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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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Assessing Normality in ANOVA - Dependent Variables or the Studentized Residuals?

I ran an between-subjects repeated measures (2*2*2) ANOVA in SPSS using GLM. One of my dependent variables didn't meet the Test of Normality (Shapiro-Wilk p = 0.047) according to the table. The Q-Q ...
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Does conditional intensity function of some model must perfectly match with data intensity if model is true?

I consider some emperical dataset characterized by a single parameter - the arrival times of events {$t_0,t_1,t_2,...,t_i$} as is commonly adopted for point processes. The Hawkes model is tested for ...
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23 views

Residual plot for panel data question

Currently, I am doing a panel data analysis to predict/forecast the housing prices, and I want to use a residual plot to detect if my model is ok or not. I have been reading many articles showing how ...
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1answer
31 views

Can I assess the relationship between a normally and non-normally distributed variable?

My study is related to the visual attractiveness of route-plans in a logistics context. In practice, route-plans are rejected based on the fact that they "do not look nice". I have conducted an ...
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23 views

What is the difference between Noise, error and residuals?

I was reading about Kalman filter. http://web.mit.edu/kirtley/kirtley/binlustuff/literature/control/Kalman%20filter.pdf They talk about additive noise and error. I need to understand difference ...
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1answer
21 views

Studentized Residuals in 'METAFOR' package: Meta Analysis with Mixed Effects

I am using the metafor package (documentation) to conduct meta analysis with mixed effects in R. I have noticed, however, that there are no studentized residuals available for the particular model ...
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1answer
30 views

Dealing with heteroscedasticity when dependent variable is already log-transformed

I have already log-transformed the dependent variable but there is still heteroscedasticity in the residual-fitted plot. What one usually does in situations like ...
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42 views

Residuals in Poisson regression in R [duplicate]

While performing Poisson regression in R, I realized that the residuals, as given in the object slot (model$residuals), differ both from the values returned by the <...
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32 views

Can I fit a GLMM to near-ceiling binary accuracy data?

I would like to analyse some binary response accuracy data that is near-ceiling (90% correct or above) across all experimental conditions---essentially, I'm interested in whether my independent ...
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57 views

Multiple linear regression or simple linear regression on residuals

I have several small datasets of few (9 to 12) observations each, and I do have to treat these datasets separately. For each dataset, I want to test for the relative contribution of two continuous ...
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29 views

Issues with linearity?

Thanks in advance for your help. I have searched and read the answers to similar questions, however I am still not sure I have the appropriate solution. I am running multiple regression with 4 ...
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1answer
36 views

Assumption of ARIMA and relation to ARCH/GARCH model?

I only have a very basic understanding of time series analysis. As I am learning ARIMA and then ARCH/GARCH models, I have some subtle (at least for me) questions on the common procedure to build such ...
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residuals of latent variable in Tobit estimation

I'm applying a Tobit model $$ y^* = x\beta + e$$ $$y = \max(y^*,0), $$ where $y$ and $x$ are observed. For consistency, the residual cannot be heteroskedastic; the latent residual $e$ is distributed $...
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29 views

No ARCH effect in some series in the data set?

Of the 60 series in my dataset, 26 don't exhibit an ARCH effect. I have first fitted an ARIMA model (auto.arima() in R) and tested it's squared residuals for ...
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7 views

Question on using the ante variance structure in MCMCglmm

I am having tremendous trouble finding any examples that use the ante[] variance structure for residual variance in MCMCglmm. I have a bivariate gaussian multiresponse model and I would like to fit a ...
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33 views

What causes a regression model to have positive error when output is large and negative error when output is small? [duplicate]

I have been playing with the Kaggle House Prices dataset for sometime. I have been using only the non-categorical features. After fitting LASSO I plotted the residual error vs true value scatter plot....
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1answer
47 views

Interpretation of relationship between residuals and predicted values in a mixed model

I'm using a linear mixed effects model (varying slope + intercept, with glmer from "lme4") to look at the association of the interaction between two categorical predictors (time + X1 - where X1 is a ...
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1answer
21 views

How does gbm for classification work?

