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.

learn more… | top users | synonyms (1)

0
votes
0answers
17 views

Why do the residual sum of squares and the mean absolute percentage error conflict with each other?

I carried out regression with 7th degree and 8th degree polynomials. As expected, the residual sum of squares for 8th degree polynomial regression is less than that of 7th degree polynomial ...
0
votes
0answers
16 views

Long tails vs fat tails in residuals, always the same approach?

Both are examples of a non-normal distribution and the answer to that seems to always be using a robust estimator that will assign a smaller weight to the 'outliers'. But are they the same? As I ...
0
votes
1answer
30 views

Increasing ACF results when fitting AR(1) or ARMA(1,1) structure to correlated residuals from mixed-effects model

So, I am trying to understand some odd results in one of my mixed-effects models. I am fitting data from 50 individual units over 20 timepoints each. There is also a time varying covariate $C$ which ...
0
votes
1answer
11 views

Correlation between standardized residuals and fitted values in a linear mixed effect model: Course of action?

I am fitting a linear mixed effect model in R with lme from nlmer, using the approach described in Zuur et al. "Mixed Effects ...
2
votes
0answers
26 views

Interpreting linearity in regression when there are outliers

I am trying to determine whether this regression meets all of the assumptions one needs to adhere to when carrying out a multiple linear regression. In looking at the residual plots below, it seems to ...
1
vote
0answers
23 views

Odd looking residual plot - not sure what transform to use if any

I am concerned about the residual plot shown. The (count) data are over-dispersed, with about 40% 0s, median is 2, maximum is 300 or so. I am not sure what how to proceed with this - it is not ...
6
votes
1answer
103 views

Interpretation of $\mathbf{y}^T(\mathbf{I}-\mathbf{H})\mathbf{y}$ in OLS

In classic OLS regression it is well-known that $(\mathbf{I}-\mathbf{H})\mathbf{y}=\mathbf{r}$, where $\mathbf{I}$ is the identity matrix, $\mathbf{H}$ is the hat matrix, $\mathbf{y}$ is the vector of ...
2
votes
2answers
38 views

GLM diagnostics and Deviance residual

From my understanding, the deviance residual of a GLM model, when plotted against the fitted values, should give a scatterplot distributed with mean 0 and constant variance? Does this hold for any GLM ...
1
vote
0answers
23 views

Diagnostics and residual analysis for Poisson regression

Recently, I was asked to check for serial correlation after doing a panel Poisson regression. I haven't seen such a test and in general, researchers (at least in the econom(etr)ics literature) don't ...
0
votes
1answer
29 views

Ljung Box test for residuals of constrained ARIMAX(2,1,0) model

I have this ARIMA(2,1,0) model with one exogenous variable: $$\Delta y_t=c+\phi_2 \Delta y_{t-2}+\beta_x x_t+\varepsilon_t$$ I want to run Ljung Box test of residual autocorrelation with test ...
5
votes
0answers
60 views

Pearson VS Deviance Residuals in logistics regression

I know that Pearson Residuals are obtained in a traditional probabilistic way: $$ r_i = \frac{y_i-\pi_i}{\sqrt{\pi_i(1-\pi_i)}}$$ and Deviance Residuals are obtained through a more statistical way ...
1
vote
1answer
36 views

How exactly are standardized residuals calculated

I'm working on a model for something and at the moment I prefer working solely in Excel. I've been double checking the results of the linear model in JMP, Minitab, and Statistica, and (more or less) ...
0
votes
0answers
12 views

Post-Hoc Chi-Sq test - conclusions drawn from comparing individual categories

My question is very similar to this one: (Post hoc $\chi^2$ test with R), but I'm still confused, and tried to provide as much detail as possible. I have two categories of students: Domestic and ...
1
vote
0answers
11 views

How to model a scale and its component subscales

I am investigating the use of psychological strategies (PS) and athlete engagement (AE) in soccer players and what to predict if global / whole PS predicts AE as a whole using SPSS. I also want to ...
0
votes
3answers
59 views

Question on Residuals [closed]

After generating the regression model in R using lm, the results will be passed to summary function. results <- lm(y~x, data) summary(results) This function ...
1
vote
1answer
36 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 ...
3
votes
1answer
14 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 ...
1
vote
1answer
66 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 ...
2
votes
2answers
117 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 ...
0
votes
1answer
47 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 ...
1
vote
0answers
16 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 ...
1
vote
1answer
68 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 ...
0
votes
1answer
23 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 ...
2
votes
1answer
58 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 ...
0
votes
0answers
46 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 ...
2
votes
1answer
49 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 ...
1
vote
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}, ...
2
votes
0answers
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 ...
1
vote
0answers
132 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): ...
0
votes
1answer
130 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 ...
0
votes
0answers
47 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
0
votes
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 ...
1
vote
1answer
32 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 ...
0
votes
1answer
44 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 ...
4
votes
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 ...
0
votes
1answer
35 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 ...
0
votes
0answers
47 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 ...
4
votes
0answers
40 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 ...
3
votes
1answer
62 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 ...
10
votes
2answers
554 views

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 ...
0
votes
1answer
166 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: ...
2
votes
2answers
139 views

How to verify a linear model?

Given a dataset and liner model, how can I verify its sufficient quality? ...
0
votes
0answers
46 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 ...
0
votes
1answer
60 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 ...
2
votes
1answer
167 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
votes
2answers
92 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 ...
2
votes
1answer
75 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 ...
0
votes
0answers
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 ...
0
votes
0answers
54 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: ...