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 to calculate model residuals from MCMCregress [migrated]

I'm doing classwork using Bayesian inference. For this, I'm using the MCMCregress function, from MCMCpack. The problem comes ...
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44 views

choosing $β_0$ and $β_1$ to minimize the residual sum of squares

I'm reading a book called An Introduction to Statistical Learning: with Applications in R, and I have a question in regards to the material inside. I understand that we can find the residual sum of ...
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1answer
18 views

Analyzing regression results

I have done a regression model where i determine the number of cubes (independent variable) based on the amount of units i started with for each product type (dependent variables, ...
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19 views

Correlation fitted-residuals in mixed models

IN OLS linear models, fitted (predicted) and residuals scores are uncorrelated. I was under the impression that the same held true in mixed models. However, I have here an example model where fitted ...
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15 views

Use of Deviance Residuals for Leave-One-Out Cross Validation

I am a newbie to stats and having some difficulties understanding how to use deviance residuals for leave-one-out cross validation for a logistic regression model. The problem that I am trying to ...
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1answer
27 views

Durbin Watson test statistic

I applied the DW test to my regression model in R and I got a DW test statistic of 1.78 and a p-value of 2.2e-16 = 0. Does this mean there is no autocorrelation between the residuals because the ...
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1answer
44 views

Poisson Regression Residuals

I'm modeling the number of doctor visits (a count variable) on factors such as income, chronic condition, insurance, etc. I use the canned Stata command ...
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2answers
60 views

Logistic regression and error terms

In logistic regression, if we considered residuals, could they only take on the values $0$ or $1$? The data points themselves take on only $1$ or $0$. The logistic curve can take on any value between ...
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1answer
17 views

What is the method for calculating stdres in {MASS}

The documentation for the MASS package does not detail the calculation method for the standardized residuals using stdres(). I ...
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1answer
20 views

Non-constant standard deviation in residuals

I am fitting a model in the frequency domain, and my fit looks as follows: As you can see, the model function does not fit the data perfectly, especially in the higher frequencies. So, I examined ...
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20 views

How to corretly scale sum of squared residuals of two different sets of data in order to compare them?

I did numerical simulations of two different systems that returned me N=1000 histograms expressed as $\{x,y,y'\}$, where $x$ is the independent variable, $y=P(x)$ is the probability distribution ...
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34 views

Problem with Sales Regression Residuals

I'm trying to build a model for the ticket sales for different sporting events over a period of 30 days before the game to the day of the game. The problem that I'm having is that I can't seem to fit ...
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27 views

Testing residuals from a cox model with time dependent covariates

I'm doing survival analysis with time dependent covariates, using the counting process style. I already have a set of models and I want to test de residuals. I'm having trouble with the lack of ...
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45 views

Which type of residuals to use for the Durbin-Watson test (autocorrelation)

I want to check if there is residual autocorrelation in my model and the test for this is the Durbin-Watson test. I am using R and my question is if it makes a difference which type of residuals one ...
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2answers
51 views

Time Series on Oil Filter Pressure

I am not really strong with time series but I have a project I am working on.. I have a problem where I am trying to model a time series of the difference in pressure before and after oil has passed ...
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1answer
124 views

Heteroskedasticity in residuals vs. fitted plot

I am testing whether price per ounce of beer (continuous variable, range of values mostly between 0.1 and 0.5 dollars) and the presence of promotion, advertisement, and display (all binary) have ...
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1answer
39 views

Bias of Panel Generalization of Durbin-Watson

I'm working with an unbalanced panel dataset. (Country-Time) of approximate dimensions H=100 individuals i and average time length over individuals $mean(T_i)\approx7.5$. And about n= 8 regressors ...
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1answer
254 views

Are normally distributed X and Y more likely to result in normally distributed residuals?

Here the misinterpretation of the assumption of normality in linear regression is discussed (that the 'normality' refers the the X and/or Y rather than the residuals), and the poster asks if it is ...
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1answer
28 views

Predicting variance of heteroscedastic data

I am trying to do a regression on heteroscedastic data where I'm trying to predict the error variances as well as the mean values in terms of a linear model. Something like this: $$\begin{align}\\ ...
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27 views

How can I correct for residual autocorrelation in a fixed effect panel model?

The residuals have an AR(2) structure. Is it appropriate to add AR terms to a fixed-effects panel model?
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1answer
61 views

How to treat this OLS based on residual diagnostics

I am struggling already a couple of days with this simple OLS, can you help? Outcome years in function of predictor score, very simple linear model. The residual plot does absolutely not look good ...
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29 views

Sample autocovariance of Durbin–Watson test

I understand Durbin–Watson test, but I can't understand this sentence. I cannot prove it. The Durbin-Watson test statistics is asymptotically equivalent to (rootT*C), where C is the sample ...
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28 views

Is the variance of the residuals of a linear regression useful for estimating experimental sample sizes?