I have a got a fair idea about how it works in regression where each successive decision tree tries to predict the residual (negative gradient for loss function) and the predicted value gets added to ...
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1answer
52 views

Linear Regression Model (Residual vs fitted and Normal QQ-plot)

I would like to ask according to these graphs, does it appear as if a simple linear regression model is appropriate for these data?
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1answer
32 views

How should I interpret this residuals plot

Doing my thesis I came up on a problem where I can't find the answer on. I have a dataset with only categorical predictors with sometimes many levels and a numeric outcome variable bounded between ...
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14 views

Can you find the standard deviation of the residuals of a linear regression using R-squared?

Ridham Kamath, CFA, is an equity analyst with Morgan Yelnats India Ltd. The firm has more than $10 billion of assets under management. Kamath also contributes quantitative analysis for asset valuation....
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Standardized residual for point with 0 variance

So I was fitting a curve to some data. The data looks as follows: $E = [14.9, 22.7, 28.4, 12.5, 10.5, 14.0, 9.3, 11.5, 7.1, 22.0, 5]$ $A = [924.5, 1067.8, 1124.9, 577.0, 430.3, 880.3, 333.0, 569.3, ...
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1answer
31 views

OLS and Probit possible on large sample enough?

I think I understood that normality of residuals may not be a problem if the sample is large enough (cf, here). My question is: Would my sample be large enough to be analysed using a probit and an ...
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26 views

Bonferroni/Holm correction when performing chi-squared residual analysis

Let's say I am performing two t-tests and one chi-squared test for a 5*2 table (for example levels of education vs. sex). I am further interested in which categories of education differ among sexes, ...
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2answers
29 views

Compare models using residuals

Is it statistically correct to compare two models using their residuals? For example, I have two dose-response models, then am comparing their residuals and concluding they are not statistically ...
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1answer
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Is there a specific standard error for an individual residual?

On page 97 of Introduction to Statistical Learning book, there is a paragraph on studentized residuals within the context of looking for outliers. But in practice, it can be difficult to decide how ...
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32 views

Is this residuals plot shows non-linearity?

I was doing multiple linear regression and i made a plot of $x3$ vs the residuals i found this. Does it show that there is a nonlinear relationship between the residuals and x3?And What should ...
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1answer
23 views

How to check if the random effects in a random effect model are uncorrelated with the input variables?

Some asked before "Why do random effect models require the effects to be uncorrelated with the input variables, while fixed effect models allow correlation?" My question is: how do you check this ...
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8 views

Correlation of residuals between equations

What are the conclusions in the case of a correlation (or absence of the correlation) between residuals from different equations in simultaneous equations model? Is it connected with ommited variables?...
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17 views

Splitting residuals in maximum likelihood estimation

I would like to estimate the parameters of a state space model with maximum likelihood. The model has non-smooth transition—I would like to split the estimated residuals into two groups dependent on ...
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64 views

Interpreting residual plots from a regression problem using CNNs on image data

My dataset consists of 799 images and each image is associated with a real number. I have split my dataset into 3 parts (80-10-10 split) randomly. I have trained my model using split1. The values ...
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3answers
86 views

Central limit theorem and residuals

I have often read that thanks to the CLT, the residuals of a model are asymptotically normal. This argument always seemed odd to me since CLT states that The sum of a number of independent and ...
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1answer
167 views

Beginner Q: Residual Sum Squared (RSS) and R2

I'm new to the forum and posting my first of many questions. I'm working on a Linear Regression model and the $R^2$ is 0.89 which tells me my regression line is a good fit. When I calculated the ...
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Is there an equivalent to the study of algorithmic fairness in traditional statistics?

