# Tag Info

Accepted

### What happens if the explanatory and response variables are sorted independently before regression?

I'm not sure what your boss thinks "more predictive" means. Many people incorrectly believe that lower $p$-values mean a better / more predictive model. That is not necessarily true (this being a ...

### What happens if the explanatory and response variables are sorted independently before regression?

If you want to convince your boss, you can show what is happening with simulated, random, independent $x,y$ data. With R: ...

### What happens if the explanatory and response variables are sorted independently before regression?

Your intuition is correct: the independently sorted data have no reliable meaning because the inputs and outputs are being randomly mapped to one another rather than what the observed relationship was....
Accepted

### Does no correlation imply no causality?

does an absence of correlation imply absence of causality? No. Any controlled system is a counterexample. Without causal relationships control is clearly impossible, but successful control means - ...
Accepted

### Does correlation = 0.2 mean that there is an association "in only 1 in 5 people"?

The quoted passage is indeed incorrect. A correlation coefficient quantifies the degree of association throughout an entire population (or sample, in the case of the sample correlation coefficient). ...

### When to remove insignificant variables?

Let me first ask this: What is the goal of the model? If you are only interested in predicting if a customer will buy, then statistcal hypothesis tests really aren't your main concern. Instead, you ...
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### Why zero correlation does not necessarily imply independence

Correlation measures linear association between two given variables and it has no obligation to detect any other form of association else. So those two variables might be associated in several other ...

### Generate a random variable with a defined correlation to an existing variable(s)

I will describe the most general possible solution. Solving the problem in this generality allows us to achieve a remarkably compact software implementation: just two short lines of ...
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### Is there any relationship among cosine similarity, pearson correlation, and z-score?

The cosine similarity between two vectors $a$ and $b$ is just the angle between them $$\cos\theta = \frac{a\cdot b}{\lVert{a}\rVert \, \lVert{b}\rVert}$$ In many applications that use cosine ...

### What happens if the explanatory and response variables are sorted independently before regression?

Actually, let's make this really obvious and simple. Suppose I conduct an experiment in which I measure out 1 liter of water in a standardized container, and I look at the amount of water remaining ...
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### Generating correlated binomial random variables

Binomial variables are usually created by summing independent Bernoulli variables. Let's see whether we can start with a pair of correlated Bernoulli variables $(X,Y)$ and do the same thing. Suppose ...

### Example where $X$ and $Z$ are correlated, $Y$ and $Z$ are correlated, but $X$ and $Y$ are independent

Intuitive example: $Z = X + Y$, where $X$ and $Y$ are any two independent random variables with finite nonzero variance.
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### Difference between Random Forest and Extremely Randomized Trees

The Extra-(Randomized)-Trees (ET) article contains a bias-variance analysis. In Fig. 6 (on page 16), you can see a comparison with multiple methods including RF on six tests (tree classification and ...

### When A and B are positively related variables, can they have opposite effect on their outcome variable C?

The other answers are truly marvelous - they give real life examples. I want to explain why this can happen despite our intuition to the contrary. See this geometrically! Correlation is the cosine of ...

### Interview question: If correlation doesn't imply causation, how do you detect causation?

There are a few ways around this. You are right that A/B testing is one of these. The economics Nobel this year was awarded for the pioneering of field experiments in the study of policies against ...
Accepted

### Why zero correlation does not necessarily imply independence

There is a generalized lack of rigor in the use of the word "correlation" for the simple reason that it can have widely differing assumptions and meanings. The simplest, loosest and most common usage ...