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Questions tagged [residuals]

The residuals of a model are the actual values minus the predicted values. Many statistical models make assumptions about the error, which is estimated by the residuals.

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How to interprete this Quantile Plot?

I did a multiple regression analysis for several production sites with energy consumption as dependent variable, and 2 other independent predictors (Floor space, production). When checking the ...
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Change variable to log transformed or keep original?

A log transformation of the dependent variable is sometimes recommended as a remedy for some cases of non-normal distribution of residuals after fitting a linear regression model. What is the proper ...
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How can I get the correlation matrix of the residuals of a VAR model in R? [closed]

I have implemented a VAR model (with two variables) in R and would like to check the correlation of the error terms in order to see the importance of the ordering of the variables. How is that ...
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How can I determine, in what extent the fit to experimental data is good in Matlab?

I have experimental spectrum in which y-axis is intensity values, and x-axis is frequency values. Int - array of experimental intensities (y-axis). w - array of frequencies (x-axis). I know the view ...
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What if errors (residuals) follow other distribution rather than linear regression?

At first, sorry for the bad english. I'm not good at english because I'm a Korean. Recently, I'm studying linear regression. I've heard that errors always follow normal distribution because they are ...
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Which statistical test to use when some residuals are normal and some are non-normal?

I have some response data from an experiment which uses appraisal methods to assign scores based on various attributes. The scores are awarded (in part) from visual observations of biological ...
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Estimating likelihood from the Residual Sum of Squares

I'm start studying Bayesian statistics, but I've found that I'm having troubles with the likelihoods. Let's say that I have a vector of observations $y$ and I want to calculate how likely it is $y$ ...
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why do residuals of the model show heteroscedasticity when plotted against time

Following up on question Dealing with heteroscedasticity in mixed models I collected crop yield data for many years across multiple locations, which are nested under provinces and some associated ...
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How to read Partial Regression Plot?

Partial regression plot is a plot: • X's: residuals from model X[k] ~ X[-k] • Y's: residuals from model Y ~ X[-k]. But how to read it? What does it show? Can I expect sth and if it appears/does not ...
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Why does the Breusch Pagan test use unstandardized residuals and predicted values?

If I understand correctly, there are different ways to test for heteroscedasticity. I first learned to do it by looking at a scatterplot of standardized residuals vs. standardized predicted values. I ...
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Are studentized deleted residuals &/or DFfits applicable in logistic regression?

Are studentized deleted residuals and DFfits applicable in logistic regression? In some statistical packages (Stata for example) these statistics are available in linear regression analysis, but not ...
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residual plot and non linearity

I was taught that linearity assumption in linear model can be checked by using the residuals plot. If there is a pattern then the assumption is most likely violated. Can someone explain the mechanisms ...
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Regression: Are these residuals normally distributed?

I have read a lot about the importance of the residuals being normally distributed. In order to check whether my own regression fulfils the OLS assumptions, I plotted the following QQ plot: I ...
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Relationship Between Required Sample Size and Number of Predictors in the Model

Is it true to say that, in (logistic) regression, the required sample size to detect a given effect size for a single predictor increases with the total number of predictors included in the regression ...
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Does it make sense to use residuals as an independent variable?

I recently ran a regression of the following form: mod <- lm(log(y) ~ log(x)) To examine how y scales as a function of x. I then examined the top 20 (super-...
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Why clustering residuals for localisation makes coefficient estimates to become significant?

I have a cross section dataset for a sample of individual firms (n=874) located in a Norwegian county. I test with a probit model, the probability for the firms to adopt a certain technology X, using ...
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What is the difference between Residual Covariance Matrix in Linear Weighted Least Square and Non-Linear Weighted Least Square?

We have these two models : z = h(x) + e, r1 = z - z_hat = h(x) - h(x_hat) z = Bx + e, r2 = z - z_hat = Bx - Bx_hat in the first equation x is estimated by nonlinear weighted least square and second ...
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Confidence interval to use when residuals non normal?

I have done regression but residuals not normal ... When I take out outlier residual are normal. But the outlier is important data so I leave it in ... In order to use my regression result do I reduce ...
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Homoskedasticity of the residuals

When, I fit an ARMA model to data, I look at the standardized residuals plot to assess if they behaves like uncorrelated random variables with zero mean and costant variance (if the model is good). ...
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Do these standardized residuals show heteroskedasticity?

I'm practising in the individuation of heteroskedasticity from the standardized residuals. I know that, if the time series is homoskedastic, the spread of the residuals should be constant and random ...
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Is my interpretation correct for these residuals plots?

In preparation for my exam, I'm trying to interpret the residuals in order to understand if the time series has been modelled correctly. Otherwise, I have to suggest an improvement. Here is the text: ...
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1answer
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If diagnostics for multiple linear regression are ok, are diagnostics of the component variables needed?

This is a follow-on question from here. I received two conflicting answers to the question posed in the title of this post. The diagnostics of the multiple regression looked okay (see link), but it ...
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How do we perform residual analysis on binomial model with small counts?

I know that both Pearson and Deviance residuals tend to be approximately normal for Poisson and Binomial model with large counts when standardized, so we can exploit that to perform the residual ...
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Rules of thumb for partial residual (component + residual) plots as diagnostics for linearity?

Here are the standard R diagnostic plots of a multiple linear regression model that includes an autoregressive term at lag-1 (i.e. AR(1)). I have logged & z-scored my input data. Ben Bolker says ...
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Evaluating goodness of fit for Bernoulli glm

I am trying to fit a model estimating the success probability of the Bernoulli distributed random variable with the logistic link function. However, I am stuck with testing the goodness of fit of my ...
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How to deal with auto-correlation in generalized linear modelling?

