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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482 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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20 views

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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90 views

Coefficients in a Randomized Block Design

If, for example, I am running a GLM with Poisson distribution (it could be any distribution) and I have a Randomized Block Design (RBD) [Note: I don't wanna run a GLMM just to put the blocks as a ...
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1answer
108 views

AMOS: CFA testing invariance, but cannot name intercepts

I'm using AMOS to run a 2-factor model with 5 indicators each (10 in total). I'm assessing the invariance. So I'm assessing the invariance for sex. While the configural and metric invariance worked ...
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1answer
869 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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1answer
388 views

Calculating variance components and ICC of a random intercept model by hand

When I really want to understand a measure or parameter, I tend to do the calculation by hand with simplified data. Today I have attempted to do the same with the ICC, but somehow keep failing. I was ...
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1answer
2k views

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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1answer
54 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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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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1answer
154 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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45 views

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
113 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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1answer
1k views

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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1answer
1k views

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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1answer
1k views

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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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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108 views

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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1answer
65 views

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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535 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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36 views

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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189 views

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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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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1answer
50 views

Selecting predictor in regression: What is more important - significance of the intercept or residual standard error

I am trying to find the best predictor for Leaf Area Index (LAI, a plant growth indicator) among several spectral indices (these are calculated from reflectances measured in different spectral wave ...
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1answer
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
507 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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211 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
8k views

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
1k views

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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1answer
99 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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776 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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0answers
38 views

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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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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3answers
578 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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2answers
4k views

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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0answers
2k views

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
211 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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40 views

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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1answer
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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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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

Ridge Regression: When should the intercept be included ? What is the purpose of the intercept term? [duplicate]

I am trying to determine what is the purpose of including the intercept term in ridge regression. In what situations should I include the intercept term ? And in what situations should I not ...
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102 views

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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0answers
2k views

How to determine bias in simple neural network

I have built a very simple feed-forward neural network which given an input $x \in \{0, 1\}$, it is trained to learn $f(x) = x$, the identity function. Below is a model where on iteration $i$, $x_i$ ...
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0answers
124 views

Deming regression implementation: force intercept to 0

I implemented Deming Regression in a known programming language, using the algorithm from here: https://en.wikipedia.org/wiki/Deming_regression However, the algo does not specify what to do in case we ...
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1answer
688 views

Does R glmnet regularize on intercept?

Both this post and original paper, suggest R glmnet does not regularize the intercept. But why I am observing the intercept ...
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2answers
444 views

How to find and correct y-axis offset in time series?

I have usage data of many machines like this: In this machine, the usage grows linear with the time. However, in early 2016, someone or something messed with the total usage in hours and the next ...
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1answer
245 views

Do we include the intercept term when predicting in simple linear regression?

In "Introduction to statistical learning wit R", there's a simple linear regression fit on a 'TV' feature where the target class is the 'Sales'. Beta 0 is 7.03 and Beta 1 is 0.0475 Now we want to ...
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1answer
272 views

Logistic model output when all inputs are zero

Consider a case where I have developed a predictive model using logistic regression. Now the logistic models gives a probability even when all the inputs are zero (because of the intercept). Now ...
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1answer
107 views

Detect a change in linear regression model's error

At time T0: A linear model is deployed to predict outcome Y as a function of X with equation Y = m1*x + c1 At time T1: The underlying process drifts to a new mean, resulting in consistently positive ...
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701 views

Negative and not significant intercept in multilevel model

the objective of my work is to estimate whether policies can increase men's time investment in housework. In order to estimate whether the regulation of normal weekly working hours affects men's time ...