# Tagged Questions

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### GLM (conditional/unconditional) distribution

Based on my readings about GLM, I am pretty sure that when we say the distribution of the response variable $y$ is a member of exponential family of distribution, what we really mean is that ...
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### Difference between normality of residuals vs normality in each group.

I've been searching on the internet and books for quite a long time now and have come to the conclusion that normality of the residuals (each values minus the mean of each group) is the same as ...
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### Interpretation of a residual scatter plot

Hi all, I need to make a basic statement about whether this residual scatterplot looks normal, homoscedastic and linear. I understand that there are probably too few data points to make any conclusive ...
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### Plot residuals from a known linear model in R

This question is similar to this one, where I would like to plot the residuals, except that my residuals are known, since I'm simply comparing simulated and observed values with an expected 1:1 linear ...
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### 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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### Standardized residuals vs fitted values for Poisson regression

McCullagh and Nelder's book on glm suggest to plot standardized deviance residuals against either the linear predictor ($\hat{\eta}$) or the fitted values ($\hat{\mu}$) transformed to the constant ...
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### 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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### 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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### 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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### When forecasting a time series using artificial intelligence, why aren't the errors diagnositic?

Recent, modern methods for predict or forecast time series has widely used. several modern methods are neural network, fuzzy logic, ANFIS, etc. When we use these method for time series forecasting, ...
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### 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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### 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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### Residual Not Normal for Model Seasonal Time Series in R

I got a problem when choose the model for forecasting with time series. I'm in a middle writing my Thesis. My data have a seasonal pattern so, i tried use this model ...
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### Positive serial correlation

Blows are the pictures from my course lecture. The lecture states only the second picture shows a positive serial correlation, and the first picture requires time to be added as a predictor while ...
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### Regression Analysis — Correlation of Residuals

I see a lot of info on how to detect correlation of residuals and why it might negatively impact the quality of our model. I however dont see much info on how to mitigate the bad effects of these ...
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### What causes bands/stripes in residual plots?

I ran a model and got the following residuals: I proceeded to log the fitted values to get an idea of what's happening at the lower end of my predicted values: It was then I saw on the left side ...
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### When should we use Absolute Deviance Residual Plot or Deviance Residual Plot?

My lecturer mentioned that Absolute Deviance Residual Plot is better to use than the Deviance Residual Plot when analyzing fit of model in the GLM process. I was wondering what do you guys think about ...
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### Residuals plot interpretation

These are plots created in R. All of them are residuals (errors) vs. fitted values. They come from multiple linear regression models fitted by least squares. The five plots represent 5 different ...
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### TReading Residual Plot: Omitted Variable Bias of Dummy Variable

I have a plot of the residuals versus fitted values of an OLS model such that the shape of the plot are two identical randomly scattered clouds, one above and one below the $\hat{e} = 0$ line. Can I ...
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### Does this graph show homoscedasticity or heteroscedasticity? Are the errors random?

I think this graph shows homoscedasticity. Is this true?
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### Estimating Studentized Residuals (or Another Similar Measure) After Linear Regression With Robust Standard Errors

I have estimated a linear multiple regression with robust standard errors using Stata (regress depvar indepvar1 indepvar2 indepvar3 indepvar4 indepvar5, robust). ...
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### How to verify a linear model?

Given a dataset and liner model, how can I verify its sufficient quality? ...
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### 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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### 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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### Degrees of freedom with duplicate data points

The degrees of freedom of the residual in an OLS model is $n - p - 1$, where $n$ is the number of samples, and $p$ is the number of independent variables. I.e., the data matrix $X$ is $n\times p$. If ...
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### Arima Models Diagnostics

I'm doing a forecasting using seasonal ARIMA method. I'm using astsa package in r and I'm testing two models that I can't decide which one is better to use than the other The ACf and PACF for the ...