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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Are these diagnostic plots from lmer too far away from normal and showing heteroscedasticity?

I have read similar posts in this website to help me assess whether my diagnostic plots are too far away from normal and if they are showing heteroscedasticity (Interpretation of residuals vs fitted ...
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6 views

Unbalanced binary features in LASSO regression

I have a target $y$ that I want to predict from variables $x_1, x_2, \ldots x_k$. Suppose the first of these variables, $x_1$, is a binary variable (i.e., only taking on one of 2 values). If I use ...
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12 views

normal distribution histogram of the residual from a simple regression model?

why residual histogram will follow a standard normal distribution? because independent variable can be different values, I can see all obersavations at one certain X value will follow normal ...
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13 views

Jackknife residuals formula

I know that the jackknife residuals are $$t_i={y_i-\hat y_{(i)}\over \hat \sigma^2_{(i)}(1+x^t_i(X^t_iX_i)^{-1}x_i)^{1/2}}$$ But there is alsa a formula for computing these residuals: ...
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62 views

Does this residual plot indicate heteroscedasticity?

These are two versions of the same residual plot, just with a different scales, (I'm not sure which is easier to interpret so I included both). I don't need to know major details (for the assignment ...
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27 views

Residual network dimension changing blocks identity function

In trying to implement ResNet with bottleneck blocks for myself, I got very confused about the identity function residual blocks with different dimensions. They compared identity, conv projections on ...
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1answer
21 views

calculate the internally studentized residual

it says that ...an ordinary residual divided by an estimate of its standard deviation $s(e_{i})$ As we can see from the example that mean for four residuals is 0, so ...
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1answer
46 views

variance decreases when x gets farther from the average x?

I just read the description of Studentized residual on Wikipeida. I'm confused about what it says about variance, it says that "the residuals, unlike the errors, do not all have the same ...
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1answer
64 views

Differentiating the RSS w.r.t. $\beta$ in Linear Model

I am reading the book "The Elements of Statistical Learning". The book says But when I try to prove it, I get the following: $$RSS(\beta) = (y - X\beta)^T(y-X\beta)$$ $$RSS(\beta) = y^Ty ...
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1answer
11 views

Absolute Average deviation in percentage calculation

Sorry if my terminology is incorrect. I am trying to calculate the average error of prediction to be represented in percentage. For example, I should be able to say, the predicted values are on ...
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19 views

is normality of raw data ever important? [duplicate]

http://www2.psychology.uiowa.edu/faculty/mordkoff/GradStats/part%201/I.07%20normal.pdf https://pubs.er.usgs.gov/publication/5224239 The two links above seem to me to claim the opposite. Is normality ...
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14 views

What does Tukey Test's p-value means in residual plot analysis?

After having called the residual plots command in order to graphically analyse residuals, I obtain also a written output where I can find the p-value and Test stat associated to each independent ...
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23 views

How do bottleneck architectures work in neural networks?

We define a bottleneck architecture as the type found in the ResNet paper where [two 3x3 conv layers] are replaced by [one 1x1 conv, one 3x3 conv, and another 1x1 conv layer]. I understand that the ...
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35 views

How to standardise linear regression

I have a set of death rates (that range from about 0.1 to 0.5), a set of body weights (that range from about 2 to 80), and I want to calculate standardised residuals for the death rates after ...
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1answer
18 views

Why square root for RSE?

Why should we put square root to get RSE ? what for?
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31 views

Why divide RSS by n-2 to get RSE?

Context: Simple Linear Regression, an intercept and a slope I have 2 question regarding this issue. Why should we divide RSS ? Why the divisor should be n-2, not n or n-1 ?
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1answer
30 views

Analyzing bad lm plots in R (Two parallel lines in Residuals and Normal QQ)

I am working on some stock analysis that I picked up to help me learn more about modeling. I have become comfortable analyzing these plots when they are more as expected but I can't figure out why ...
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32 views

Why are principal components of the residuals from a multivariate regression correlated with the estimated coefficients?

