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-1

For understanding what residuals should look like and if your residuals look like they should (no identifiable problems), or indicate some more work should be done I recommend reading this paper: Buja, A., Cook, D. Hofmann, H., Lawrence, M. Lee, E.-K., Swayne, D.F and Wickham, H. (2009) Statistical Inference for exploratory data analysis and model ...


2

I suspect this is the result of fitting a logistic regression to binary data and computing the residuals. I can recreate a similar plot by doing so These sorts of residuals aren't super useful, as the quantity $Y - \hat{Y}$ for logistic regression isn't a nice distribution unlike linear regression. There are a bunch of other types of residuals you can ...


1

in principle, the interpretation of the plots is explained in the help of ?plotResiduals: If form is a factor, a boxplot will be plotted instead of a scatter plot. The distribution for each factor level should be uniformly distributed, so the box should go from 0.25 to 0.75, with the median line at 0.5. Again, chance deviations from this will increases when ...


2

Consider an ARMA(1,1)-GARCH(1,1) model$\color{blue}{^{*}}$ \begin{aligned} x_t &= \varphi_0+\varphi_1 x_{t-1}+\varepsilon_t+\theta_1\varepsilon_{t-1}, \\ \varepsilon_t &= \sigma_t z_t, \\ \sigma_t^2 &= \omega+\alpha_1\varepsilon_{t-1}^2+\beta_1\sigma_{t-1}^2, \\ z_t &\sim i.i.d.(0,1) \end{aligned} for some zero-mean, unit-variance ...


1

As far as I understand, illustration on the right shows that input to this block already has 256 features. So we are deep into some ResNet architecture and already created 256 features (we lost some w x h due to conv 3x3 before but gained features instead). Still, calculating 256 channels (features) can take too much time, and authors proposed using 1x1 conv ...


1

If the pattern of the innovations explains perfectly the movement of the whole time series (also extent of movements) then you failed to capture anything. Why? Because for a good fit, the remaining innovation in the residuals should be as small as possible and further, it should definitely not be essential to describe the data. In general, you predict by ...


0

Simply: Residuals vs. fitted and residuals vs. independent variables have a similar purpose. While you can catch some forms of heteroscedasticity seeing a typical "funnel" shaped distribution of residuals, that's not all these plots are for. With residuals versus fitted values or predictors, you can also catch "curvilinearity" when the ...


4

It is important not to over-interpret these plots. The first plot of residuals vs fitted values is a little misleading in my opinion if you only focus on the red line, partly due to the fairly small sample size. Yes, the red line has a curved shape, but looking at the data points, it is not clear at all that there is nonlinearity. This type of pattern can ...


0

The residual standard error is $\sqrt{MSE}$. The $MSE$ is an unbiased estimator of $\sigma^2$, where $\sigma^2 = Var(y|x)$. To make it more clear of the answer by @Silverfish and @Waldir Leoncio. A summary of all definitions was shown below. Always got confused by these terms, put it here instead of making it as a comment for better formatting. Anova table ...


1

For the Cox model deviance residuals, see this page for discussion. Censored cases necessarily have negative deviance residuals; they don't have observed event times, so their event times can't be earlier than predicted (the requirement for a positive deviance residual). Deviance residuals can be helpful in identifying outliers, but your data don't suggest ...


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