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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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Expected value of residuals for LASSO model?

For simple OLS models the expected value of the residuals E(ϵ)=0 can be shown to be zero if an intercept is included in the regression equation. I am using a LASSO model and was wondering if the ...
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23 views

Residuals Diagnostics Forecasting principales [on hold]

Help me please Are the following statements true or false? Explain your answer. Good forecast methods should have normally distributed residuals. A model with small residuals will give good ...
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1answer
37 views

Orthogonality of residuals in linear regression

In multiple linear regression, I came across the statement that both $e$(residual) and predicted $y$ are projections of actual y and $e$ is orthogonal to predicted $y$. I was trying to visualize the ...
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0answers
25 views

Partial residual plot for GLMs

I'm trying to understand how exactly partial residual plots are computed for Generalized Linear Models. Lets say you have a response variable $Y$ and three explanatory variables, where a Poisson error ...
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0answers
18 views

How to deal with autocorrelated residuals from a GARCH model?

I am performing GARCH model on some log returns $r$. If time series of $r$ is autocorrelated, I explicitely model it through a AR model. Then I want to perform the GARCH on the same time series: I ...
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1answer
28 views

Different length in variable and residuals from the model

After having posted another question on the subject, I'm trying this time on my real data (unfortunately not openly publishable) to find the the best variable transformation that yields linearity in ...
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22 views

Diagonal straight lines in residual vs predicted values: can it be fixed with bootstrap resampling?

I am studying a health-related-quality-of life scale and I run a multiple linear model for each of its subscales. For a few of these subscales I came across the pattern of several diagonal straight ...
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1answer
37 views

How to remove the effect of one variable by using linear model residuals

My data set has species with a number of morphological variables, including body mass: ...
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0answers
19 views

How to interpret and fix linear pattern in residuals plot

It's my first question, I am not so experienced in stats: feel free to point me to the right direction. I am doing a regression to predict a price. I wanted to check the residuals (the difference ...
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0answers
11 views

How to calculate residual standard error for a regression model with log link in R

I want to compare residual standard error across a series of different model specifications as one way of assessing model fit. I assumed that calling sigma on a ...
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0answers
22 views

Interpretation of a residuals vs fitted values plot

My objective is to predict the taxi demand depending on location and time. I transformed the data to be more or less normally distributed and centered & scaled it. Then, I ran a linear regression ...
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0answers
29 views

How do I compute the residuals from glmnet in r? [closed]

I am working with glmnet and i would like to compute the residuals for the model with lasso penalty. I've simulated data split into training and testing set. My ...
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0answers
89 views

Expected value of the residuals

How would one prove that the expected value of the residuals from OLS regression is zero? I will make two cases. In the first case I treat $X_i$ as random and in the second case I treat it is non-...
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0answers
22 views

Prediction of time series with neural network

Suppose I get a forecast, from MLP or LSTM - next 7 time steps into the future. I can assess its quality using mean absolute error using cross validation. However, it is not clear, what I should do ...
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0answers
3 views

Allowing cluster-level residuals to covary in Proc Glimmix

I am modeling the probability of a child being retained in kindergarten based on individual and school-level factors. The model includes random intercepts and slopes, as follows: ...
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0answers
6 views

Moving Averages in terms of the Difference Operator?

I am given $$ S_t = \frac{1}{2}(Y_t+Y_{t-1}) $$ $$ S_t' = \frac{1}{3}(Y_{t+1}+Y_t+Y_{t-1}) $$ and I am supposed to express the residual series $Y_t - S_t$ and $Y_t - S_t'$ in terms of the difference ...
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3answers
136 views

Regressing Logistic Regression Residuals on other Regressors

With OLS regression applied to continuous response, one can build up the multiple regression equation by sequentially running regressions of the residuals on each covariate. My question is, is there a ...
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1answer
35 views

Dependent variable - bimodal?

I have a dependent variable, days.to.event, that looks almost bimodal at 0 and 30. I understand that there is no transformation that can normalize this. In fact, when I fit a linear model (lm) with ...
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1answer
57 views

Mixed models with lmer: Residual diagnostics

I fitted a linear mixed model as follows: fit=lmer(Time.to.obtain.loan ~ borrower.Gender+ borrowing.Amount + (1|borrower.Country) + (1|borrowing.Sector)) The ...
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22 views

When fitting an arima model, how do I pick the residuals?