Say I have some data that follows a general linear model: $$ Y = XB + E $$ for which: $Y \in \Re^{n \times m}$, $X \in \Re^{n \times p}$ and $B \in \Re^{p \times m}$ Further, let's assume (1) that ...
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11 views

Visual examination of residuals for a large dataset

Often, as part of verifying that the assumptions of a model (such as OLS) are reasonable, I see advice to visually check that the model residuals are distributed relatively consistently around 0 as ...
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1answer
32 views

Correlation residuals vs standardized residuals in SEM package in R

I've been working with SEM package in R recently that I happened to read it's manual for the standardizedResiduals. In the manual, Residuals are defined as S - C, where S is the sample covariance ...
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9 views

Estimating the residual variance by using a varFunc in nlme

I'm using a linear model to predict a dependent variable (the score to a test) starting by the age of a person. As shown in the figure below, the variability decreases when the age increases (data are ...
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1answer
19 views

Why is the covariance matrix of the OLS regression error written as $\mathrm{E}({\bf e}{\bf e^\prime} | {\bf X})$?

In Hansen (2016) I read that the conditional covariance matrix of the regression error $\bf e$ is $\mathrm{E}({\bf e}{\bf e^\prime} | {\bf X})$. How is this related to the covariance formula: ...
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9 views

What is the effect of center points on residual plots?

I've carried out a $2^3$ factorial experiment with 4 added center points. I wanted to see if the assumptions about the errors were violated so I plotted the typical graphs, normal probability plot/ ...
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1answer
54 views

GARCH diagnostics: autocorrelation in standardized residuals but not in their squares

Fitting an ARMA-GARCH model, I checked the Weighted Ljung-Box test on standardized residuals and squared residuals to verify if the model is adeguate in describing the linear dependence in the return ...
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30 views

Do my non-normal data (per S-W test) require the use of nonparametric alternative to linear regression?

First time posting here so please be kind. My sample size is 64 (31, and 33 in each group, betw subj design) and when testing for normality found significant Shapiro-Wilk statistic for each subset of ...
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31 views

Difference between errors and residuals. What is the mean and variance of each of them?

Suppose there is a simple linear model $y=\beta_0+\beta_1x+u$. Can we state that $\bar y=\beta_0+\beta_1 \bar x + \bar u$? I have this question because I come up with $Var(\bar u)$ when doing some ...
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25 views

What is the interpretation of 2nd Q-Q plot in diagnostic plot in regression

With reference to http://analyticspro.org/2016/03/07/r-tutorial-how-to-use-diagnostic-plots-for-regression-models/ in the post to correct the problem of curved residual pattern a qudratic term is ...
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1answer
29 views

GLM Residual Plot

I am currently completing quasi-binomial regression and I am using this line of R code to plot the residuals. plot(residuals(mylogit) ~ ...
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37 views

Residual plot is wrong but why?

I have 10 numerical observations. I have grouped them into two groups, and plotted them against 10 numerical covariates. There is clearly a linear relationship, and one of the groups ranks higher than ...
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39 views

Inference of Cook's Distance Plot

What can we infer from cook's distance or the cook's distance plot of regression model? How can it be used to refine model further ? Should we remove the values which are high influencers or lie ...
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16 views

Plots of residuals in linear regression

I wanted to know the intuition behind the plots of residuals vs time, residuals vs fitted values and residuals vs explanatory variables. Could anyone intuitively explain to me what they are supposed ...
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49 views

why does the same repeated measures anova using ezANOVA() vs. aov() yield different distributions of model residuals?

I am attempting to do a repeated measures anova using r with the aov() command from the {car} package. I wanted to be sure that I wrote my code for this approach correctly (see below), so I ...
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15 views

How to transform predictor variable to fix residual distribution

I have a linear model with several predictors, and this graph of residuals v fitted values. I am pretty sure the non random nature is being caused by one predictor, as when I plot the residuals ...
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30 views

How to test model fit (residuals?) for a linear regression with a binomial independent variable?

