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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Choosing the correct anova model

How does one choose the best model based on ANOVA's result? I mean I have 3 model outputs 1st is linear+all interaction, 2nd is linear+pair wise interaction and 3rd is linear and I am asked to choose ...
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20 views

Input EGARCH model (idiosyncratic volatility)

I have a time-series of historical volatility observations. I want to use an EGARCH model because I believe it is a better representation of the behaviour of these volatilities. Can I estimate an ...
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29 views

Estimating AR process for Logistic Regression

I'm fitting a time-series model with independent $X$ variables coded as months of the year (so there are 12 of them) and the dependent $y$ variable is some proportion, bounded between 0 and 1. As a ...
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1answer
29 views

How can we have non-random patterns in the plot of simple linear regression residuals vs the predictor variable?

A) When considering a simple linear regression model, it is important to check the linearity assumption. Graphing the residuals vs the predictor variable can often give a good idea of whether or not ...
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471 views

Why is the normality of residuals “barely important at all” for the purpose of estimating the regression line?

Gelman and Hill (2006) write on p46 that: The regression assumption that is generally least important is that the errors are normally distributed. In fact, for the purpose of estimating the ...
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56 views

Residual variance formulas difference

There is a bi-dimensional table of frequencies: Doing the regression analysis with the fit formula being $\hat y=a+bx^2$, where $\hat y$ is the same as $y^{est}$, the filled table looks like this: ...
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2answers
126 views

How to verify a linear model?

Given a dataset and liner model, how can I verify its sufficient quality? ...
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16 views

Concerns regarding correlation structures and random variance using lme

I’m modeling some variables repeatedly measured over a three months period for a total of 300 individuals. These variables (e.g. activity) were measured at three different time scales: daily (90 ...
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1answer
53 views

Can I say that residuals are white noise?

I want to check whether residuals are white noise or not. When I look at the plot, all lags do not pass(exceed) the significance band except for fourth lag. However, fourth lag's p-value of 0.228 is ...
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1answer
52 views

Interpreting the spread-level plot from R

I created a spreadlevel plot on my simple linear regression model in R. Here is my code, spreadLevelPlot(ols_reg) where ...
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2answers
36 views

Heavy-tailed residuals for OLS regression with large n. Implications?

I am trying to fit a multiple regression on a dataset with n=8619. First of all, using an untransformed Y as the response variable (ie Y = aX + bX +..) resulted in a residual plot with increasing ...
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1answer
51 views

Residuals Interpretation:Time Series Data

I am trying to use multiple regression for a time series dataset. I have values corresponding to a variable measured by 24 hrs for 4 months. Since there was a pattern which repeated every 24 hours I ...
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25 views

distribution of residuals in logistic regession

I am fitting binary outcome using generalized linear mixed model (glmm). I checked the Studentized and Pearson residual and they do not seem to be normal. Is it expected that residuals in logistic ...
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19 views

How are residuals calculated in rugarch package

I have a question regarding the "rugarch" package in R. I try to fit a ARMA(1,1)+GARCH(1,1) to a time series $x$ using the following command: ...
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58 views

Residuals Diagnostics, transformation or non-linear model

I am struggling with my data (hit counts for multiple target detection trials) To start, it is heavily negatively skewed: 00000000000000000000000000000000000 ...
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2answers
40 views

Errors and Residuals

In Wikipedia , it is written that : the sum of the residuals within a random sample is necessarily zero, and thus the residuals are necessarily not independent. The statistical errors on the other ...
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1answer
47 views

For the model $y_i=\beta_0+\beta_1x_{1i}+e_i,\quad i=1,\ldots,n$ , does $e_1=e_2$ imply $y_1=y_2$?

Which one notation is correct and why ? $y_1=\beta_0+\beta_1x_{11}+\epsilon_1$ or, $y_1=\beta_0+\beta_1x_{11}+e_1$ or, $Y_1=\beta_0+\beta_1x_{11}+\epsilon_1$ or, ...
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9 views

Calculating leverage/cook's distance for a Weighted Spatial Simultaneous Autoregression Model

I am estimating a Weighted Spatial Simultaneous Autoregression Model (spdep::spautolm --> Link) in R and I would like to do some residual analysis. Unfortunately ...
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48 views

Residuals - What are they? How can i obtain them?

