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 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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1answer
21 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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1answer
63 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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1answer
32 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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26 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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15 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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0answers
17 views

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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3answers
265 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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0answers
41 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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35 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
63 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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31 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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42 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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0answers
34 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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0answers
80 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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26 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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0answers
9 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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16 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
40 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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19 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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15 views

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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26 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
46 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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0answers
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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16 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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34 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
31 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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0answers
25 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 ...
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1answer
58 views

Why would the residuals from these two models result in the wrong AIC being calculated?

We run two linear regressions, Model 1 and Model 2. The residuals from these two models are plotted against the predicted values. If I understand correctly, the AIC from these two models would be ...
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2answers
39 views

How do I identify a particular residual from a mixed-effects model in R?

Here's a plot of my residuals from a mixed-effects model in R (using lme4). There's one 'outlying' residual with a value of around 35 (index circa 90) that seems anomalous. I don't know if it has ...
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29 views

Measure based on the absolute residuals of an OLS with/without intercept

A typical measure for firms’ use of earnings management in the finance literature is based on the absolute value of the residual (|e|) of a OLS regression estimated separately for firms in ...
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26 views

Trending Residuals in Negative Binomial Panel Regressions with Patent Data

A commonly faced problem for researchers working with patent data is that we need to work with negative binomial models because our dependent variable is an overdispersed count variable. I am using ...
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1answer
34 views

What is the estimated variance of residuals? From R [duplicate]

I am trying to figure out what is the estimated variance (i.e. the estimated "error") of residuals around a fitted line. ...
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2answers
115 views

Normality of residuals - contradiction between 'symplot' and 'qnorm'?

After running a multiple linear regression analysis, I wanted to assess normality of residuals. I plotted a histogram which showed an almost normal distribution of residuals. I also used ...
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1answer
85 views

Analyzing residuals in logistic regression

Greetings statistics experts, I am having a try with the kaggle titanic dataset and am wondering what to do with the residuals after fitting models. In the case of linear regression you can look at a ...
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0answers
6 views

FE Model: independence of residual and firm specific component

I'm estimating a fixed effects model and want to consider Petersen's (2009) suggestion: "The components of X (μ and ν) and ε (γ and η) have zero mean, finite variance, and are independent of each ...
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1answer
98 views

How to deal with non-normally distributed residuals?

I'm fitting a multiple linear regression model. I've read that the residuals of my regression need to be normally distributed in order for the p and t values to be accurate. Now my residuals (see ...
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0answers
27 views

How to create an index to compare regression lines

Suppose I have the actual and fitted values of two regression lines. Each regression line is modeling the sales of some good. The fitted and actual values of one of the regression lines is much ...
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52 views

When to use non-additive stochastic error term

I have encountered the following two versions of the Cobb-Douglas production function as an illustration of the differences between intrinsically non-linear and linearisable non-linear regression ...
4
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1answer
73 views

S-curve in residuals plot: a problem?

I am doing some linear regression and am predicting a absolutely non-normal dependent variable (for context: we are forecasting the amount of units sold for a shop). Therefore, we have transformed the ...
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1answer
42 views

What is the difference between errors and residuals?

While these two ubiquitous terms are often used synonymously, there sometimes seems to be a distinction. Is there indeed a difference, or are they exactly synonymous?
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2answers
126 views

Are the model residuals well-behaved (homoscedasticity)?

Can I say looking at this residuals-vs-fitted plots, that my residuals are homoscedastic?
2
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1answer
128 views

Diagonal lines in residuals vs fitted values plot for ANOVA

I'm experiencing strange patterns of residuals. The following chart is a scatterplot of Standard residuals (Sres) versus Fits. I'm interested in the diagonal lines that mean that a higher fit leads to ...
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0answers
34 views

Distribution of residuals in multinomial / ordinal logistic regression

In simple logistic regression, the standardized residuals are assumed to be normally distributed. Are there any such assumptions for ordinal or multinomial logistic regression? Because in these ...
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2answers
195 views

Which residuals to analyse when dependent variable is transformed?

I am running a multiple linear regression where the dependent variable is sqrt-transformed. As far as I understand, the residuals from the regression are different from the residuals calculated as ...
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0answers
50 views

Residuals are not normally distributed in linear regression model

I have a linear regression model and residuals look like this: what does it mean for my model? Is my model inappropriate because residuals are not normally distributed?
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1answer
128 views

Standard deviation of residuals from a linear regression

I've ran this linear regression: mtcars_lm <- lm(mpg ~ wt, mtcars) Lets say I observe a value of mpg that is 2 above the ...
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1answer
30 views

Complex level 1 variance mixed effects models in R

Take this mixed effects model in R: $y_i = \beta_0 + \beta_1X_{ij} + u_{j} + e_{ij}$ where $u$ is a random effect (level 2 residual) with groups $j$. It is possible to allow the variance of $e_{ij}$ ...
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37 views

What's the difference between error distribution and residual distribution in generalized linear models?

I have met with generalized linear model, but I'm confused with the errors and residuals? Can anyone help me out? I have got three questions. (1)what's the difference between error and residual? ...