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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58 views

Why does using residuals as predictor not alter coefficient?

I am working with a data set describing a set of US Senators, their votes on a climate bill, and several characteristics of the state they represent. One of the variables, 'imptot', describes the ...
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0answers
14 views

Does residual autocorrelation beyond the first lag have any implication in a regular regression?

I have seen the review of a multiple regression analysis using time series with a quarterly frequency. The original modeler advanced that the model's residuals were not autocorrelated by disclosing a ...
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24 views

What's wrong with my jackknife procedure in R?

Well, the reason I think my jackknife procedure is wrong is that it gives me the same graph as the residuals. Here's the problem description: Use a loop to create n=50 models. In step i, make a model ...
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0answers
17 views

3D plot of the residual sum of squares in linear regression [migrated]

I'm trying to reproduce Figure 3.2 from the book Introduction to Statistical Learning. Figure describes 3D plot of the residual sum of squares (RSS) on the Advertising data, using ...
4
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1answer
53 views

Residual Vs. Fitted Plot with Outliers

I have a model relating fuel consumption to other vehicle parameters, which produces the following Residuals Vs. Fitted plot. My Question: Is the skew to the right simply an indication of outliers ...
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1answer
31 views

R: Explanation of a multiple linear regression summary [duplicate]

I am quite new with R and while i am able to perform the basics i am not yet able to understand the output results. For example: summary(lmodel) generates the ...
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0answers
4 views

Saving level 2 residuals in SPSS [migrated]

I am estimating a twolevel regression model in SPSS using the mixed procedure and would like to plot the level-2 residuals; however, I only get residuals for the observations at level-1. Can anyone ...
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0answers
22 views

extract residuals from adonis function in vegan

I am using the adonis function in the vegan package to determine effects of different environmental factors in forest plant community composition in different regions. I would like to first use adonis ...
5
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1answer
244 views

Is it ever okay to ignore heteroskedastic residuals and continue with analysis?

My data is misbehaving and I can't seem to get residuals with constant variance despite doing more transformations than Optimus Prime. Is it ever okay to just continue with analysis in and just make a ...
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1answer
35 views

Visually random model residuals, yet heteroskedastic? ( very small Breusch-Pagan Test P-Value)

Can anyone explain why the BP, Breusch-Pagan, test rejects homoscedasticity with such an apparently randomized plot of residuals?
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1answer
32 views

Estimation of residual in ARIMA model

How do I estimate the residual $\varepsilon_{t}$ of a Seasonal ARIMA model $\hat{Y}_t=\hat{\phi}{Y}_{t-1}+\hat{\Phi}{Y}_{t-12}+\varepsilon_{t}$? If the MSE is 0.114, what does it mean?
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1answer
46 views

How do i normalize residuals?

I am trying to adjust a hierarchical multiple regression model and no matter which transformations I use (z-transformation, sqrt, cuberoot, inv, inv sqrt ...), I do not manage to get the residuals ...
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56 views

Use predicted values with or without random part to plot Residuals with binnedplot of a logistic regression in glmer (lme4 package) in R?

Which binnedplot of the glmer should I use to check the model? The residuals against the predicted values without random part(REform=NA) or residuals against the predicted values with random ...
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1answer
33 views

residuals plots from four linear models

I've made 4 linear models. For each of these models, I've plotted the residuals against the fitted values. First plot: generalised linear model with quasibinomial link function Second ...
3
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1answer
148 views

Analysis of the Residuals vs Fitted

I have a model for which I gathered 10 observations from each person, a total of 25 people, then 250 observations. Well, this is part of my summary of the model, ...
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1answer
46 views

Understanding covariance of errors in regression

I am having a hard time understanding the elements of an error covariance matrix for a class. Can someone clarify? First, the diagonal. The variance is $E(e_i^2) - E(e_i)^2$. $E(e_i) = 0$, so it's ...
4
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3answers
243 views

Residuals follow exactly same pattern as data points

I have regressed data for rainfall on years 1990-2010. This was a simple linear regression in R using the lm() function. The data represent mean yearly amount of ...
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2answers
89 views

Does this residual plot look bad?

