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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18 views

How does the R function arima() calculate its residuals?

I am new to time series and I am trying to figure out exactly what does on beyond the scenes in R. Say I have the MA process: $$y_t - \mu = a_t+\theta_1 a_{t-1} + \theta_2 a_{t-2}$$ where $a_t$ are ...
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1answer
11 views

KS test for normality on residuals from OLS vs. MLE

This is a conceptual issue. Suppose, one wants to test the residuals $e_t$ from the regression for normality. So, he runs the regression, obtains the estimates of error variance $\sigma^2$, and forms ...
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1answer
40 views

rpart classification: why is my predict() output not adhering to type=“class”?

I have a dataframe, 'datas', with 200 observations and a series of columns (some numeric, dummy, etc) and a binary class variable to be predicted that is called "bad_econ." I would like to get the ...
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2answers
80 views

What to do if residuals are not normally distributed?

I was wondering what to do with the following non-normal distribution of residuals of my multiple regression. Normality test of standardized residual ...
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0answers
30 views

Is my regression model ok? [closed]

I am trying to set up a model for determinants of CEO compensation. I am posting the residual graphs. They look unusual. Could you please tell me if my model is ok or should I make some changes? ...
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1answer
34 views

ARIMA modeling white noise probabilities vs. residual autocorrelation/PACF

I have moderate understanding of statistics and time series analysis. I trying to forecast a weekly time series with lots of outliers and trend shifts. After correcting all of the outliers, I'm left ...
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14 views

Classifying treatment levels as categorical or continuous

I am running a GLMM where one of the independent variables is treatment in terms of pesticide concentration, with four levels: 0ppb, 4.8ppb, 20ppb and 133ppb. I am unsure whether to class this ...
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1answer
64 views

What is the difference between bias and residuals?

I'm aware of the bias variance trade off. Intuitively I understand how as the model becomes more complex the variance decreases and the bias increases, after a certain point. But I don't really ...
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1answer
14 views

Correlogram q-statistics of residuals

I am currently try to get information from the correlogram of residuals in eviews from a certain equation; I am supposed to understand if residuals are white noise or not and to adfirm that they are ...
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1answer
48 views

What to do if residual plot looks good but qq-plot doesn't, after transforming the predictor and response variables?

I'm doing a multiple regression model on environmental data and am stuck on checking the assumptions. Ultimately, I need to do a model selection for the data. There are various explanatory variables ...
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30 views

How to estimate Carry-over effects in 2x2 Crossover study using R?

I am struggling to understand how to estimate the carry-over effect in a 2x2 Crossover experiment using R, there are several examples using SAS but (1) I don't understand the syntax and (2) I would ...
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1answer
45 views

Model to predict Residuals of another model

I am using a random forest for a 2 class classification problem. But eventually using probability of class "1" returned by the model for my task and not the label. I get AUC of about 70% Then I ...
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1answer
61 views

What is this called?

We have several time series: $Y, X_1, X_2, X_3, ..., X_n$ The steps taken are: Regress $X_2, X_3, ..., X_n$ on $X_1$ to get residuals of each $X_{(>1)}$ Regress $Y$ on $X_1, r_{X_2}, r_{X_3}, ...
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28 views

Logistic regression: Absolute values for P

I am stuck with a problem (actually two problems). I have a dataset of about 150 cases and 30 or so dichotonous (yes/no) parameters. I selected 6 parameters (after literature study and crosstabs) for ...
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0answers
100 views

How many degrees of freedom in logistic regression?

I did an experiment where 1600 people either responded (1) or not (0) to 4 treatments (400 unique people per treatment): ...
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1answer
127 views

Residual diagnostics after a logistic regression model [duplicate]

I wonder about how the residuals of a logistic regression model should be distributed. Of course, running a linear regression model and by assuming the Normal distribution assumption, the residuals ...
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0answers
34 views

Autocorrelation in squared residuals means heteroskedasticity?

