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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63 views

Linear regression with unusual error terms

Suppose that $Y = a + b K + X$ with $0 < X$ and $0 < K$ where $X, Y$ and $K$ are random variables. What are then the expectations of the intercept and slope in the case of a linear regression of ...
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1answer
652 views

multiple regression coefficients - Standard error of intercept

I am implementing an R-type summary() function in python with the restriction to exclude use of scientific libraries. (assignment) I found this https://www.nd.edu/~rwilliam/stats1/x91.pdf material ...
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16 views

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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1answer
1k views

How to interptet Jensen Alpha statistical significance?

When you regress portfolio excess returns against relative benchmark excess return you get a model in which the beta (slope) could be interpreted as the one you get from the CAPM, that is systemic ...
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1answer
40 views

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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22k views

t test for intercept?

the null hypothesis for slope is usually H0: slope is zero,but what's thenull hypothesis for intercept? is it H0:intercept is zero as well? From the picture we can see that the p value for intercept ...
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1answer
4k views

Ways of comparing linear regression intercepts and slopes?

I'm a little bit confused about this, so any help would be appreciated! Let's say I have a repeated-measures design in which participants take part in a task where they have to rate the ...
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34 views

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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1answer
45 views

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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39 views

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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1answer
1k views

How to interpret lme() outcome with a mix of cat/non cat variables

I apologize in advance for my question that can seem redundant, but I am still struggling to interpret the outcome of my lme model, as the other posts mainly deal with several categorical variables ...
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1answer
23 views

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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1answer
36 views

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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1answer
130 views

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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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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1answer
72 views

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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1answer
33 views

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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48 views

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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27 views

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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548 views

The Intercept terms for Ridge regression, lasso , pcr and PLS (elements of statistical learning)

In table 3.3 (page 63) of the elements of statistical learning book, the intercept terms for Ridge regression, lasso , pcr and PLS differ. However, according to the theory in the book, these models ...
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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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1answer
47 views

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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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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2answers
177 views

How to interpret insignificant intercept in logistic regression with orthogonal polynomial encoding

I have conducted a logistic regression. Model <- logistf(A ~ C, family ="binomial"(link = "logit"), data=Data) The dependent variable is ...
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2answers
172 views

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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18 views

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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1answer
46 views

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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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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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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1answer
73 views

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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1answer
290 views

intercept in manually weighed regression

Why does manually weighting a regression require the intercept term to be dropped? Consider a model $$y=b_0 + b_1x + \epsilon, $$ a simple linear regression. In classically weighted regression ...
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2answers
611 views

Re-calibrating Intercept on logistic regression models for unbalance data

I have data-set that I’m modelling using logistic regression as land.cover~H1+H2+H3+H4+H6+H8+H14. My response and categorical variables are binary. However the number of 0 and 1 in my response ...
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2answers
516 views

Why does removing the constant term prevent the dummy variable trap? [duplicate]

I understand that if you have a dummy variable with $m$ categories that you should include $m-1$ categories in order to avoid perfect collinearity between regressors. However I don't understand why ...
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6answers
14k views

Reason for not shrinking the bias (intercept) term in regression

For a linear model $y=\beta_0+x\beta+\varepsilon$, the shrinkage term is always $P(\beta) $. What is the reason that we do not shrink the bias (intercept) term $\beta_0$? Should we shrink the bias ...
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1answer
46 views

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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18 views

Confidence interval x-intercept

The x-intercept of a linear regression is -y.intercept/slope. If I wanted to obtain a confidence interval (CI) for a x-intercept of a linear regression, coud it be wrong to find the CI of y-intercept ...
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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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Power calculation to test different intercepts in simple linear regression

I have two groups of data: patients and healthy controls. I perform a measurement and a modelled estimation of this measurement on both groups. I then calculate using simple linear regression ($y = b\...
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1answer
84 views

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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5answers
242 views

Different usage of the term "Bias" in stats/machine learning

I think I've seen about 4 different usages of the word "bias" in stats/ML, and all these usages seem to be non-related. I just wanted to get clarification that the usages are indeed non-...
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2answers
66k views

Removal of statistically significant intercept term increases $R^2$ in linear model

In a simple linear model with a single explanatory variable, $\alpha_i = \beta_0 + \beta_1 \delta_i + \epsilon_i$ I find that removing the intercept term improves the fit greatly (value of $R^2$ ...
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1answer
24 views

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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1answer
568 views

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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1answer
64 views

Interpreting estimates of a bivariate regression model with a categotical and a numeric variable

How to interpret the intercept in a bivariate regression with one numeric and one categorical variable? The following model has a numeric variable (log10(N_Total_e)), namely the log transformed ...
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2answers
221 views

Alternative to R$^2$ in linear regression without intercept

It has been extensively described in this website the reason why one cannot properly calculate the $R^2$ - neither the Adjusted $R^2$ - in regression models fitted without an intercept. What is a good ...
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1answer
31 views

Logit model intercept use

I want to estimate a Logit model where the independent variables are binary and one of them is categorical, so the whole data set consists of dummy variables. First of all, I am puzzled whether I ...
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0answers
84 views

Using LIME without intercept term?

I'm playing with LIME to explain the prediction of a machine learning model. LIME trains a (locally weighted) linear surrogate model around a point of interest. The weights of that surrogate model are ...

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