Let's say I have a time series $x_1, ..., x_t$. I fit an AR model and get my estimated parameters. Then I can simulate from this, but in order to do so, I also need some distribution from which I ...
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0answers
25 views

Relevance of residual normally distributed residuals in nonlinear regression

I have a mathematical equation, based on physics, that requires estimating several parameters via nonlinear regression. I have conducted such nonlinear regression estimation with a dataset of 1100 ...
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0answers
23 views

Chi^2 Test: Alpha and it's Relation to Sigma

I'm using an Extended Kalman Filter and the $Chi^2$ test to test a part of it's residual during the update. Here I want to determine if the residual lays within 3 Sigma and reject outliers that are ...
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1answer
38 views

Interprete GARCH residuals QQ plot

How to conclude, that time series' volatilty is not constant? I used GARCH, but have trouble with interpretation. I did the Kolmogorov-Smirnov test for normal distribution with GARCH residuals, which ...
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1answer
29 views

Deviance residuals in Poisson GLM

I am learning the concept of residuals in modelling. I performed a Poisson GLM for a 3x3 contingency table and I got the summary of the model. My question is: the deviance residual from the in-built ...
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0answers
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Is a visual estimate of homoscedasticity rigorous enough?

As part of my research in astronomy (quasar magnitudes at various wavelengths), I've been producing graphs such as the following: The bottom plot on each graph shows the distribution of the residuals ...
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1answer
43 views

ARIMA Model Stage 3 (Residual Diagnostic) - Is the residual a white noise?

Work Done: I have a monthly time-series data (Consumer Price Index) from 1976 to 1993. I performed first differencing and log transformation to detrend it, also, Augmented Dickey-Fuller Test has ...
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2answers
68 views

Normality within cells and non normality of residuals

In testing for the normality assumption for 2 way ANOVA, the question whether normality within cells implies normality of residuals has been asked before and I have found so far different answers from ...
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0answers
28 views

Determining how far an actual value is from a predicted value as $x$ increases

Assume you have 5 $x$ values (1, 2, 3, 4, 5) and 5 $y$ values (1, 2, 1.3, 3.75, 2.25). From this you estimate a linear equation ...
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0answers
25 views

Interpretation of residuals in linear regression

Assume I have the following regression model: $Y=\beta_0 + \beta_1*X_1 + \beta_2*X_2 + \beta_3*X_3 + \epsilon$ If I run the same model without introducing the variable $X_3$, can I interpret the new ...
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0answers
49 views

ARMA-GARCH model with t-distributed errors

I've estimated an ARMA(1,2)-GARCH(1,1) model fitted on financial data. It is very satisfactory in modeling the autocorrelation and the volatility in my data, however, the qq-plot empirical quantiles ...
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2answers
73 views

Non normal residuals for Tweedie GLM

I am using Tweedie GLM as my data contains exact zeroes. However, my stats is weak and want to confirm a few things. Does Tweedie GLM assume normality of residuals? Is shapiro.test() the way for ...
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0answers
133 views

Residual pattern for mixed models (tried lmer and glmer)

I have studied the effect of site, specific area and depth on amount of organisms on kelp blades. Each site had two different depth with three frames on each depth. From each site I have analysed a ...
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0answers
30 views

Extracting latent variable from multivariate linear model, based on residuals

I need some help with some basic regression method. Let's say that we have a tri-variate linear model with continuous variables (as dependent and as independent). $$y=\beta_0+\beta_1 x_1+\beta_2 x^*...
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0answers
17 views

Correlation coefficients and range of residuals

I've generated these plots: The upper two scatter plots show linear regressions of two different combinations of three variables ($W2$, $K$ and $R$), both against $log(z)$, with their ...
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0answers
23 views

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

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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21 views

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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0answers
34 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
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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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0answers
30 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
28 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
38 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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0answers
63 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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0answers
58 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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0answers
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
50 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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0answers
18 views

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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0answers
42 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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0answers
9 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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0answers
44 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
51 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 ...