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
42 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 ...
4
votes
2answers
204 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?
2
votes
0answers
47 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 ...
3
votes
2answers
123 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
votes
1answer
27 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 ...
4
votes
2answers
29 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 ...
0
votes
0answers
47 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 ...
2
votes
1answer
37 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 ...
6
votes
1answer
40 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: ...
1
vote
1answer
34 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
votes
1answer
32 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
votes
1answer
35 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 ...
0
votes
0answers
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 ...
2
votes
0answers
62 views
8
votes
2answers
155 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 ...
1
vote
1answer
69 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 ...
1
vote
0answers
24 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
votes
2answers
117 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 ...
0
votes
0answers
77 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
votes
1answer
39 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 ...
0
votes
0answers
22 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
votes
1answer
77 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: ...
3
votes
2answers
90 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 ...
5
votes
1answer
72 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 ...
1
vote
0answers
17 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 ...
5
votes
1answer
140 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 ...
1
vote
1answer
41 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 ...
1
vote
1answer
87 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. ...
2
votes
1answer
48 views

When to use skew normal regression via MCMC (mixture models)?

When do I use skew normal or skew t regression via MCMC? Do I use them when the data are heavily skewed, for example income data? Or do I fit a normal regression model first and inspect the residuals ...
2
votes
1answer
38 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 ...
1
vote
1answer
51 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 ...
1
vote
1answer
44 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 ...
4
votes
1answer
204 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 ...
4
votes
1answer
36 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.: ...
1
vote
2answers
47 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 ...
1
vote
1answer
37 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 ...
0
votes
2answers
169 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 ...
3
votes
1answer
108 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 ...
1
vote
0answers
31 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 ...
0
votes
0answers
27 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 ...
0
votes
0answers
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 ...
0
votes
0answers
17 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 ...
2
votes
1answer
49 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 ...
0
votes
0answers
77 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 ...
2
votes
1answer
45 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$ ...
0
votes
0answers
42 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 ...
4
votes
1answer
113 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 ...
8
votes
2answers
791 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 ...
1
vote
0answers
41 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
votes
1answer
66 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 ...