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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X-13 Seasonal Adjustment trading day peak in regarima residual

I have a time series of air passengers with a total of 143 monthly observations. Having done the seasonal adjustment using X-13-ARIMA-SEATS, the final diagnostics seem to suggest that the seasonal ...
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20 views

Mean square error of residuals

On page 15 of "An Overview of Predictive Learning and Function Approximation," Friedman claims that with the standard linear regression model in $\mathbb{R}^d$ (the true model $f(x)$ is linear, errors ...
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1answer
27 views

Definition of residuals versus prediction errors?

I always thought the definition of residuals is the difference between the statistic and the observations. And, the definition ...
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1answer
29 views

DCC GARCH model diagnostics in R

I have fitted a DCC GARCH model to my multivariate financial data. So, now I need to check the fitted model by using the standardized residual and its squared process. A good fitted model should have ...
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1answer
59 views

Off-diagonal elements of a correlation matrix after removing the first principal component

I have some data with more variables than observations, that I'd like to subject to a principal components analysis. For didactic reasons (to give an intuition for factor retention criteria under ...
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2answers
33 views

Regression Analysis — Correlation of Residuals

I see a lot of info on how to detect correlation of residuals and why it might negatively impact the quality of our model. I however dont see much info on how to mitigate the bad effects of these ...
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16 views

Differences in regards to standard deviation

Hi I'm having trouble figuring out the differences in calculating the standard deviation of a data set and the standard deviation of its residuals?
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15 views

Test for Conditional Normality?

On page 357 of this article, it states: We assume that the treatment (or its transformation) has a normal distribution conditional on the covariates. How would I go about determining if a ...
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1answer
27 views

Why does adding a time index variable help with a trend in errors?

I was reading through this example of a regression model fit to beer sales data link. After the log transformations on the data (which make sense how they correct for the compoundingly larger variance ...
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52 views

Mitigate autocorrelation in time series with AR(2) process

I have a dataframe with 4000 companies and I have calculated a liquidity measure of each of the company in the dataframe. Liquidity is highly persistent. And my analysis shows that in these indiviual ...
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23 views

Residuals of logistic regression and detecting outlying observations

Is it correct to say that the residuals of logistic regression in practice have a bimodal distribution? And how would this make it harder to detect outlying observation?
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17 views

Correction for non-normal residuals where residuals are not correlated or show heteroskedasticity

I know the implication of non-normal residuals is uncertain statistical tests because the SEs are inefficient. Can I apply the Newey-West to calculate standardized Standard Errors for an OLS ...
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2answers
398 views

Why do residuals in linear regression always sum to zero when an intercept is included?

I'm taking a course on regression models and one of the properties provided for linear regression is that the residuals always sum to zero when an intercept is included. Can someone provide a good ...
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1answer
23 views

Where do deviance residuals come from?

I'm trying to understand deviance and deviance residuals using a simple Poisson regression model as an example. Let's say we have a response variable $$ y_i \sim \text{Pois}(\lambda_i)$$ and we assume ...
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39 views

What causes bands/stripes in residual plots?

I ran a model and got the following residuals: I proceeded to log the fitted values to get an idea of what's happening at the lower end of my predicted values: It was then I saw on the left side ...
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1answer
11 views

same variances of the error terms of residual analysis?

The text book says the residual diagram suggests that the variances of the error terms are equal.But how the variances of the error equal?As You can see the variance on the right circle is greater ...
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1answer
48 views

Implementing logistic regression (R)

I am implementing a logistic regression on a 250 x 20 dataset (250 observations of 20 variables) with a dichotomous response. In this proces I have encoutered some different problems, namely: 1. ...
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0answers
36 views

Residual's plot interpretation

These are plots created in R. All of them are residuals (errors) vs. fitted values. They come from multiple linear regression models fitted by least squares. The five plots represent 5 different ...
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1answer
33 views

Tilted rectangle in residuals vs fitted plot

When performing diagnostics on an OLS model, what can make a plot of the predicted responses vs the residuals. Ideally we want a horizontal rectangle shape. But what does it mean when the plot is a ...
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0answers
17 views

Estimating unexplained variance from multivariate probit output (for imputation protocol)

I have a use case in which survey data underreports program participation, and I need to impute new recipients from within the survey data. There are two (exogenously provided) sub-objectives: ...
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14 views

TReading Residual Plot: Omitted Variable Bias of Dummy Variable

I have a plot of the residuals versus fitted values of an OLS model such that the shape of the plot are two identical randomly scattered clouds, one above and one below the $\hat{e} = 0$ line. Can I ...
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11 views

High residual reproduced correlations in factor analysis vs sample size

I am a Psychologystudent who had to execute a survey for her study. The criteria where that I had to have at least 25 people and that every scale would have at least 5 and maximum 10 items. My survey ...
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31 views

Calculating Multiple R-squared from Adjusted R-squared

I need to calculate Multiple R-squared knowing only adjusted R-squared and the number of predictors, not the number of observations within given data. However, I know (1) residual standard error, (2) ...
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32 views

Is there a theoretical distribution for the residuals of a logit/probit regression?

