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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Permutation test on the intercept in MANLY(1997) framework?

We assume to have the following regression model: $Y=β_0+β_1X_1+β_2X_2+ϵ$ I recall here the Manly procedure (from another post here :How to do permutation test on model coefficients when including an ...
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224 views

suppress intercept in regression when having more than one categorical variable coded in dummy variables

friends: according to the following link https://stats.stackexchange.com/a/11068/196391 and what I saw in some papers, we can supress the intercept and consider ALL the dummy variables (which have ...
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645 views

I computed ARMA equation from R manually but never got the same result with predict() or forecast() provided by R

I've got a little problem here. I've been doing analysis with time series data using ARMA, and it always turns out that the parameters I get from R didn't fit to my computation when I do it manually. ...
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How to fit a model that forces all points through zero while allowing for interaction effects

I'm trying to build a model to predict the percentage of a target audience reached as a function of the amount spent on several media channels (e.g. TV and radio) and the type of campaign. The fitted ...
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Why is softmax regression often written without the bias term?

I am familiar with softmax regression being written by: $$P(Y=y\mid X=x)=\frac{e^{[Wx+b]_{y}}}{\sum_{\forall i}e^{[Wx+b]_{i}}}$$ for the change of the class of $Y$ being $y$, given observations of $X$...
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What is the reason for not including an intercept term in AR and ARMA models?

In econometric literature it is usually argued that in case of estimating an equation, an intercept term must be always included regardless of its statistical importance because removing the constant ...
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935 views

Which intercept R selects (binomial glm)?

I have a problem with an analysis. I'm doing a binomial glm with two categorical factors that are loc and trat. I do not understand how R deals with the intercept (what statistical explanation does ...
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Interpreting significance of the intercept in a regression analysis

For my thesis, I'm conducting several linear regression models. In total I have 15 dependent variables, so in my appendix I have 15 regression tables including 4 models. Example: I'm trying to ...
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57 views

Include intercept/error term in logistic regression model specification

Short question, When specifying a logistic regression model as below, does one also include B0? In other words, does the bottom part of the equation look like: A. 1 + exp(-(B1X1 + B2X2) B. 1 + exp(...
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Logistic regression intercept representing baseline probability

In a linear regression, when you standardize your numeric variables, the resulting intercept has the same value as the mean of your sample. Is there any way in a logistic regression, with numeric ...
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What does the formula y ~ x + 0 in R actually calculate?

What is the statistical difference between doing a linear regression in R with the formula set to y ~ x + 0 instead of ...
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Is it necessary to include all levels as random intercepts in a multilevel model when they are perfectly nested?

I am running a mixed-effects model in R and I want to have random intercepts for two sampling levels, country and site. The ...
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1answer
133 views

Standard Error of the Intercept in ARIMAX model

I'm trying to estimate the standard error of the intercept in ARIMAX(1,0,2) model using R. Since the reported 'intercept' in regression output is actually some kind of mean value I applied this ...
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How to change a weight/bias with gradient

After watching 3Blue1Brown's tutorial series, and an array of others, I'm attempting to make my own neural network from scratch. So far, I'm able to calculate the gradient for each of the weights and ...
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Intercept increases in regression when adding explanatory variables

I am conducting an analysis, where I examine the size of the intercepts of three regression models (time-series). The models look something like this: $y_1=\alpha+\beta_1x_1+\varepsilon$ $y_2=\alpha+...
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Is it ok to remove the intercept in a linear regression model (OLS) if the results are really good? [duplicate]

So I've gone through this SE question and all the answers where the general consensus is that you should never remove the intercept of the linear regression model. The most upvoted answer says: The ...
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Unbalanced logistic regression: correction for intercept term and report [duplicate]

I am trying to run a logistic regression with one class (class 0, n = 513) over-represented compared to the other one (class 1, n = 173). So far, in order to correct for the biased intercept, I just ...
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1answer
3k views

Should I keep a non-significant intercept in a GARCH model?

I've estimated an ARMA-GARCH model. All the parameters except the intercept ($\omega$) in the GARCH part are significant. So I tried to estimate the model again imposing that $\omega = 0$. I compared ...
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When does it make sense, if ever, to remove the intercept from a logistic regression [duplicate]

I normally work with linear regression, but came across a need to use logistic regression. I started with glm(y ~ x1 + ..., data, family = binomial()). Almost none ...
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How to visualise a tiny neural network as a function

Say you have the simplest possible neural network with 1 input, 1 output and 1 hidden variable as depicted below. In this case, the activation function is logistic. I assume between x and y, the ...
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561 views

Hypothesis at 5% significant for slope and intercept coefficient

"Conduct hypotheses tests at a 5% significance level on the intercept and slope coefficient to see if the intercept is significantly different from zero and the slope coefficient is significantly ...
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Mapping R ARIMA parameters to coefficient symbols [duplicate]

I'm trying to map the information R prints for an ARIMA model to the coefficients in the formulas that I'm familiar with. Here's what I have so far ar1 = $\varphi_1$, ar2 = $\varphi_2$, ... intercept ...
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Are HAC robust standard errors robust against autoregressive conditional heteroskedasticity?