I am wondering whether testing the squared residuals of a regression would provide information on whether there exists heteroskedasticity
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1answer
26 views

Questionable diagnostics for a binary logistic model

The model including one binary outcome (0/1; incident rate ~1.2%), one main exposure, and 13 covariates. The whole model is significant and the goodness-of-fit is OK. However, model diagnostic is ...
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1answer
29 views

Hull's GARCH vs. Definition in Time Series Literature

I have been reading up on volatility estimation and I encountered GARCH in Hull's "Options, Futures and Other Derivatives" (8e). He defines $u_n = \log{S_n/S_{n-1}}$ where $S_n$ is the price of some ...
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1answer
43 views

Can heteroskedastic residuals be justified by variance in dependent variable?

This is a very basic question and I hope it is not a duplicate. Im using a pooled regression model with a log-transformed dependent variable (electricity consumption meter values). The variance of ...
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1answer
53 views

pvalues of glm coefficients and heavy tailed distributed residuals

I've seen this post but I have still some additional questions. I have a ordinary linear regression model with more then 300 predictors (which represents different conditions). I want to know which ...
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1answer
32 views

Choosing the correct anova model

How does one choose the best model based on ANOVA's result? I mean I have 3 model outputs 1st is linear+all interaction, 2nd is linear+pair wise interaction and 3rd is linear and I am asked to choose ...
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41 views

Input EGARCH model (idiosyncratic volatility)

I have a time-series of historical volatility observations. I want to use an EGARCH model because I believe it is a better representation of the behaviour of these volatilities. Can I estimate an ...
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38 views

Estimating AR process for Logistic Regression

I'm fitting a time-series model with independent $X$ variables coded as months of the year (so there are 12 of them) and the dependent $y$ variable is some proportion, bounded between 0 and 1. As a ...
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1answer
48 views

How can we have non-random patterns in the plot of simple linear regression residuals vs the predictor variable?

A) When considering a simple linear regression model, it is important to check the linearity assumption. Graphing the residuals vs the predictor variable can often give a good idea of whether or not ...
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Why is the normality of residuals “barely important at all” for the purpose of estimating the regression line?

Gelman and Hill (2006) write on p46 that: The regression assumption that is generally least important is that the errors are normally distributed. In fact, for the purpose of estimating the ...
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1answer
118 views

Residual variance formulas difference

There is a bi-dimensional table of frequencies: Doing the regression analysis with the fit formula being $\hat y=a+bx^2$, where $\hat y$ is the same as $y^{est}$, the filled table looks like this: ...
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2answers
136 views

How to verify a linear model?

Given a dataset and liner model, how can I verify its sufficient quality? ...
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39 views

Concerns regarding correlation structures and random variance using lme

I’m modeling some variables repeatedly measured over a three months period for a total of 300 individuals. These variables (e.g. activity) were measured at three different time scales: daily (90 ...
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1answer
57 views

Can I say that residuals are white noise?

I want to check whether residuals are white noise or not. When I look at the plot, all lags do not pass(exceed) the significance band except for fourth lag. However, fourth lag's p-value of 0.228 is ...
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1answer
129 views

Interpreting the spread-level plot from R

I created a spreadlevel plot on my simple linear regression model in R. Here is my code, spreadLevelPlot(ols_reg) where ...
2
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2answers
69 views

Heavy-tailed residuals for OLS regression with large n. Implications?

