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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Why the Breusch-Pagan rejects H0 on apparently non-heteroskedastic data?

Breusch-Pagan rejects the H0 on this residuals: ...
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13 views

How to get observations from residuals in an ARIMA model?

If we have residuals of an ARIMA(p,d,q) with known parameters, how can we retrieve the original observations of the time series?
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15 views

Line with discontinuous sigmoid function in half-normal residuals plot

In R, I've plotted the half-normal residuals for a few different models, i.e. halfnorm(residuals(model_object))) I notice that one plot takes a distinct S-shape ...
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25 views

How to interpret residual plots from time series regression

I am doing a time series regression between 2 variables. I used the dynlm library in R. I'm trying to understand how to interpret the results. Could you please point out where I am getting it wrong: ...
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33 views

F-adjusted Mean Residual Test in R

I'm running diagnostics on a logit model in R produced with glm(formula = formula, data = data, family = "binomial"). I'm ...
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3answers
76 views

How does the inclusion of an intercept change the variability of the residual?

I want to use the variability of the residual as a measure M and then test whether M is higher or lower after some event. However, I estimate separate regression before and after the event to obtain ...
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8 views

Classification Residual Analysis with rank-based goal

I have a dataset consisting of users, each with a number of items (ranging from 1 to 100). The end-goal is for each user to be able to predict the ranking the of the items according to some other ...
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24 views

Derivation of normalizing transform for GLMs

How is the $A(\cdot) = \int\frac{du}{V^{1/3}(\mu)}$ normalizing transform for the exponential family derived? More specifically: I tried to follow the Taylor expansion sketch on page 3, slide 1 of ...
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36 views

Non-seasonal periodicity in Time Series residuals

I have been working on a forecast model in Excel extrapolating from a small (150 data points) monthly time series. I've converted into a year/year percentage change series to get it stationary, ...
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4 views

Contribution of residuals to the mean error

I have data for 1000 students' performance over 10 different tests on a scale of 0 -100 (a 1000 rows X 10 col matrix). I calculated the mean score and the associated std. deviation for each student. ...
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41 views

Strange residuals interpretation

I have run a model and with the data I have, I wasn't expecting to produce the best model ever but my residuals are really strange. The outcome variable is number of days going to a website in a month ...
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1answer
56 views

R - Confused on Residual Terminology

Root mean square error residual sum of squares residual standard error mean squared error test error I thought I used to understand these terms but the more I do statistic problems the more I have ...
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20 views

Residual autocorrelation versus lagged dependent variable

When modeling time series one has the possibility to (1) model the correlational structure of the error terms as e.g. an AR(1) process (2) include the lagged dependent variable as an explanatory ...
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67 views

Working with residuals of regression

So the background is that the I collected yield data for past 5-6 decades and location from where I collected yield data had high yielding varieties introduced over time. I am looking at the ...
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54 views

What resolution should I be using for residuals vs fitted values plot from a linear regression?

I made this linear regression that shows how well estimated animal locations (longitude) predict actual animal locations. ...
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10 views

How to compare a measure reflected by a regression residual in a pre-post design?

Maybe a simple question, but my head is spinning: I want to see if X increased after a certain treatment in a pre-post study. Unfortunately, I have only K which is a noisy measure of X. To "clean" K ...
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47 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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34 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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22 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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23 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
42 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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54 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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64 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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24 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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28 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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25 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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30 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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47 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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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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153 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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45 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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296 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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32 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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38 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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64 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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33 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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29 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
40 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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12 views

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
62 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
51 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
282 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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39 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
160 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
66 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
44 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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58 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
93 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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324 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 ...