Recently the concept of algorithmic fairness has garnered attention in the ML community, especially with respect to criminal justice and healthcare. Has this topic already been studied in the ...
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28 views

Testing for autocorrelation. Panel data. Poisson model

I would like to test whether there is autocorrelation of the residuals from a poisson regression. I am working with panel data in Stata. My understanding is that for a nonlinear model with panel data ...
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2answers
62 views

quantile of deviance residuals in glm [R]

The summary of glm() function in R gives the quantile of deviance residuals (e.g., see below). I know how to get them (e.g., without using ...
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1answer
82 views

Li-Mak test for GARCH residuals in R

I have conducted a realized GARCH model and want to test for ARCH effects using the Li-Mak test as I have read that it is the best one for this purpose. I am struggling on the question if residuals ...
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1answer
58 views

If we add terms (e.g. interactions, polynomials etc.) to impove model fit suggested by residuals plots, is this classed as data dregding?

In the post The role of validation in estimation and hypothesis testing Frank Harrell wrote: If the adjustment variables were not pre-specified but determined by data dredging, you really need to ...
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24 views

regression diagnostics

Friends, I have a problem with a data set; it has several binary variables and two continuous and skewed variables (service_time is my DV)that have uni-variate outliers. The following two plots: ...
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What can we learn from residual of least squares?

problem description Consider the following simple least square matrix problem $$ AX=B$$ where $A,X,B$ are all matrices. Clearly the solution to $$\min_{X} \lVert AX-B \rVert_F$$ would undoubtfully ...
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1answer
36 views

Regression using residuals

My question is regarding OLS regression and their residuals. If we have a model: $$Y = B_0 + X_1B_1 + X_2B_2 + X_3B_3 + e$$ Where Y = Independent variable, X_i = Dependent variabels, B_i are the ...
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14 views

Is a data transformation effective for minimizing MSE on the original scale?

I am using simple linear regression to model some non-negative and positively skewed time series data, but the fitted vs. residual plot is showing that the linearity assumption is violated. The ...
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38 views

Why is $\mathbb{E}\left[\frac{1}{n-2}\sum\limits_{i=1}^n e_i^2\right] = \sigma^2$?

The context that we are presented with a linear model $$Y_i = \beta_0 + \beta_1X_i + \epsilon_i,$$ where $\epsilon_i \texttt{~} \mathcal{N}(0,\sigma^2)$. We obtain predictions for $X_i$ by plugging ...
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How to get the individual regression terms from a ZIP model? [closed]

I need to display a Partial Residual Plot. I know how to do it, but I can't get the individual regression terms (IRT): Partial Residual = Residual + IRT My model is a ZIP model. It has only 2 ...
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1answer
71 views

Residual vs Fitted [duplicate]

Below is the image I got from my linear regression model. I can see a straight line for the Q-Q plot, however data-points for the residuals vs fitted plot shows a pattern. The model contains seven ...
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1answer
41 views

Correlated residuals lead to low factor loadings

I am doing CFA in lavaan (3-factor model, all factors correlated). The fit of this model is quite bad and I wanted to improve it. I realized, that the full questionnaire contains four negatively-keyed ...
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1answer
45 views

Why does kurtosis of residuals vs. standardized residuals differ in GARCH models?

So I have used GARCH modelling and obtained both residuals and standardized residuals from that model but kurtosis of both of this series should be same? I am using ...
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15 views

Fixing Residual Plot [duplicate]

I have a residual plot and I am looking for a possible transformation that would make it look better --> appreciate any ideas:
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1answer
60 views

Meaning of unusual residual plot

I'm trying to use a residual plot in order to get a better understanding of my dataset and what I should be doing. My data is a series of scored labels with a bunch of distance features used to ...
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22 views

Analyzing Poisson MLM level 2 residuals for outliers

I am using HLM to analyze school discipline data. My outcome variable here is a count - the number of discipline referrals per student in the academic year - and I'm using binary predictor variables ...