I am trying to fit a multiple regression on a dataset with n=8619. First of all, using an untransformed Y as the response variable (ie Y = aX + bX +..) resulted in a residual plot with increasing ...
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1answer
67 views

Residuals Interpretation:Time Series Data

I am trying to use multiple regression for a time series dataset. I have values corresponding to a variable measured by 24 hrs for 4 months. Since there was a pattern which repeated every 24 hours I ...
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28 views

distribution of residuals in logistic regession

I am fitting binary outcome using generalized linear mixed model (glmm). I checked the Studentized and Pearson residual and they do not seem to be normal. Is it expected that residuals in logistic ...
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45 views

How are residuals calculated in rugarch package

I have a question regarding the "rugarch" package in R. I try to fit a ARMA(1,1)+GARCH(1,1) to a time series $x$ using the following command: ...
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64 views

Residuals Diagnostics, transformation or non-linear model

I am struggling with my data (hit counts for multiple target detection trials) To start, it is heavily negatively skewed: 00000000000000000000000000000000000 ...
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2answers
45 views

Errors and Residuals

In Wikipedia , it is written that : the sum of the residuals within a random sample is necessarily zero, and thus the residuals are necessarily not independent. The statistical errors on the other ...
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1answer
48 views

For the model $y_i=\beta_0+\beta_1x_{1i}+e_i,\quad i=1,\ldots,n$ , does $e_1=e_2$ imply $y_1=y_2$?

Which one notation is correct and why ? $y_1=\beta_0+\beta_1x_{11}+\epsilon_1$ or, $y_1=\beta_0+\beta_1x_{11}+e_1$ or, $Y_1=\beta_0+\beta_1x_{11}+\epsilon_1$ or, ...
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17 views

Calculating leverage/cook's distance for a Weighted Spatial Simultaneous Autoregression Model

I am estimating a Weighted Spatial Simultaneous Autoregression Model (spdep::spautolm --> Link) in R and I would like to do some residual analysis. Unfortunately ...
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53 views

Residuals - What are they? How can i obtain them?

So, i have a data set. I decide to fit an AR(1) model to it thus obtaining a model of the form $X_t - \hat{\phi} X_{t-1} = Z_t \quad Z_t$ is $WN(0,\hat{\sigma^2})$ Which in matlab is given by ...
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1answer
49 views

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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1answer
72 views

Large samples and normality of residuals

Ok I understand that normality of residuals is not really a concern in large samples. But can anyone tell how large should the sample be to ignore normality. Any cut off point? I'm working with a ...
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1answer
48 views

How can I get a reasonable residual standard error for my linear model which faces heteroscedasticity?

My goal is to get the residual standard error of my model to be as small as possible. I have a linear model lm(y~x). When I plot the standardized residual errors in function of the explanatory ...
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1answer
31 views

Residual vs fits for 2-level factorial design

So I'm analysing a 2-level factorial design, and get the residual vs fits plot below. I don't understand why it's symmetrical around 0. In any form of linear regression I've learned that the plot in ...
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1answer
71 views

R and Regression: How to determine distribution of residuals?

I have residuals from a linear regression model on my data set. I want to find an appropriate distribution of my residuals. Say, I assume my residuals are Skew-T Distributed, how can I find the ...
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1answer
71 views

What can be inferred from “covariance matrix of residuals” and “correlation matrix of residuals” after VAR?

I have this VAR: summary(VAR(V6CADModelSt45obs1D.df[,c(5,3,2,6,1,4)], p=5, type="none", ic="SC")) The following is the result of this VAR: ...
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38 views

not normally distibuted residuals

I have made an linear regression model using stata. I have made my model diagnostics - predict y, predict (rstudent) residuals. When I control the residuals for normality by a Q-Q plot, it is ...
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34 views

Is Wild Bootstrap a good strategy in General Linear Model (ANCOVA) with Assumption Violations (both normal residuals and homoscedasticy)?

I need to perform several GLM's (i.e. ANCOVA’s, with a single continuos dependent variable and several predictors, one dichotomous and some other continuos). I was looking for both a significance on ...
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Independence of residuals over time

My plots of conditional weighted residuals (CWRES) plotted against time show some sort of time trend (image attached). The response variable is on a Box_cox scale. How could I solve this problem ?
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3answers
1k views

Why do we say “Residual standard error”?

A standard error is the estimated standard deviation $\hat \sigma(\hat\theta)$ of an estimator $\hat\theta$ for a parameter $\theta$. Why is the estimated standard deviation of the residuals called ...