I am not sure about this plot if it looks good as the dots appear around the line. So I just want to ask if it looks okay. My data is quite large (almost 3000 observations) and maybe that is why it ...
0
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0answers
53 views

Correction for non-linear trend seen in residuals plot when predictor is categorical

I'm running a linear regression analysis in R. One variable is a continuous outcome variable (score2) and the other is a categorical variable for treatment group ...
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31 views

Linear regression for feature selection

Imagine we regress y on x1...x4. Now, we want to find out if ...
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0answers
24 views

Minimizing the sum of squares of autocorrelation function of residuals instead of sum of squares of residuals

I am trying to fit my multi-exponential model to some experimental data and I am using a simulated annealing algorithm. My objective function has so far been the sum of squares of the residuals: ...
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2answers
1k views

Why is a Bayesian not allowed to look at the residuals?

In the article "Discussion: Should Ecologists Become Bayesians?" Brian Dennis gives a surprisingly balanced and positive view of Bayesian statistics when his aim seems to be to warn people about it. ...
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0answers
19 views

Getting residuals from (kernel) canonical correlation analysis

I'm playing around with kernel Canonical Correlation Analysis, as implemented in the R package kernlab. Is there a simple way to extract the residuals after fitting? (Is this a well-defined quantity?) ...
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71 views

Residual analysis and diagnostics for GEE Models in R

Some colleagues asked me to perform a residual analysis on both linear models and generalized estimating equation (GEE) models. I know it is a faux-pas in some circles to remove outliers, but in our ...
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29 views

Calculate residual after SPSS runs ANOVA

I have a task something like compute residuals in dollars for one observed person (with gender code, a class they're in, their age, and they make let's say 50,000 a year-the Dependent Var). After ...
4
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1answer
64 views

Non-normal residuals - P-values higher or lower?

Background: I have estimated a model using panel data with the Arellano Bond estimator (see e.g., http://www.fordham.edu/economics/mcleod/Elitz-usingArellano%E2%80%93BondGMMEstimators.pdf) and n=300. ...
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4answers
327 views

Regression residual distribution assumptions

Why is it necessary to place the distributional assumption on the errors, i.e. $y_i = X\beta + \epsilon_{i}$, with $\epsilon_{i} \sim \mathcal{N}(0,\sigma^{2})$. Why not write $y_i = X\beta + ...
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1answer
226 views

How do I interpret this fitted vs residuals plot

I don't really understand heteroscedasticity. I would like to know whether my model is appropriate or not according to this plot.
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30 views

Reason to worry if the emp. residual distribution is more dense around zero compared to a theoretical normal?

My goal was to evaluate, if a marketing scheme did benefit or not. I observed data about the price ($P_t$) of a specific product over time. Since my dependend variable is only defined on ...
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0answers
35 views

Conditional heteroskedasticity/variance and uncertainty in estimated residuals

Say you've got a simple cross-sectional model $$ y=\alpha + \beta T +\epsilon $$ where $T$ is binary. This is basically a t-test, but lets treat it like a regression. You're interested in the ...
0
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1answer
113 views

Outlier detection in ARIMA model with R

After fitting my time series with an ARIMA model, I want to test outliers in the residuals' series. Are there any functions in R that could do this test and furtherly test whether the outlier is ...
3
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1answer
194 views

Do autocorrelated residual patterns remain even in models with appropriate correlation structures, & how to select the best models?

Context This question uses R, but is about general statistical issues. I'm analysing the effects of mortality factors (% mortality due to disease and parasitism) on moth population growth rate over ...
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94 views

Patterns in residuals plot from linear regression: do they tell us what model to use?