Suppose I have a GARCH(p,q) model with constant conditional mean, \begin{aligned} y_t &= \mu + u_t, \\ u_t &= \sigma_t \varepsilon_t, \\ \sigma_t^2 &= \omega + \alpha_1 u_{t-1}^2 + \dotsc +...
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How to treat categorical predictors in LASSO

I am running a LASSO that has some categorical variable predictors and some continuous ones. I have a question about the categorical variables. The first step I understand is to break each of them ...
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Dropping the intercept [duplicate]

any help is appreciated. When is it OK to drop the intercept term in a Binomial GLM? That sounds like the data would have to go through the origin but that doesn't seem so bad, does it since we are ...
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Bias initialization in convolutional neural network

What is the correct way to initialize biases in convolutional neural networks (tf.zeros, tf.truncated_normal, ...
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1k views

Baseline adjustment in growth models: Random Intercept or Baseline Covariate

Let's say I have outcome data at four time-points (baseline, 3 months, 6 months, 12 months) which I want to regress on an explicit time variable ($t_1 = 0$, $t_2 = 1$, $t_3 = 2$, $t_4 = 3$) to ...
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1answer
737 views

How centering can ease interpretation of the intercept of a linear model

In Statistical Rethinking, Chap. 4 - page 99, when talking about table of estimates of a linear model $\mu_i = \alpha + \beta x_i$ where the objective is to estimate the height given the weigth ($x_i$)...
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225 views

Bayesian linear regression with parameter restrictions

I am a little confused on incorporating parameter restrictions in the Bayesian linear regression setup. Assume the multivariate regression $$R = \iota\alpha+X\beta+U_R$$ where $R$ is a $T \times N$ ...
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2answers
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Interpreting a negative intercept in linear regression

This is my first time of having a negative intercept, so I'm a bit confused. My line of regression is: $$ \text{starting monthly income} = -7.5 + 0.75\times \text{years of education}. $$ How would ...
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1answer
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Explanation of Mincer-Zarnowiz regression

I am confused about what the Mincer-Zarnowiz regression does. What I understand is that it checks if the forecast we make is biased or not. Let's say we have the following example: ...
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111 views

Both variables of my GLMM output are significant. Don't know how to interpret it?

This is more of an interpretation question than anything. I have run a GLMM with two fixed factors (both of which have two levels) and two random factors. The outputs from the model are as such: <...
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820 views

No intercept model with multiple categorical variables - linear regression

Does running a no-intercept model with multiple categorical predictors and interaction between the predictors result in valid estimates? I am modeling differences within paired data and am using a no-...
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Why does the intercept account for the measurement error in the predictor of a simple regression model?

Baguley (2012) mentions that regression, compared to correlation, is usually deemed the superior statistical technique. Among some of the reasons mentioned, he states that in regression, X (predictor) ...
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Role of the bias term in regression [closed]

I was trying to understand the role of the bias term in linear regression which is given by, y=w^T. phi(x)+b From what I understand it allows for any fixed ...
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1answer
1k views

Specifying constant as intercept in logistic regression using R

I am trying to replicate a logistic regression analysis from a paper using R in lme4 (the specific analysis in the paper uses the glmfit function in Matlab). In it, ...
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1answer
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VAR models in R: Constant, Trend, Constant+Trend, None

I currently apply a VAR models with the vars package in R. There are the options to select "both", "none", ...
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3answers
653 views

In a regression is the Y-intercept a measure of unaccounted biases?

I have been working on a set of data which contains information on the width, age, weight of statues and relate them to the price (I am not actually working on that, but I cannot disclose the topic of ...
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Explain the fit_intercept parameter in some scikit learn classifiers [duplicate]

I'm fairly new to machine learning and I am using the Linear SVM classifier to classify some text data and I was wondering what exactly does the fit_intercept parameter does and what would be a good ...
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1answer
220 views

Can we fit a count data model that can predict zeros on the basis of data that does not contain the zeros?

Suppose that I have a set of count data where I have complete data for observations where at least one event happened (i.e. there are cases with zero observations but they do not appear in my data). I ...
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Why is PCA “a regressional model without intercept”?

As stated in How does centering the data get rid of the intercept in regression and PCA?, PCA is a regressional model without intercept. Thus, principal components inevitably come through the ...
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903 views

standard error of slope and intercept estimate

In the linear model $\mathbf{Y} = \mathbf{X}\beta + \epsilon$, where $\epsilon \sim N(0, \sigma^2 \mathbb{I})$, it is known the the standard error of the estimator $\hat{\beta}$ is given by $$Var(\...
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Estimating intercept term in simulation study

I am working on a simulation study in which I have generated data to mimic a scenario with treated and untreated members of a population along with a number of baseline covariates. I am using those ...
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123 views

How to Interprete Constant Intercept in Log Models?

Even though this seems like an especially simple question, I am not 100% sure about what the constant in a log-log model, log-level, or level-log model means. For example, in log(weight) = 8.29 - 0....
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Minimizing error of intercept estimate for a given N

Suppose you know that $y = a + bx + \epsilon$ is your generating process, where $\epsilon$ is $N(0, \sigma^2)$, but you don't know the parameters $a, b, \sigma$. You have a limited number of trials ...
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Why are bias nodes used in neural networks?

Why are bias nodes used in neural networks? How many you should use? In which layers you should use them: all hidden layers and the output layer?
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The difference between with or without intercept model in logistic regression

I like to understand the difference between with or without intercept model in logistic regression Is there any difference between them except that with the intercept the coefficients regard the log(...
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Calculate output nodes (consumer acceptance) of neutal network

To make it a bit easier I am using round numbers (integers) in this example. We have to calculate the value for consumer acceptance. Therefore we have the following input variables (fat = 3; salt = 2)...
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950 views

Does the intercept in a logistic regression capture the unobserved effects?

Theoretically, does the intercept term in a logistic regression model capture all unobserved effects? In other words, in a logistic regression model with a perfect fit (i.e. all relevant variables ...