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 the application of the Frisch-Waugh-Lovell Theorem really necessary?

Suppose I have a model \begin{eqnarray} y = X_1 \beta + X_2 \gamma + \epsilon \\ X = Z \Pi + V \end{eqnarray} where $X_1$ is endogenous, Z are instruments, $X_2$ are exogenous. If I however include ...
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1answer
26 views

How Residuals of Instrumental Variables Estimation are calculated and why you can have a negative R-squared?

I would like to understand, precisely, why you can have a negative $R^2$ with a 2SLS estimation, such as you have in commands like ivreg2 in Stata. There is ...
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17 views

Probability that LM with lesser RSS has greater residual for individual i (or opposite sign)?

You have fitted a basic linear Model #1 (i.e., GLM with identity-link) based on observed data with residuals: $$ Model 1: y_i = \beta_0 + \beta_1 x_{1i} + \beta_2 x_{2i} ... + R_i $$ A colleague ...
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10 views

Correlated Proportions shown in a Mosaic Plot. What is the fitted model that generates residuals?

I have a 2-by-2 table of correlated proportions where I am plotting the positivity of two diagnostic methods applied on a sample of 216 individuals: ...
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25 views

Interpreting Residuals for Specific Data Points

I want to know if this is an appropriate interpretation of a regression residual and more generally, whether it's an appropriate use for regression. Let's say you gathered data on the performance ...
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1answer
24 views

Stationarity and seasonality of residuals

Why is it necessary to evaluate stationarity and seasonality of model residuals? Or is it? The model in question is an OLS model that represents a relationship between Y and a bunch of economic ...
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18 views

Determining the p-value of two consecutive residuals

I am performing an outlier detection test in a monthly process to detect errors (for each month I have more or less 22 business days). I am using a Simple Linear Regression model. What would be the ...
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1answer
47 views

Why would the residuals from these two models result in the wrong AIC being calculated?

We run two linear regressions, Model 1 and Model 2. The residuals from these two models are plotted against the predicted values. If I understand correctly, the AIC from these two models would be ...
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2answers
31 views

How do I identify a particular residual from a mixed-effects model in R?

Here's a plot of my residuals from a mixed-effects model in R (using lme4). There's one 'outlying' residual with a value of around 35 (index circa 90) that seems anomalous. I don't know if it has ...
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25 views

Measure based on the absolute residual of an OLS regression with/without intercept

A typical measure for firms’ use of earnings management in the finance literature is based on the absolute value of the residual (|e|) of a OLS regression estimated separately for firms in each ...
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13 views

Trending Residuals in Negative Binomial Panel Regressions with Patent Data

A commonly faced problem for researchers working with patent data is that we need to work with negative binomial models because our dependent variable is an overdispersed count variable. I am using ...
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1answer
18 views

What is the estimated variance of residuals? From R [duplicate]

I am trying to figure out what is the estimated variance (i.e. the estimated "error") of residuals around a fitted line. ...
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2answers
57 views

Normality of residuals - contradiction between 'symplot' and 'qnorm'?

After running a multiple linear regression analysis, I wanted to assess normality of residuals. I plotted a histogram which showed an almost normal distribution of residuals. I also used ...
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2answers
80 views

Analyzing residuals in logistic regression

Greetings statistics experts, I am having a try with the kaggle titanic dataset and am wondering what to do with the residuals after fitting models. In the case of linear regression you can look at a ...
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6 views

FE Model: independence of residual and firm specific component

I'm estimating a fixed effects model and want to consider Petersen's (2009) suggestion: "The components of X (μ and ν) and ε (γ and η) have zero mean, finite variance, and are independent of each ...
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1answer
78 views

How to deal with non-normally distributed residuals?

I'm fitting a multiple linear regression model. I've read that the residuals of my regression need to be normally distributed in order for the p and t values to be accurate. Now my residuals (see ...
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27 views

How to create an index to compare regression lines

Suppose I have the actual and fitted values of two regression lines. Each regression line is modeling the sales of some good. The fitted and actual values of one of the regression lines is much ...
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32 views

When to use non-additive stochastic error term

I have encountered the following two versions of the Cobb-Douglas production function as an illustration of the differences between intrinsically non-linear and linearisable non-linear regression ...
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1answer
61 views

S-curve in residuals plot: a problem?

I am doing some linear regression and am predicting a absolutely non-normal dependent variable (for context: we are forecasting the amount of units sold for a shop). Therefore, we have transformed the ...
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1answer
34 views

What is the difference between errors and residuals?