This must be common knowledge and asked so many times, but I can't find it. I'm a bit of a rookie, so my apologies if it's a redundant question. I am doing a linear regression with a binomial ...
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28 views

Why points of fitted vs. residuals plot are dependant of random effect level in my mixed model?

I have fitted a linear mixed model. The fitted vs. residuals plot is colored by the random effect level. As the model takes care of the random effect, I would expect that the fitted vs residuals ...
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16 views

Standardized residuals in fgarch package

I'm using the fGARCH package in R to fit a GARCH time series process. However, I'm getting different results when I inspect the standardized residuals manually vs when I set the parameter flag TRUE. ...
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31 views

Mathematical Explanation of Issues with Autocorrelated Residuals in Linear Regression

I am performing linear regression - regressing loss rate (value of loans written off in a quarter / total value of loans outstanding in a quarter) on macro economics variables (unemployment rate, CPI, ...
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31 views

Strange residuals pattern

I fit a linear model that obviously needs some work. Here is an example of my data: ...
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33 views

Too many high residuals in PCA

My question is similar to How do I interpret high residuals for the reproduced correlations in factor analysis?. I have 5-item Likert-scale questionnaire. I carried out a PCA with N=1253 and I ...
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25 views

Residual non-normality and prediction intervals

Normal residuals are generally understood to be necessary for valid prediction intervals in OLS regression -- but I've never seen a definitive guidance on just how much non-normality can be tolerated, ...
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1answer
29 views

Weird Residual plots for a repeated measure model using PROC MIXED

Suppose $y_{ijt}$ is the weight for subject $j$ of treatment $i$ at week $t$, then the model looks like this: $$y_{ijt} = \alpha_i + \beta_i t + \gamma_i t^2 + e_{ijt}$$ The codes look like this ...
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16 views

Is there a bound of percentage/number of influential points for a given size sample?

Consider for a given data set of size $N$, and we do a linear regression analysis on it. We know that we can define influential points among this dataset by setting a threshold value on the Cook's ...
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1answer
36 views

Proof of the distribution of the residual standard error

In my notes from university I have written down that the residual standard error (from normal linear regression) has the following distribution $\frac{\hat{\sigma}^2}{\sigma^2}\sim ...
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33 views

beta regression creating a wild residual vs. fitted plot- whats going on?

I recently ran a beta regression model in R using the betareg package. I am modeling a continuous dependent variable (a fraction out of 1) that is bound between 0 ...
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12 views

Creating a meaningful metric from a multiple regression residual

I want to show a scatter plot and accompanying best fit line for a regression equation I am using for, say, number of cigarettes smoked (x-axis) predicting visible skin blotches (y-axis). A ...
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12 views

Continuous, sometimes negative residuals from Poisson-distributed variable - how to analyze?

It's been years since I've taken my grad school stats courses, and it's a subject I struggle with, so bear with me. I am attempting to analyze a dataset containing two Poisson-distributed variables ...
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21 views

interpreting residual plot from nonlinear mixed effect model

I am developing a nonlinear mixed effect model to model selectivity of a survey gear. I have worked through Mixed Effect Models in S & SPlus and Nonlinear Regression with R to learn how to model ...
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1answer
47 views

How to studentize residuals

The lecture slide (from PennState Eberly College of Science, STAT 501, Lesson 11.3) says "an ordinary residual divided by an estimate of its standard deviation", but the standard deviation for ...
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3answers
152 views

Why does the sum of residuals equal 0 from a graphical perspective?

I've seen the proof for why in least squares regression the sum of residuals is always equal to 0, and I kind of understand why from that algebraic perspective. Basically, you're finding the minimum ...
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34 views

What do my residuals say about my data?

I am new to R and I am trying to find a relationship between Wing length (mm) and Weight (g) of black-capped chickadees using a data set of over 4000 data points. I did a regression analysis and ...