So, i have a data set. I decide to fit an AR(1) model to it thus obtaining a model of the form $X_t - \hat{\phi} X_{t-1} = Z_t \quad Z_t$ is $WN(0,\hat{\sigma^2})$ Which in matlab is given by ...
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40 views

Goodness of regression model

What are the main indicators of goodness of a regression model? Are they MSE (mean squared error) http://en.wikipedia.org/wiki/Mean_squared_error , R-squared and adjusted R-squared only? Can mean of ...
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56 views

Large samples and normality of residuals

Ok I understand that normality of residuals is not really a concern in large samples. But can anyone tell how large should the sample be to ignore normality. Any cut off point? I'm working with a ...
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31 views

How can I get a reasonable residual standard error for my linear model which faces heteroscedasticity?

My goal is to get the residual standard error of my model to be as small as possible. I have a linear model lm(y~x). When I plot the standardized residual errors in function of the explanatory ...
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25 views

Residual vs fits for 2-level factorial design

So I'm analysing a 2-level factorial design, and get the residual vs fits plot below. I don't understand why it's symmetrical around 0. In any form of linear regression I've learned that the plot in ...
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66 views

R and Regression: How to determine distribution of residuals?

I have residuals from a linear regression model on my data set. I want to find an appropriate distribution of my residuals. Say, I assume my residuals are Skew-T Distributed, how can I find the ...
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47 views

What can be inferred from “covariance matrix of residuals” and “correlation matrix of residuals” after VAR?

I have this VAR: summary(VAR(V6CADModelSt45obs1D.df[,c(5,3,2,6,1,4)], p=5, type="none", ic="SC")) The following is the result of this VAR: ...
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31 views

not normally distibuted residuals

I have made an linear regression model using stata. I have made my model diagnostics - predict y, predict (rstudent) residuals. When I control the residuals for normality by a Q-Q plot, it is ...
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22 views

Is Wild Bootstrap a good strategy in General Linear Model (ANCOVA) with Assumption Violations (both normal residuals and homoscedasticy)?

I need to perform several GLM's (i.e. ANCOVA’s, with a single continuos dependent variable and several predictors, one dichotomous and some other continuos). I was looking for both a significance on ...
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Independence of residuals over time

My plots of conditional weighted residuals (CWRES) plotted against time show some sort of time trend (image attached). The response variable is on a Box_cox scale. How could I solve this problem ?
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374 views

Why do we say “Residual standard error”?

A standard error is the estimated standard deviation $\hat \sigma(\hat\theta)$ of an estimator $\hat\theta$ for a parameter $\theta$. Why is the estimated standard deviation of the residuals called ...
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51 views

Can I use deviance to compare the fit of a model to different datasets?

I'm using R's nls to fit different datasets to the same model. I've read that using R-squared is usually not correct for ...
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38 views

Time series error assumption

I have a time series of annual maxima. Theoretical arguments - where the maxima of any arbitrary distribution converge to a Generalized Extreme Value (GEV) distribution - along with empirical checks, ...
4
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1answer
81 views

non-normal residuals in ARIMA

I am trying to fit an ARIMA model and I have already evaluated a few variations which I finally selected ARIMA(1,1,3) model. The residuals seems to be uncorrelated and all the lags are significant. ...
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50 views

Schoenfeld residual independent of time?

I've seen it claimed (e.g. in these notes ) that "Schoenfeld residuals are, in principle, independent of time." Can this be right? Consider the following situation: You are using a Cox model to ...
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45 views

Is the the dependence of the residual of a ARMA time series model only based on AR term?

