# Tag Info

### Assumptions of multiple regression: how is normality assumption different from constant variance assumption?

1. Normal distribution of residuals: The normality condition comes into play when you're trying to get confidence intervals and/or p-values. $\varepsilon\vert X\sim N (0,\sigma^2 I_n)$ is not a ...
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### Why are survival times assumed to be exponentially distributed?

Exponential distributions are often used to model survival times because they are the simplest distributions that can be used to characterize survival / reliability data. This is because they are ...
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### Family of GLM represents the distribution of the response variable or residuals?

The family argument for glm models determines the distribution family for the conditional distribution of the response, not of the residuals (except for the quasi-models). Look at this way: For the ...
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### Why are survival times assumed to be exponentially distributed?

To add a bit of mathematical intuition behind how exponents pop up in survival distributions: The probability density of a survival variable is $f(t) = h(t)S(t)$, where $h(t)$ is the current hazard ...
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### Family of GLM represents the distribution of the response variable or residuals?

Further to Kjetil's excellent answer, I wanted to add some specific examples to help clarify the meaning of a conditional distribution, which can be a bit of an elusive concept. Let's say you took a ...
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### Are 50% confidence intervals more robustly estimated than 95% confidence intervals?

This answer analyzes the meaning of the quotation and offers the results of a simulation study to illustrate it and help understand what it might be trying to say. The study can easily be extended by ...
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### Multicollinearity and predictive performance

Let's assume that you have trained a model on a training dataset, and want to predict some values in a test/holdout dataset. Multicollinearity in your training dataset should only reduce predictive ...
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### Realistically, does the i.i.d. assumption hold for the vast majority of supervised learning tasks?

The operational meaning of the IID condition is given by the celebrated "representation theorem" of Bruno de Finetti (which, in my humble opinion, is one of the greatest innovations of ...
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### Why does including $x\ln(x)$ interaction term in logistic regression model helps to assess linearity assumption?

Box and Tidwell (1962) [1] presented a somewhat general approach for estimating transformations of the individual predictors (IVs), and work through the specific case of estimating power ...
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### What is the need of assumptions in linear regression?

You are correct - you do not need to satisfy these assumptions to fit a least squares line to the points. You need these assumptions to interpret the results. For example, assuming there was no ...
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### What is a complete list of the usual assumptions for linear regression?

The following diagrams show which assumptions are required to get which implications in the finite and asymptotic scenarios. Linear Regression Assumptions: Key Points Generally the assumptions can ...
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### Why do I see a pattern in the residuals in this well specified model?

How close the residuals at specific $x$ values are to zero depends on the sample size. Now, the sample size in real examples will be whatever it is, so there's not much use saying it should be bigger, ...
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### What are the assumptions for applying a quantile regression model?

Quantile regression assumes the normal regression assumptions of linearity and additivity (unless you add more terms to the model) independence of observations very large sample size, as quantile ...
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### Model assumptions - not worth the effort?

Well, there is some truth to it, but it's problematic. It would lower the publication rate. OK. But getting rid of bad publications is a good thing. Too much garbage is published. Checking model ...
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