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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Is 0 mean of residuals assumption crucial for every model?

I am writing a seminar paper about sales forecasting. I am doing couple of models and I am choosing which one gives the best forecasts (Decomposition method, SARIMA, Brown Exponential Smoothing, Holt ...
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13 views

Linear mixed effects models: what to do when normal Q-Q- plot residuals look non-normal

I have four linear mixed effect models of similar structure: model1 <- lmer(index1 ~ biophony + anthrophony + (1 | Site), data = df, REML = F) model2 <- lmer(index2 ~ biophony + anthrophony + ...
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2answers
109 views

How do residuals relate to the underlying disturbances?

In the least squares method we want to estimate the unknown parameters in the model: $$Y_j = \alpha + \beta x_j + \varepsilon_j \enspace (j=1...n)$$ Once we have done that (for some observed ...
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1answer
51 views

Analysis of residuals

For my master thesis I have implemented following forecasting models: naive (just to check) decomposition method exponential smoothing (single/double/holt-winters) SARIMA Now I need to do the ...
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14 views

Gamma vs tweedie distribution for large productivity dataset

I'm running some GAMs using the mgcv R package on a dataset with ~8.5k observations, where productivity is the response and environmental conditions are the covariates. However I am unsure of which ...
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2answers
112 views

What really happens when we transform the data using $f(x) = \sin(\sqrt{x})$?

I need to perform a two-way ANOVA on my data ($Y$: sleeping hours). My data is quite normal $p$-value = $0.07$ with Shapiro-Wilk test but when I run the normality test for my residual, $p$-value is ...
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44 views

Residual Diagnostics and Homogeneity of variances in linear mixed model

Before asking this question, I did search our site and found a lot of similar questions, (like here, here, and here). But I feel those related questions were not well responded or discussed, thus ...
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1answer
25 views

How to compute the standard deviation of residuals from a regression line or curve?

After fitting a line or curve, it is easy to compute each residual as the difference between the actual Y value and the Y value predicted by the model fit by regression. For standard regression, the ...
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17 views

covariance matrix of residuals from a fitted model to decorrelate residuals

I fit a geeglm model with clustered data and now I would like to decorrelate the residuals of the model in order to run model diagnostics. I read that if I can obtain the covariance matrix of the ...
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1answer
70 views

Studentized residuals undefined

I am wondering if anyone could explain why there are some states where Studentized residuals are undefined. For example I got the following R code: ...
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2answers
80 views

Confirmation of normality using residuals from an linear regression

95% of my residuals from an linear regression lie within 2 standard deviations of the predicted values. Is this enough to confirm normality or could any other distributions have 95% of residuals that ...
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1answer
67 views

Assuming a probability density for MLE to do model selection

Motivation: I am trying to use Akaike Information Criterion to assess model ranking and over-fitting risk for a set of nonlinear models. I am an electrical engineer with no formal statistical training ...
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16 views

Multiple Reg with 2 Independent Variables that are Correlated - Orthogonalizing the IV's

I have two Ind. V's, $x_1$ and $x_2$. They are slightly correlated with eachother. $x_1$ explains a significant portion of $y$'s variability. Rather than just modeling $y = \beta_0 +\beta_1 x_1 ...
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1answer
139 views

Are normally distributed residuals not necessarily homoskedastic?

Let's say I've ran a linear regression and I'm checking the model diagnostics. I made a histogram of the residuals and they appear more or less normally distributed as below. I thought for a long ...
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1answer
35 views

How to assess the functional form of covariates in the Cox model with martingale residuals in R?

I want to find if the functional forms of covariates in my Cox model are linear. I understand the way to do this is to plot the Martingale residuals against the covariate of interest. I have found ...
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1answer
78 views

Not sure about the interpretation of this residual plot

I'm analyzing a residual plot of the residuals vs the fitted values. I'm not quite sure how to interpret this plot since there looks like there is a pattern and the average is not actually zero. ...
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1answer
36 views

How Are Regression Residuals Calculated - Specific Example

I am trying to figure out how regression residuals are calculated using the specific example in the attached graphic. Would I simply B-A (Red letters in graphic) to get C so: 22-30 = - 8 in this ...
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1answer
48 views

Multiple Regression - Residual Analysis

I am doing a multiple regression analysis regressing GPA against several 0/1 indicator variables (representing course completions). My fitted vs. residual plot is biased and looks awful. See below. Is ...
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22 views

Residuals plot from ripley K function on spatstat

I am a rookie on R and on spatstat package. I would like some help with the Kres function on spatstat. As is always wise to plot the residuals from any kind of ...
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1answer
120 views

R: test normality of residuals of linear model - which residuals to use

I would like to do a Shapiro Wilk's W test and Kolmogorov-Smirnov test on the residuals of a linear model to check for normality. I was just wondering what residuals should be used for this - the raw ...
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1answer
34 views

Assessing the fit of GLMM implimentation of a Rasch model to binary data using lme4

I'd like to assess the fit of the kinds of models described by de Boeck et al (2011) (http://www.jstatsoft.org/v39/i12). They are GLMM implementation of Rasch family models, e.g.: ...
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2answers
37 views

Beta regression

I have a data set where the response variable Y is a rate between 0 and 1, where the histogram of Y is bimodal. So I feel the linear regression is not suitable.s I have been reading papers about ...
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1answer
35 views

Assessing residuals from a regression model

I am trying to understand what the residuals from a regression convey about the model's adequacy/ability to explain the variance in the data. I read that if we are able to take the residuals from a ...
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2answers
122 views

how to detect outliers from residual plot?

I have the following residual plot. Can I detect outliers from residual plot? I want to remove 200 outliers in my data set, but I do not know how should I do that in R ? residual plots: scatter ...
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1answer
104 views

Does “residual” always imply a positive value?

In the context of calculating standard deviation Wikipedia says that the residual is the difference between an observation and the mean. Is the actual term "residual" referring to an observed ...
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23 views

Testing GLMM residuals against specific families and link functions (R)

When running a GLMM in R with family=gaussian and link=identity, it's easy enough to test whether normality and homoscedasticity ...
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21 views

SLR Residual Plots vs predictor or fitted values?

In our regression class, the professor said we can either plot the residuals vs the predictor values or vs the fitted values. I asked if there was a difference in the two plots (i.e. might you be able ...
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19 views

Mean in Cumulative frequencies distribution

Monthly expense Cumulative Freq. up to 50 7 up to 80 25 up to 120 49 up to 200 58 over 200 60 Calculate ...
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16 views

interpret regression slope of residuals against an independent variable

I did a linear regression of crop yield against year and took the residuals of this regression for my further analysis ...
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1answer
44 views

Exponential regression residual check

If you have an exponential regression of the form log(y) = b0 + b1x with predicted equation ŷ = 10^(b0 + b1x) and you need to ...
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45 views

How to interpret residual vs fitted values plot with clustered points

I am performing a multiple linear regression and I have a plot of the my first two explanatory variables vs the residuals and also a plot with the residuals vs the fitted values. I am not quite sure ...
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1answer
43 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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39 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 ...
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1answer
81 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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541 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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31 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 ...
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1answer
58 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 ...
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1answer
68 views

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

Breusch-Pagan rejects the H0 on this residuals: ...
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20 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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38 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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95 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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47 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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102 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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12 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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1answer
48 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
7 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
50 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
126 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
77 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 ...