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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20 views

SLR: Variance of a residual

I am having problems calculating the variance of a residual in an SLR setting, ie $\text{var}$$(y_i- \hat{y_i})$. Here is what I have thus far. If $ \hat{y_i}= \hat{\beta_0} + \hat{\beta_1}x_i$ ...
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0answers
26 views

Controlling for categorical variables before correlation using residuals?

I’m looking for a way to control for the effect of multiple categorical variables, all of which contain two independent categories, on two continuous variables before I correlate these continuous ...
3
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1answer
23 views

Residual Plots and Transformations in Linear Regression

What does it typically mean when the plot of residuals vs. fitted values in a linear regression forms a parabola symmetric about the y-axis (for both convex and concave parabolas)? How can one infer ...
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6 views

labelling residuals [migrated]

Hi everyone I have made a linear regression model in R with 3 continuous independent variables and one continuous dependent variable. I have generated the diagnostic plots. I would now like to ...
7
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2answers
258 views

In simple linear regression, where does the formula for the variance of the residuals come from?

According to a text that I'm using, the formula for the variance of the $i^{th}$ residual is given by: $\sigma^2\left ( 1-\frac{1}{n}-\frac{(x_{i}-\overline{x})^2}{S_{xx}} \right )$ I find this hard ...
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0answers
15 views

Struggling with non-normality in generalized linear model

Dear statistics experts, I am looking for correlations between certain measures of brain structural integrity (fractional anisotropy, given as ratio between two hemisphere ==> rational data range ...
0
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1answer
31 views

Validating residual plot count data (different levels)

I am studying the distribution of a marine species using the number of sightings as a dependent variable. When I am trying to validate the plots of the best model I am getting a non-usual pattern, and ...
0
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1answer
40 views

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

Breusch-Pagan rejects the H0 on this residuals: ...
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0answers
19 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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20 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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0answers
39 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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0answers
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
80 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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0answers
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 ...
2
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0answers
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 ...
3
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1answer
38 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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0answers
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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1answer
43 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 ...
0
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1answer
61 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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1answer
29 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 ...
4
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1answer
68 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 ...
3
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1answer
69 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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0answers
11 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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0answers
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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1answer
41 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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0answers
24 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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0answers
26 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
49 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
62 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
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 ...
0
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1answer
27 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 ...
3
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1answer
31 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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0answers
27 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 ...
0
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0answers
35 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 ...
0
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0answers
34 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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53 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
52 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 ...
6
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2answers
171 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 ...
1
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1answer
55 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 ...
10
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2answers
302 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 ...
4
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1answer
34 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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0answers
45 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?
3
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1answer
65 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 ...
0
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0answers
34 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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0answers
32 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 ...
0
votes
1answer
44 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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0answers
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 ...
0
votes
1answer
69 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
57 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
333 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 ...