logistic mixed-effects model to a value other than 0? Specifically, I have two choice alternatives and try to predict choices. My intercept would then tell ...
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How to calculate the intercept (b) of a gaussian kernel support vector regression

I know the dual problem of an SVR problem is given as: where \alpha_i and \alpha^*_i are dual variables and they are also decision variables in the above problem. \epsilon specifies the epsilon-tube ...
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If I consider the fixed factor as a random slope, the p-value changes from p<0,05 to p>0,05

I'm having a hard time trying to understand the differences between these two models and why the first one shows correlation (p-value < 0,05) but the other one doesn´t (p-value > 0,05). I would ...
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Interpretation of a $P$ value of a categorical variable?

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Consistency of OLS when no intercept

Suppose I have a model $y_i = \beta_0 + \beta_1 x_i + e_i$ but instead I estimate $y_i = \beta_1 x_i + u_i$ using OLS. That is, I ignore the intercept. Working out the algebra, based on this post, we ...
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What is the difference (if any) when talking about bias from a ML point of view and from a DL point of view

I'm reading around Machine Learning and Deep Learning and can't seem to understand the difference or similarity between bias in both. If we look at the simplest linear regression formula y = b0 + b1x1 ...
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How to obtain a 0 intercept in quantile regression

Quantile regression models are a type of models that provide estimates of the quantiles of a response variable $y$ given a set of covariates $X$ in the form of a linear equation such as $$ y = \beta_0 ...
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VAR-model include constant or not?

I am estimating a var model with four variables: GDP, investemnt, inflation and unemployment. (all in growth rates). Now I estimated it once with a constant and one without. The model is not changing ...
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Simple linear regression model without intercept

I am a new beginner at linear regression. So here is my question: given that we have simple linear regression without the intercept: $$y_{i}=\beta x_{i}+\varepsilon_{i}$$ the question assumes that $\...
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Intercept in 2nd-stage Error Correction Model (ECM) regression -- yes or no?

When doing a two-step ECM regression, do we add an intercept in the 2nd stage regression? I've seen course notes that add an intercept in the ECM, but some do not, so I'm confused if I should include ...
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Is there a way to use the covariance matrix to find coefficients for multiple regression WITHOUT intercept?

Given: $$ y=\alpha + \beta x $$ The problem on how to get regression coefficients $\alpha, \beta_0, \beta_1,...,\beta_n$ from the covariance matrix is solved here: Is there a way to use the covariance ...
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Concerns about pre-trend stability testing

In this discussion, @Thomas Bilach well explains the equation to test pre-trend stability. $$ y_{kt} = \alpha_k + \lambda_t + \delta_{-2} d_{k,t-2} + \delta_{-1} d_{k,t-1} + \delta d_{kt} + \delta_{+1}...
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Different values for intercept estimate in linear regression

I'm reading about linear regression from two sources. In here: https://online.stat.psu.edu/stat415/lesson/7/7.3 the estimate for the intercept is just $\bar y$. However over here: https://www....
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Collinearity between the intercept and (logged) continuous variable: centering to fix it?

I have found a lot of information when there is collinearity between intercept and dummy variables. However, my collinearity diagnostics is showing a condition index > 30 (36) and it indicates ...
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Why is the intercept different in an AR(1) model compared to a lagged endogenous variable model? [closed]

In other words, why is that when estimating in EViews y = c ar(1) yields a different coefficient for c when compared to ...
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Simple linear regression without intercept - Expected Value and Variance Estimator (Slope) [duplicate]

I'm solving an exercise while studying for exam, I have been asked to find the estimator of simple linear model without intercept estimator, its expected value and variance. I got for the Estimator B1 ...
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Mixed model fails to converge - do I delete the random intercept or the random slope, and what does the variance of the random effects say?

I'm in the process of building my mixed models, and unfortunately I encountered a problem when creating the random effects structure. I have two random effects: ResponseId (i.e., participant number) ...
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Interpreting constant in regression with an interaction term

In a regression model with a single categorical exposure and no interaction term of the form: $y = \beta_0+\beta_1x_1$ the $\beta_0$ can be interpreted as the result in the reference group. So for a ...
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In R there is a problem of intercept and without intercept ,Pearson's Correlation does not follow! Why? (see the bolded resuls)

Xvec <- rnorm(200) Yvec <- 2.6*Xvec + rnorm(200) lmodxy <- lm(Xvec ~ Yvec) lmodyx <- lm(Yvec ~ Xvec) summary(lmodxy) Output ...
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How to correctly use I-Splines for monotone non-decreasing/ increasing regression?

I have the following data to which I want to fit a monotone non-decreasing spline. ...
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Test for comparing x-intercepts of two linear regression

I would like to know how to compare, and then calculate significant differences, if any, between the x-intercepts of two regression lines. Practially, I shoud compare the values of x when y=0. I know ...
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Uncovering the make up of the intercept in a generalized linear mixed model

I could use some help Finding the make up of the intercept in a generalized linear mixed model. FYI, I use a 2013 Macbook Pro with a 2.4 GHz dual-core intel chip, 8 GB of ram, macOS big sur 11.2.2, ...
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Why the does the intercept of my null model not equal the mean when I log transform the outcome variable? How do I interpret it?

I have an outcome variable that is right skewed, so I log transformed it. I made a null model with only the log-transformed outcome variable, but when I exponentiate the estimate, it does not equal ...
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