I have carried out a linear regression. This is the form of the model: bounded (0-1) response variable ~ factor1 (2 levels) + factor2 (5 levels) + interaction between factor1:factor2 + factor3 (2 ...
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49 views

non-normal residuals. Significant variable

The question is simple. My residuals after performing a linear regression are non-normal. I am not sure whether or not one of my variables is significant. I know that I cannot use p-values. Can you ...
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80 views

Modeling conditional variance (heteroskedasticity) using the gamma distribution

The application is that I want to know how $X$ maps not only to $y$, but to the variance of $y$. I think I've worked out a reasonable solution for doing so using the gamma distribution and the ...
0
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1answer
139 views

How to make linear regression model while 'control' confounding variables?

I have data from survey, and Trying to build a linear regression model using R like A~ B however, want to control C, D, E, F, G. like Age, Sex, and other confounding variables. I tried to make some ...
0
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1answer
129 views

Checking assumptions LMM: residual plot with diamond shape

I am running a linear mixed model and want to check its assumptions. The model I run is comparing if males and females behave differently over time (timeclass=1,2,3,4): ...
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37 views

Mean of residuals in quantile regression are significantly differ from 0

Is it necessary to have mean of residuals which is equal to 0 in Quantile regression?
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1answer
75 views

How to describe the failure of this linear modelling?

I have a time series $X_t$, which is shown in the first plot. In the second plot, I am doing a linear regression on $X_t\sim X_{t-1}$. The regression line is very close to $y=x$. But this is tricky ...
0
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1answer
58 views

How to distinguish these two linear regressions?

I have two linear regressions. The linear coefficients of both of them are very close to $1$. The first plot seems reasonable linear regression, while the second one is tricky since if the bottom left ...
7
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2answers
211 views

Why some people test regression-like model assumptions on their raw data and other people test them on the residual?

I am a Phd Student in experimental psychology and I try hard to improve my skills and knowledge about how to analyze my data. Until my 5th year in Psychology, I thought that the regression-like ...
2
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0answers
46 views

Take the residual of a logistic regression model and use it as a response variable in another model

In linear regression we can do something like this $$ y' = resid(y \sim \beta_0 + \beta_1 c1 + \beta_2 c2 ) $$ where $c1, c2$ are covariates, and then fit $y'$ in another model: $$ y' \sim b_0 + ...
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0answers
93 views

How can I estimate optimal cut-off using linear regression-models

To build two linear regression model, (dependant var : B, independant vars : A1, A2, A3) I have to set the cut point of A1. (high A1 and low A2) I want to pick up the model*s*(a model for high A1, and ...
3
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1answer
121 views

What is “estimated unbiased variance of the error term”?

Disclosure: This is a homework question. I have fit a multiple linear regression model in eviews, and I am asked to calculate "estimated unbiased variance of the error term, i.e., $\hat\sigma^2$". ...
9
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1answer
274 views

Why are diagnostics based on residuals?

In simple linear regression one often wants to verify if certain assumptions are met to be able to do inference (e.g. residuals are normally distributed). Is it reasonable to check the assumptions ...
0
votes
1answer
69 views

Robustly standardize residuals in MM regression

Does anyone know how we can robustly standardize the residuals in MM regression? First we perform MM regression and then obtain the residuals: how can we robustly standardize the residuals obtained ...
2
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4answers
214 views

Linear regression with strongly non-normal response variable

I have carried out a linear regression. The plot below shows the distribution of the response variable: I believe the response variable is beta distributed, therefore virtually the exact opposite ...
3
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2answers
251 views

When to use residual plots?

I have performed a simple regression analysis between one dependent variable (DV) and one explanatory variable (IV). If the p-value from the regression analysis for the IV is not significant, should ...
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votes
2answers
555 views

Mean Squared Error and Residual Sum of Squares

Looking at the Wikipedia definitions of: Mean Squared Error (MSE) Residual Sum of Squares (RSS) It looks to me that $MSE = \frac{1}{N} RSS = \frac{1}{N} \sum (f_i -y_i)^2$ where $N$ is he ...
0
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3answers
93 views

Simple regression assumptions (homoscedasticity)

There is a simple regression model table I was looking at in a textbook with IQ values grouped into 5 intervals and each group had an N number associated with it. There was also information given ...