What is a (mathematical) model?

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"Model" is a vague term that means different things in different contexts. Here I clear it all up in the context of statistics!

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I have been a modeler for 11 years. I really like your expression about "model is a relationship". Just want to add a bit of my point of view. To me, statistical model is a relationship derived from examining the data using statistical theories. The relationships from these models usually can not derive from a physical law. Whether or not the relationship is linear/nonlinear/exponential/log, they are all pure speculations based on data. There are also physical models, such as modeling the speed of a car according to its weight. These are also models but the relationships are derived from the physical laws (in this case, Newton). Also in engineering, there are lots of empirical models, where the relationships ranges from non-physical to semi-physical, such as Manning's equation. Part of the model can be explained by physics, but part of it is not. Just my two cents to share.

Uynix

To make things simple to understand without making them empty of their substance. This is the essence of being human, able to internalize things in such a way that sharing with others is like singing a song.

Patrick_Bentolila

Thank you for the great explanation. I have been learning all these complicated concepts evolving around MCMC. Only now have I realized that I wasn't completly sure what the term model was supposed to be in that context.

developandplay

I love your content! It makes it so easy to understand topics that can be deeply technical.

You are awesome!

oscarrosalescorzo

Model means so many things and can be associated to any field, may it be in science or art. I have been in the field of engineering for years now, and I like that it is expressed in simple terms which can be understood be so many while being really catchy. I dreaded the term model especially in statistics as it was one of the hardest subjects for me while studying, but this simple "relationship" is derived from the data collected by experimentation or given by the scenario. I saw a comment in the video wherein he/she stated that whatever the relationship is, there are purely speculations based on the data, which I think is clever way to see it. From this relationship, one can see the trend and prepare a equation or a prediction of the trend which most of the technology heavily relies on. While the model can provide the mathematical equation, it can only approximate or assume the answer to the missing variable. This is where I think a model has a flaw unless is there is an infinite amount of data in the set (which is impossible to have given the time and given why people opt to use a model).

batteryCELLE

Thank you so much for your lovely explanation. I was wondering about how to use models to come up with data and now I understand. Thanks.

olanola

This dude even explains what is model, he knows everything, Inifinite Bam for Him!!!!

harryliu

Your intro BGM makes me feel so comfortable. Triple Bam! haha

dsd

I love the introduction song ! nice bro well done

for me it is very difficulty subject to understand but your approach was different !

God bless !

anthonyraj

the dotted lines are not actually the distance from the model to the actual data points. the distance between a point and a line is the perpendicular drawn from the point up to that line

perjoraxperj

Thank you! I loved your work on GLM, would really appreciate it if you had a look at mixed models as well

DanielSoll

You are awesome❤❤❤❤❤❤ thank you for making Stat fun. Can you do videos on econometrics?

setarehbakhshi

Sir make videos on (negative binomial, beta and gamma )
Distributions by covering their examples.

anaswahid

Good morning!
At 2:37 you mention, 'sometimes, a model isn't a straight line.'
Please elaborate.
Thanks

amitabhjayaswal

So, in terms of machilne learning, can we say that the model is the hypothesis? Since a hypothesis is an equation that best represents/estimates the relationship between certain factors or features (eg mouse size and weight)

PRATIK