While these two ubiquitous terms are often used synonymously, there sometimes seems to be a distinction. Is there indeed a difference, or are they exactly synonymous?
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99 views

Are the model residuals well-behaved (homoscedasticity)?

Can I say looking at this residuals-vs-fitted plots, that my residuals are homoscedastic?
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1answer
79 views

Diagonal lines in residuals vs fitted values plot for ANOVA

I'm experiencing strange patterns of residuals. The following chart is a scatterplot of Standard residuals (Sres) versus Fits. I'm interested in the diagonal lines that mean that a higher fit leads to ...
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24 views

Distribution of residuals in multinomial / ordinal logistic regression

In simple logistic regression, the standardized residuals are assumed to be normally distributed. Are there any such assumptions for ordinal or multinomial logistic regression? Because in these ...
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176 views

Which residuals to analyse when dependent variable is transformed?

I am running a multiple linear regression where the dependent variable is sqrt-transformed. As far as I understand, the residuals from the regression are different from the residuals calculated as ...
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38 views

Residuals are not normally distributed in linear regression model

I have a linear regression model and residuals look like this: what does it mean for my model? Is my model inappropriate because residuals are not normally distributed?
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1answer
61 views

Standard deviation of residuals from a linear regression

I've ran this linear regression: mtcars_lm <- lm(mpg ~ wt, mtcars) Lets say I observe a value of mpg that is 2 above the ...
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1answer
26 views

Complex level 1 variance mixed effects models in R

Take this mixed effects model in R: $y_i = \beta_0 + \beta_1X_{ij} + u_{j} + e_{ij}$ where $u$ is a random effect (level 2 residual) with groups $j$. It is possible to allow the variance of $e_{ij}$ ...
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25 views

What's the difference between error distribution and residual distribution in generalized linear models?

I have met with generalized linear model, but I'm confused with the errors and residuals? Can anyone help me out? I have got three questions. (1)what's the difference between error and residual? ...
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55 views

Correcting data for mean but also variance

My data: I have data that range from 0 to 2 for numerous individuals. The scores are more or less normally distributed and vary continuously, but the scores are always between 0 at the minimum and 2 ...
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2answers
235 views

Weird fitted values/residuals plot

I am doing some regressions on real earnings as a function of some different variables and this came out: Is this because earnings cannot be negative?
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120 views

Converting Chi Square Adjusted Residuals to p values

I am running a chi squared analysis in SPSS on a 5 x 2 contingency table. The overall chi square p value was < 0.0005, so I ran post hoc tests (adjusted standardized residuals on the individual ...
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2answers
195 views

Do the residual plot and QQ plot look normal?

I am doing linear mixed model and would like to check the assumptions using residual plot and QQ plot. Here is my code: ...
3
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1answer
108 views

Residual variance for glmer

I am running a glmer model and I want to determine the total variance. My data is for survival and it is coded as 0 and 1, where 1 represents that the individual survived and 0 represents that the ...
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2answers
34 views

Should I take the Shapiro Wilk test with a pinch of salt here?

So I'm trying to determine whether the residuals from a seasonal ARIMA model are normal or not. Upon using the shapiro wilk test, I get a staggeringly low p-value leading me to think that the ...
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51 views

Looking for an intuitive and simple way of visualizing the effects of factors in a GLMM analysis

This is a conceptual question. I have data to which I fit a GLMM. The data are numerical observations (a metabolite concentration in the blood, hence defined over the positive real), obtained from 2 ...
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1answer
41 views

Relation between $R^2$ and $R^2_{(i)}$

Is there a relation between $R^2$ and $R^2_{(i)}$ (where $R^2_{(i)}$ is the $R^2$ of a regression without the point ith. For example if the ith point is an outlier) without having to recalculate all ...
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1answer
47 views

How to tell that a reciprocal relationship exists by a residual plot?

I'm following an example from the book "R by Example", where they talk about two-way ANOVA. The database used in poison. The analysis is: ...
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1answer
36 views

Analysing the residuals themselves

As far as I know, it is possible to fit a linear regression model and then fit a second model to predict the residuals from the first model by using some other variables. By this you can understand ...
2
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1answer
35 views

Residuals from lowess curve

I am trying to obtain the residuals from a lowess fit. I’m using the lowess( ) function. Is there a way to do this?
2
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1answer
44 views

Residuals perfectly symmetric about zero against fitted values

Consider a modelling a response $Y$ against two categorical variables (which can take $4\times 2=8$ possible combinations). We have 16 values for the response, with two values for every combination of ...
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20 views

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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154 views
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166 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
75 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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49 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 ...
3
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2answers
128 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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195 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 ...
2
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1answer
67 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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27 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 ...
3
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1answer
104 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: ...