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The Hidden Relationship Behind Better Decisions: Correlation and Covariance

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Tags: probabilitycovariancecorrelationintroductory-probability-course

When we think about probability, statistics, and distributions, we often focus on modeling a single variable. Doing so, however, can make us miss how variables interact — and these interactions can completely change our decisions and insights. In this video, we explore covariance and correlation, showing why looking only at individual (marginal) distributions can be misleading. You’ll see how the joint behavior of variables reveals insights you wouldn’t get from marginals alone, with applications in fields like finance. We’ll cover: - Marginal distributions and expected values - Joint distributions, covariance, and correlation - A realistic finance example By the end, you’ll understand how considering relationships between variables can reveal insights and guide better decisions that you would otherwise miss.

Analytics

6.53 Overall score*

50 Rank

12 Votes

9 Comments

Comments

7.3

Never learned how the correlation is computed or what it actually means only ever seen it and wondered about it. Learned something new today! You give some really clear examples and I like that! While you reference other videos this one still stands on its own two feet. The title seems fairly unrelated to the video, as it lacks an example of the better decision-making.

To be honest, I can’t think of much to say about this one. I’m not much of a stats guy and had never seen the formal definition of correlation and had never even heard of covariance, so I learned a decent amount.

6.4

The discussion at the end with Z = X+Y (expectation unchanged but standard deviation modified) is the good point of the video, and should be emphasized. What bothers me is that the outcome of a toss is so favourable that it can be confusing. Also the fact that Tod and Franch outcome ar identical, whereas covariance and correlation applies on general cases, that is too restrictive, and can induce confusion for the students. In brief : it is a good introduction, but it appeals for a second video with a more general context. Also I suggest that at the end of this first video, a wrap up is made : “what nave we leartnt”, whith 3-4 bullet points. That helps to fiw the ideas.

6.9

A nice Manim animation on the 2D case, with a everyday scenario.

8.3

The explanations are very clear and you give great intuition about the topic. I really enjoyed your video. By the way, I suppose Frank and Todd are twins, because they look exactly the same ;)

The scatter plot of the joint distribution, the key visual, is sparse which invites confusion.

4.5

It’s a bit confusing to use an example with no correlation to motivate the study of correlation. Maybe start with an example of correlated data to justify the definition, then take a step back and ask what would happen if the points were independent. Otherwise, the explanation is pretty clear.

5.5

Such a tease! Correlation-Vector connection would have been the best idea to follow through on or make the entire video about.

When there were two plots towards the end, the left one was static, given the first case. Could’ve been more dynamic.

6.7

This is really good! It gives a good, nice intro to the concepts. It is not a revolutionary problem but it is still something that people often misunderstand. One piece of feedback: sometimes the variable names are confusing for new viewers - what is $\mu$ ? What is standard deviation? It seems to build on some of your other videos (which is not necessarily bad). Good job!