I have a data set of $y$ values that is not particularly normally distributed. However, the $y$s do partially depend on several other parameters. A linear regression model $y=c+\mathbf{ \beta ...
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1answer
33 views

fitted() function in R vs adding the residuals to the original data

I've found a discrepancy between the output of the fitted() function and adding the residuals to the original data set. Is the fitted() function not doing what I think it should be doing?
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Residuals from model missing interaction

In a plot of residuals against fitted values from a generalised linear model, I'm wondering what the plot would look like if an interaction was missing from the model. Can anyone simulate a model that ...
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1answer
54 views

First order condition of sum of squares with respect to variance of residuals

Consider the criterion function for ordinary least squares $$ S(b)=(Y-X'b)'(Y-X'b) $$ with Y, a matrix of dependent variables, and X, a matrix of explanatory variables. It is of course known that: ...
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1answer
47 views

Checking model quality in linear regression

I found that in linear regression to check the model quality you can look at the plots described below (my questions are in bold). scatter plot: plot Y against each X separately scatter plot: plot ...
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3answers
227 views

Assumptions of linear models and what to do if the residuals are not normally distributed

I am a little bit confused on what the assumptions of linear regression are. So far I checked whether: all of the explanatory variables correlated linearly with the response variable. (This was the ...
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31 views

Lack of fit and Pure error

I don't understand the concepts of lack of fit error and pure error. What I know is: $\bullet$ Lack of fit error: Error that occurs when the analysis omits one or more important terms or factors ...
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1answer
147 views

Violation Proportionality Cox model - Repeat analysis?

I'm new to survival analysis, but I've been reading some papers and books and I got a nice model. However, one of the variables (Sit) does not met the proportionality assumption for the Cox model. ...
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1answer
61 views

Do these residual plots violate the linearity and homogeneity assumptions for linear regression?

There seem to be too many points clustered around negative values for all the plots And while 3 & 4 seem to have random enough patterns, 1 & 2 seems to have negatively sloped trend. If ...
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1answer
40 views

Changes in R-squared

I was reading online, and I found that If the Variance of X increases then the value of R-squared increases If the Variance of the residuals increases then the value of R-squared decreases Can ...
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1answer
54 views

Weird looking binned residual plot

My binned residual plot is quite strange looking, the 95% confidence lines are so very jagged, with points between. I have colored this "inside" of the 95% confidence interval because it is really ...
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1answer
82 views

Why does poisson regression need to assume observations are poisson distributed?

Zuur (2013) 'Beginners Guide to GLM and GLMM' states that if the Pearson residuals, when plotted against fitted values from a poisson regression, show the pattern below then the assumption of poisson ...
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295 views

Why are Pearson's residuals from a negative binomial regression smaller than those from a poisson regression?

I have these data: set.seed(1) predictor <- rnorm(20) set.seed(1) counts <- c(sample(1:1000, 20)) df <- data.frame(counts, predictor) I ran a poisson ...
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1answer
168 views

Interpreting a binned residual plot in logistic regression

I am carrying out a logistic regression with $24$ independent variables and $123,996$ observations. I am evaluating the model fit in order to determine if the data meet the model assumptions and have ...
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1answer
144 views

Why are Pearsons residuals from a poisson regression so large?

As I understand it, Pearsons residuals are ordinary residuals expressed in standard deviations. I've ran this poisson regression: ...
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1answer
75 views

Residuals in poisson regression

Zuur 2013 Beginners Guide to GLM & GLMM suggests validating a Poisson regression by plotting Pearsons residuals against fitted values. Zuur states we shouldn't see the residuals fanning out as ...
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1answer
55 views

Transformation for negative skewness data

My analysis involved some behavioral data on swine. One measure we had was standing time (min) for pigs using accelerometers. Using SAS, I checked for normality, and results showed data to be ...
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1answer
105 views

How can multiple regression be performed as a sequence of univariate regressions?

Let's say $x$ is correlated to both $y_1$, and $y_2$. Why are the residuals of the nested regression of $x$ against $y_1$ and $y_2$, not equal to the residuals of the simultaneous (multiple) ...
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1answer
55 views

Are studentized deleted residuals a form of k-fold cross validation when K=N?

Are Studentized deleted residuals a form of k-fold cross validation when K=N? (this question is asked in the context of the discussion here)
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1answer
42 views

Building a ML ordered logit regression model

I am building a ML ordered logistic regression. First of all, I really don't know if this is the best way to fit a model to my data, as I am not too confident in ML ordered logit regressions, compared ...
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30 views

cox.zph says the standard deviation is zero

I need to compare my observed point vs random points that have been constrained to be relevant to that observation. In my case, I am looking at habitat selection along transects of animal movements. ...
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1answer
57 views

Formula for computing the Pearson $\chi^2$, comparison with R

I suspect this question is really about basic definition, but I could not find the ressource I need to solve my problem. I want to understand why the pearson $\chi^2$ test statistic, and ...
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1answer
66 views

validity of regression assumptions on residual plot

I am learning regression course.For a homework given the residual plot I have to analyze it.This is how I interpreted it.I want to know if there are any wrong interpretations. 1)Since the variability ...
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1answer
77 views

Trend in residuals vs dependent - but not in residuals vs fitted

I am fitting a linear model to a problem, and a little confused by what is going on. Without the details here are the two plots confusing me: Residuals vs Fitted Residuals vs Y Now the ...
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1answer
60 views

How to interpet residual plot?

As a part of a design of experiments course I'm taking, I ran an experiment at home. The experiment was checking how water boiling time changes under certain factors (5 overall factors) all which had ...
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23 views

assumption GARCH (1,1)

We have a problem with parameters’ estimation of GARCH(1,1). Our return equation is $$ r_t = \mu + h_t^{1/2} \cdot z_t, $$ where $z_t$ has normal distribution and $h_t$ is the conditional variance and ...
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1answer
71 views

Residuals from glm model with log link function

In the following example: ...
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90 views

Why doesn't correlation of residuals matter when testing for normality?

When $Y = AX + \varepsilon$ (i.e., $Y$ comes from linear regression model), $$\varepsilon \sim \mathcal{N}(0, \sigma^2 I) \hspace{1em} \Rightarrow \hspace{1em} \hat{e} = (I - H) Y \sim \mathcal{N}(0, ...