# Questions tagged [residuals]

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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### Summarizing unexplained variability within groups using fitted random effects or residuals

I have repeated observations (count data) conducted in different plots (say, 5 times each plot). I would like to conduct a regression analysis of the observation data at the plot level with plot-level ...
33 views

### Vector Autoregressive Models (VAR) and error terms correlation

Before all I want to clarify, I am not looking for a direct answer in the following question but more of a clarification. I am doing a master's degree and the question is part of an assignment, so i ...
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### Meaning of a term in the residual variance

Studying my course notes about regression, the assumptions about the residuals are put this way: $$\varepsilon \sim {N_n}\left( {0,{\sigma ^2}{I_n}} \right)$$ There are two things that bug me - are ...
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### How are $n$ and $Var(\varepsilon)$ affecting to Variance of Estimation of Slope Parameter $\beta_1$ in Simple Linear Regression

Once I have derived the variance of $\hat{\beta_1}$ as: $\text{Var}(\hat{\beta_1})= \frac{\sigma^2}{\sum(x_i-\overline{x})^2}$ I would like to know how are affecting to this formula: the size of ...
60 views

### Dealing with heavy-tailed residuals when fitting hierarchical linear models using lme4

This is my first time posting, so please excuse any issues with respect to my description of the problem and the presentation of the data and code I have supplied. Summary of the Design 30 listeners ...
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### Interpreting residual plots for heteroscedasticity

I am trying to measure the effect of different antibiotics on the growth of E. coli and S.aureus. Since my data for both bacteria is not normal I have chosen to do a Kruskal–Wallis test. But one of ...
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### Assumption of normally distributed residuals in linear regression [duplicate]

Let us consider the simple linear model $y = \beta_0 + \beta_1 X + \epsilon$, where $y$ is real number, $X$ a matrix of reals and $\epsilon$ is the random "noise". The least-square estimate of the ...
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### Find actual mass given actual length, residual, and regression line

A study shows the following regression line of length of alligators given mass: length-hat = 125 + .5(mass) If an alligator has actual length of 500 cm, and residual is 60 cm, find the actual mass. I ...
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### Interpreting a Dependent Variable that is Standard Deviation of Regression Residuals

I have a regression (OLS) output and was hoping to get some suggestions on how I might be able to interpret the coefficient using Stata or SAS. The dependent variable is ‘standard deviation of ...
31 views

### Using residuals from one regression as the dependent variable in a second regression

I'm not sure if this technique has a name. I've recently learned that some people perform a two-step regression where, in the second step, they regress the residuals from the first step on some new ...
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### Can I use a residual variable (from a binary variable) as response variable in binomial glmm or glm?

I'm working on Rstudio and I have a question about residues in a binomial glm's case. I used a glm to correct my response variable (germination (ger_b), encode 0, 1) by the light, because this ...
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### What should've been done when residual plots show a curved pattern

If a residual plot of a simple linear regression (y vs fitted values) shows a curved pattern, would adding quadratic term of the predictor and running a multiple regression fix the problem?
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### Interpreting patterns in the residual plot from OLS regression

Below are some residual plots from an OLS regression. The dependent variable is quality of life in patients measured on the 0-1 scale and independent variables are a mix of continuous and categorical ...
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### How to assess the quality and goodness of fit of a lasso model?

So far I evaluate the lasso model by its out-of-sample predictions and by the $R^2$ for the goodness of fit. What other measures should I look at? Particularly, do I need to examine the residuals for ...
44 views

### Residuals in regression

When evaluating residuals for a linear model, do we plot them against the fitted values or the x values. Here I have an example in R. Do we want the first or second ...
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### How to test randomness when one of two groups variables is modified?

I am not a statistician but understands enough to be able to grasp concepts. I am looking for pointers towards some direction. Question : I have a dataset which was generated from an actual ...
13 views

### Interpretation of time series residual and stationarity

Does it mean that time series model is well generalized (or is a better model) if residual from time series data and model prediction is stationary? Or it means something else?
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### Comparing Modelled/sampled distance time graphs

I am comparing the journey times of modelled vs observed of vehicles along a set of roads. Usually this would be done visually but obviously the line will always be biased to appear to be correlated ...
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### True or False: The pattern of the residuals vs predicted values and the residuals vs a predictor based on a 2nd order model are exactly the same

I'm currently working on an assignment for a course in Statistics and was wondering anyones thoughts on this. My friends and I keep going back and forth on which one it is. I think it's true for the ...
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### Interpretation of the ACF of standardised residuals vs actual residuals

Is there any scientific reason why a lot of studies and packages choose the ACF plot of the standardised residuals rather than the residuals themselves?
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### Assessing variability in a repeated measures study

I want to assess technical variability/dispersion between several same-subject measurements (i.e which groups have more variability): My data consists of a set of cases (with age and sex variables) ...
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### rstandard vs stdres have different behaviour (the hat matrix)

To obtain the standardized residuals in R, the the residuals minus their mean are divided by their standard deviation (calculated with the model degrees of freedom). It is also calculated using the ...
38 views

### The form of the residual vector in the multiple linear regression model

I have 2 questions about multiple linear regression model. Does the residual vector in the multiple linear regression model have the form $y-(X(X^T X)^{-1} X^T)^2 y$? And, is it true that the ...
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### Logistic Regression Residual Analysis in R (replicate influence command from SAS)

I'm looking for a quick reference on how to do some residual analysis for logistic regression in R. Oddly enough, this has not been easy to find. The data set I am working with is the Add.dat which ...
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### Polynomial regression : how to find the best polynomial degree ? Chi2 or equivalent already built-in in Python numpy?