I've built a generalized linear model by using glm.nb function (my response is a count type of data) using a single predictor. The model summary is given below. <...
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significant $\chi^2$, breakdown shows nothing interesting

Someone I know told me that he had performed $\chi^2$ test of independence with Yates's correction on a $2\times n$ contingency table, seen that $p\lt10\%$ (good enough for his purposes), and ...
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Regressing a response on predictors at a lower level of aggregation: combined election and survey data

Combining two secondary datasets, we are interested in finding out the effect of political outcome variables (e.g. mayor's party and percentage of vote) at a low administrative level (e.g. township) ...
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1answer
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nonlinear regression with time series error

I have a question about data analysis. I fitted my data to non linear regression by using nls function in R. Then I plot the residuals. The residuals are non ...
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1answer
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How to motivate a POLS?

How would you justify the usage of Pooled OLS regression instead of Fixed effects? If I am calculating just correlation between two phenomena, may I get rid of these fixed effects? May I choose to ...
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normality of independent variables [duplicate]

I am running a generalized linear model. The dependent variable is binomial and independent variables are categorical and continuous variables. My question is : 1. Does the continuous independent ...
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1answer
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How to read checkresiduals graphics in R?

I need to check the residuals of two models in R so I can determine how bad or good are said models. First, I've started simulating an INAR(2) model and wanted to fit a more convenient model, then, ...
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Dealing with correlated variables and choosing between models

One of the things I've always been confused about is the framework around model selection in the cases where $n$ predictor variables $x_i$'s are correlated. My thoughts on the different approaches: ...
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GAM residuals , GAM check

I am doing my GAM regression analysis in R and by using the gam.check() function from the ...
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Residuals and the law of large numbers

Can I apply the law of large numbers (LLN) to $ê$ (the observed residuals)? For example, can I use LLN for ($1/n)∑ê$ and say that converge to $E[e]$ (where $e$ is the true error)? I think that I can'...
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Violation of normality of residuals in glmm [duplicate]

I'm a newbie, so apologies in advance if this Q is missing any useful detail. I'm trying to test the effect of condition upon the number of times certain behaviors are produced by a group of ...
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Comparing Residual sum of squares

I have 30 sets of experimental data which I am then modelling with coupled differential equations. Not every data set has the same range (some lists are longer than others). For each data set I have ...
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residual network clarification

Consider the following pseudocode for standard backprop ...
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Does it matter whether the predictor or fitted value goes on the x axis in a residual plot?

For example, say you fit the model: $$ y = \beta_0 + \beta_1x_1 + \beta_2x_2 + \epsilon $$ where the residuals are $e_i = y_i - \hat y_i$. I often see residual plots of $e$ vs $\hat y$ as so: ...
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1answer
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Interpreting Regression Diagnostic Plots

I'm sorry if this is a broad question but can someone explain to me how to interpret these regression diagnostic plots? I understand the Normal Q-Q show's how normal the spread of the data is, but the ...
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1answer
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GAM using a cyclic spline improves residual structure but reduces fit

I'm working on a dataset monitoring soil moisture levels throughout the summer. The general trend in the data is the following: When I use a GAM with default thin-plate spline and AR(1)process there ...
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How do Component + Residual Plots look like in Polynomial Regression?

Components + resiudal plots or partial residual plots can be used to detect deviations from linearity in multiple linear regression. They work by plotting the variable on the x-axis and the component+...
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1answer
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ResNet 34 training with custom dataset

I am a beginner in Neural Networks and wanted to implement ResNet34 for a pet project at my workplace. Due to confidentiality issues, I do not want to use ImageNet trained weights. I have a dataset ...
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Poisson residuals

I have been working with count data (n=66) recently, trying to fit a simple model to explain distribution in an outcome whereby the count (number of successful trials in a region) is relative to an ...
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Autocorrelation: Multiple observations at lag 0

I have data recorded over 100 days. For each day there are ~5-10 observations. How can you check whether residuals of one day are correlated at lag 0? More precisely: Are residuals of the same day ...
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Residuals of a model using the training set vs the testing set vs the full set

I have a Gamma GLM with a log link function to predict face amounts of insurance. This model was created using the training set, which is 75% of the full data, randomly sampled. Now that I have this ...
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When can Autocorrelation of Residuals be ignored?

One assumption of OLS regression is that residuals are idependent, so that there is no autocorrelation. When I checked the assumption, I noticed that autocorrelation is present. Now here are two ...
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Calculate $R^2$, $R^2_{adj}$, and F-statistic from $\text{R}$ model summary

I am given the full model, $M_{\tt f}$, with the regression line $$ {\tt response} = \beta_0 + \beta_1{\tt A} + \beta_2{\tt B} + \beta_2{\tt C} + \beta_4{\tt D} + \beta_5{\tt E} + \beta_6{\tt F} + ...
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1answer
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Introducing random slopes in nested model improves model fit but residuals variances become unequal

I have measured boldness scores (continuous variable) across time (trials) for individuals (ID) within colonies (colony). The data is coded such that individuals 1-30 belong to one colony, 31-60 to ...
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The feasible generalised least squares residuals

Consider the FGLS estimator. Let $\Psi'\Psi = \Omega^{-1}$ be the weighting matrix using the Cholesky decomposition. Suppose that $\Psi$ is known or already estimated. Consider the transformed ...