I know there are a number of ways to define residuals for logit/probit regression but is there any theoretical distribution? I've also heard these residuals can be bimodal so maybe there is no closed ...
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1answer
35 views

Interpretation of covariance estimates glmm (proc glimmix)

I am using the glimmix procedure in SAS to model a generalize linear mixed model with and binomial distribution and a logit link function. I am modeling both the G-side and the R-side covariance ...
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42 views

Using residuals as a dependent variable (multiple times)

Probably a noob question, but does it even make sense? Let's say I have several 2-3 independent variables pools and I want to take independent variables from each pool and regress them agains the ...
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19 views

Residuals from a mixed effect model

I'm running a beta-binomial mixed effects model that estimates the effect size (B) and partitions variance into a random effect (g) and error (e). I would like to calculate the residuals (e), but only ...
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197 views

Diagnostics for generalized linear (mixed) models (specifically residuals)

I am currently struggling with finding the right model for difficult count data (dependent variable). I have tried various different models (mixed effects models are necessary for my kind of data) ...
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9 views

normality tests of residuals in repeated measures design

I have a repeated measures design where I have plotted the residuals and the majority of my data are not normally distributed. As I understand it, repeated measures designs are quite robust when using ...
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2answers
53 views

How are the values of residuals (white noise) calculated in ARMA model?

I am trying to implement ARMA model in Java. I have trouble with calculating residuals (white noise) in Moving average part of the model. From the answer on this question (Fitted values of ARMA model) ...
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46 views

Shouldn't the root mean square error (RMSE) be called root mean square residual?

As far as I understand, estimating the error of a model, say an artificial neural network, requires to know the "true" model. Wikipedia says in its article "Errors and residuals": "The error (or ...
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25 views

Estimating Studentized Residuals (or Another Similar Measure) After Linear Regression With Robust Standard Errors

I have estimated a linear multiple regression with robust standard errors using Stata (regress depvar indepvar1 indepvar2 indepvar3 indepvar4 indepvar5, robust). ...
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3answers
109 views

VAR model residuals having significant correlation at lag 12

I have tried to fit a VAR model for two stationary time series dlogsl_ts and dlogllc_ts(tested by PP test and ADF test), the ...
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49 views

Why is my logistic regression fit that bad?

I was requested by a professor to analyze a high dimensional dataset (92 cases, 400+ variables, and a lot of NAs...) of various patient outcomes (gaussian distributed, counts, and binary) and their ...
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126 views

Where is the explanatory effect of common variance among covariates accounted for in regression procedures?

As a follow up to the excellent answers provided for: Does the order of explanatory variables matter when calculating their regression coefficients? (Which I've found incredibly useful from a ...
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27 views

Residual plot looks like inverted change plot for prediction model

I have a very big problem with my predictive model. What i essentially do is that I predict the volume in a tank by studying the flow into and out of the tank. I use the two flows to construct a ...
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1answer
84 views

Interpretation of residuals vs fitted plot

I am checking that I have met the assumptions for multiple regression using the built in diagnostics within R. I think that from my online research, the DV violates the assumption of homoscedasticity ...
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1answer
36 views

Multiple regression - Interpreting the plots

I used the inbuilt dataset stackloss here. I used following R code for creating the multiple regression model. ...
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61 views

Non-normality of residuals in a negative binomial GLMM

I am testing for the effect of treatment and fish length on the school size of fish. Treatment is a categorical variable with two levels (e.g., treatment A & treatment B). Fish length is ...
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20 views

Problems in finding outliers and leverage points in non-linear regression

I'm implementing diagnostic of non-linear regression model $(y=ax^b)$. I'm trying to find out where outliers and leverage points in my model ...
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1answer
75 views

Check for White Noise Residuals for AR(1) Model

I was going through the SAS documentation for PROC ARIMA and got stuck at this point. ...
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7 views

Create ANOVA table

I have an analysis of deviance table that includes : Degrees of freedom, Deviance residual, Degrees of freedom residual and deviation How can I use this to fill in an ANOVA table ?
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1answer
37 views

Help interpreting Residuals vs Fitted Plots

I'm analysing some data which compares treatment effects. My anovas have all indicated that there is no significant differences between treatments. I have also applied a transformation and re-fitted ...
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58 views

ARIMA diagnostic testing in Stata

I am using an ARIMA(1,1,0) in Stata. I have already executed estat aroots and wntestq (white noise test) for the residuals. I ...
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1answer
44 views

Standardized residuals vs fitted values: OLS assumptions satisfied?

Based on only the above plot, what comments would you make about whether the OLS assumptions are satisfied? In particular homoskedasticity, normality. I just want to know if I'm right. It seems to ...
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1answer
68 views

How can I improve this glm and do I need to dummy code?

I have percentage disease data taken from leaves of wheat in a disease trial which were artificially inoculated with isolates of disease from different source plants. The basic question is, are ...
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6 views

Whats the background of the mean squared error? [duplicate]

I'm trying to find out how to measure the accuracy of different regression algorithms. Why is the "squared" in the mean squared error? For me it would feel more intuitive to have the mean error of my ...
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1answer
88 views

Fitted values and residuals: are they random vectors?

I'm trying to understand the expression $Cov(\hat y,\hat \epsilon)$ in regards to the usual linear regression model/assumptions $y = \beta_0 + \beta_1 x_1 + \beta_2 x_2 + ... \beta_n x_n +\epsilon$. ...
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23 views

Estimating multiple residual terms for mixed effects model in R

I was told that it may be useful to estimate multiple residual terms in a mixed effects model I am trying to build. This is possible in ML-win, but since I am only familiar with R, I am hoping that it ...
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1answer
119 views

Question about the assumption that residuals are uncorrelated with the predictors

I'm studying the review for one of my graduate classes, Correlation and Regression Analysis, and this is one of the questions: A friend says that you don't have to worry about the assumption that ...