I am studying the stability of numerical derivatives as a function of the step I take to compute these derivatives. With a derivative with 15 points (obtained by the finite difference method), I get ...
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### Inconsistent Ljung-Box test result and plot of autocorrelation function of residuals

I get an inconsistent result for the Ljung-Box test: in fact when I run it using the Box.test function it doesn't make me reject the null hypothesis of residuals being white noise, but when I plot the ...
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### Residuals difference between simple and multiple regression [duplicate]

In simple linear regression of function f(x), when I am checking residuals in simple regression I plot them with respect to x. Than I check for example randomness among them. How is this different in ...
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### What is the binomial residual in logits for an all-success trial?

In binomial regression, I have a trial where the model predicts 2 logits (88% predicted success rate) and one data point is 10 successes out of 10 trials (100% observed success rate). What is the ...
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### Checking the normality assumption for ANOVA test [duplicate]

Let's see if I understand this correctly. The normality assumption means that for each group I am testing the response within each group is normally distributed. So in order to check all the groups ...
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### What are the necessary conditions so that the residuals of an ARIMA model behave as a normal distribution?

Simple and direct question I just had while implementing a solution: What are the necessary conditions so that the residuals of an ARIMA model behave as a normal distribution?
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### How to interpret “quantile residuals”

The DHARMa package in R aims to provide scaled (quantile) residuals that, according to the DHARMa vignette, "can be interpreted as intuitively as residuals from ...
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### How to correctly transform variables in linear models using residual plots?

So I have a linear model as follows; Mod=lm(PRICPTM ~ DISTANCE + PCTLOAD + ORIGIN + MARKET + DEREG + PRODUCT,data=x) summary(Mod) residualPlots(model = Mod) ...
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### Should the residuals of a machine learning regression model be i.i.d.?

This is a basic question but I did not find the answer in most common statistical learning books. In linear regression we assume that the residuals are i.i.d. Do we assume the same for a regression ...
30 views

### Heteroscedasticity - interpretation of residual plot and P-P plot

Could you please help me interpret the following residual plot and P-P plot from a multiple regression analysis? I'd say that this shows evidence of heteroscedasticity as the residuals are grouped ...
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### ResNet Reduce Block

I am building a ResNet. I have two separate blocks: Cnn block, Reduce block. Cnn block - 1 cnn layer, activation, Batch Normal -> 1 cnn, activation, Batch Normal, so 2 CNN in this block. In Reduce ...
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### How do I interpret this Residuals Plot?

I have some data where the histogram shows insurance premiums normally distributed except for a "spike" at the upper bound. (x-axis = price, y-axis = n_observations) I am visualising the results of a ...
36 views

### What happens when we model outliers as dummy's in a VAR-system?

I am wondering what is going on "under the hood" or intuitively of what the implication of modelling outliers as dummy's in a VAR-model. To make this question more clear I will provide an example. ...
746 views

### How to interpret Residuals vs. Fitted Plot

I am investigating the effects of weather on restaurant demand. Currently, I am testing the model assumptions for my multiple linear regression model. My model specification (simplified) is as ...
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### Why is R returning NA coefficient-values on dummy variables in VAR-model?

When estimating this VAR-model the returned coefficients on BNP.min4 and INT.min4 are NA, which I do not understand. My intuition is that there should not be any collinearity between these variables. ...
35 views

### Explain the estimated residual variance in a Gamma mixed model, using glmer()

I am applying a generalized mix model, where the response has a gamma distribution, as below: ...
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### Using the DHARMa package to test for temporal autocorrelation when time values are not unique?

I have fit a glmm using the glmer function from the lme4 package. I have found the DHARMa package very helpful for evaluating the fit of my model but am stuck as to what to do to evaluate temporal ...
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### Measuring the variability of a distance measure vector

I have calculated the distance of data points according to the Maalanobis distance. Now I have a vector of distances that I am trying to measure its variability to identify the residuals. I was ...
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### How to interpret these residual plots in regression analysis?

I did multiple regression analysis. There are 2 independence variables and one dependence variable. Because there are heteroscedasticity problem, I did log transport about dependence variable. All ...
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### What does the root mean square difference tell me that the mean difference doesn't?

If I have the below data and my difference measure is "actual/extrapolated-1" for the same observation. What does the RMSD tell me that the mean difference doesn't? If I understand the 'mean ...
53 views

### Interpreting a pattern in a residual plot produced by gam.check()

I'm working on creating a model that examines the effect of ocean characteristics on fishing outcomes. I have spatial data on a 0.5 degree grid and I created the following model: ...
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### residuals in the simple regression model

The residuals in the simple regression model have to sum up to 0?
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### Type of residuals to check linear regression assumptions

I would like to better understand some recommendations usually given to chose one or another type of residuals when checking the assumptions of a linar model. Lets define the raw residuals as the ...
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### Specification on power spectral density for population data

What is the best way to put a specification on the single-side auto-power spectral density (PSD)? We have a product for which we have a time signal. For this signal we calculate the PSD (or ...
The Ljung-Box test statistic $Q$ is defined as $$Q := n(n+2) \sum_{j=1}^{\ell} \frac{\hat{r}_{j}^2}{n-j},$$ where $\ell$ is the number of lags and  \hat{r}_{j} := \frac{1}{\left\|a \right\|_{2}^2} ...