Lets suppose we fit two time series models AR(1) and ARMA(1,1) to a data series. Should be the results of the ljung-Box test for the residuals be the same for these models? I mean does MA term affect ...
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38 views

Type III SS, anova - comparison to residuals

Apologies if this topic seems to have been beaten to death, but I couldn't find an exact duplicate. Take this data in R: ...
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93 views

How to use residual analysis to remove the effect of confounding variables in a model in R

I want to find which soil variables better explain plant productivity, using a database that contains information for about 100 forests plots across Europe. These plots have only one species per plot, ...
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28 views

Analysis of how one variable explains residuals

I have run an lm in R and extracted the residuals, say: fit <- lm(size~metric,data=db) fit.res <- residuals(fit) How can I now analyse if the residuals can ...
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11 views

Comparing regressions: usual regressor vs regressed-out regressor

I'm comparing the regression coefficients between 2 models: Model 1: $$ Y = \beta_1X_1 + \beta_2X_2 + u $$ Model 2: $$ Y = \beta_1'X_1' + \beta_2'X_2 + v $$ where $X_1' = ...
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17 views

Correlation between binned residuals and an endogenous variable

I have performed a logistic regression and calculated a binned residual plot: library(arm) binnedplot(x, y) The final plot looks like this: ...
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1answer
54 views

Stata's predict uhat, residuals function in R

I'm having trouble figuring out how to replicate Stata's command "predict uhat, residuals" in R for creating residuals. Do I have to generate a normal sampling to accomplish this? Thank you.
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25 views

R: Plotting GLM residuals vs. linear predictor or response variable?

When assessing a GLM fit, why is it customary to plot residuals against the linear predictor rather than the response variable? I noticed that plot(glm) defaults to ...
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32 views

Is the sum of all elements of the residual matrix equal zero under OLS?

I have the following OLS model $$ y_i= α+βx_i+ε_i , i = 1,...,N $$ I want to prove that $$ \sum_{k=1}^N\sum_{j=1}^N e_je_k =0$$ I did the following $$ \sum_{k=1}^N (e_1+e_2+e_3+...+e_n) e_k ...
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non-uniform residuals in repeated measures mixed model; larger residuals further in time

I am analysing data from a longitudinal study in SAS and see time-dependent patterns in the residuals. Subjects in four groups (A to D) were given a treatment at time=0; and continuous response ...
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37 views

Is the application of the Frisch-Waugh-Lovell Theorem really necessary?

Suppose I have a model \begin{eqnarray} y = X_1 \beta + X_2 \gamma + \epsilon \\ X = Z \Pi + V \end{eqnarray} where $X_1$ is endogenous, Z are instruments, $X_2$ are exogenous. If I however include ...
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1answer
62 views

How Residuals of Instrumental Variables Estimation are calculated and why you can have a negative R-squared?

I would like to understand, precisely, why you can have a negative $R^2$ with a 2SLS estimation, such as you have in commands like ivreg2 in Stata. There is ...
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21 views

Probability that LM with lesser RSS has greater residual for individual i (or opposite sign)?

You have fitted a basic linear Model #1 (i.e., GLM with identity-link) based on observed data with residuals: $$ Model 1: y_i = \beta_0 + \beta_1 x_{1i} + \beta_2 x_{2i} ... + R_i $$ A colleague ...
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19 views

Correlated Proportions shown in a Mosaic Plot. What is the fitted model that generates residuals?

I have a 2-by-2 table of correlated proportions where I am plotting the positivity of two diagnostic methods applied on a sample of 216 individuals: ...
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36 views

Interpreting Residuals for Specific Data Points

I want to know if this is an appropriate interpretation of a regression residual and more generally, whether it's an appropriate use for regression. Let's say you gathered data on the performance ...
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1answer
34 views

Stationarity and seasonality of residuals

Why is it necessary to evaluate stationarity and seasonality of model residuals? Or is it? The model in question is an OLS model that represents a relationship between Y and a bunch of economic ...
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32 views

Determining the p-value of two consecutive residuals

I am performing an outlier detection test in a monthly process to detect errors (for each month I have more or less 22 business days). I am using a Simple Linear Regression model. What would be the ...