 happens with that, with everything else removed. And that gives us a really good cause and effect kind of relationship with high, you know, predictive power as to whether or not, you know, one thing is causing another thing. That's going to be like a one to one comparison. Anytime we can do that, that would be great. Because then we'd be able to, you know, that's what we tend to try to do to isolate things to see a cause and effect. But obviously when systems get more complex, and the real world when we're looking at systems, the combination of things could result in different results that you cannot get to, you can't because the combination becomes to some a different result than if then the individual parts, right? So so now you have so that means that you have to look at some systems, you would think using multiple factors to see if there's a cause and effect relationship. Now, just realize, obviously, that if you have a one to one comparison, it's much easier to measure to see if there's a correlation than if you have multiple things going on. So the level of complexity will will expand greatly. Once you go to multiple regression type of analysis and your models will be a whole lot more complex. That's what you have to do. But again, the the the the surety that you have that your model is producing the right stuff becomes way more complex as you as you introduce more items into the into the factor. So for example, when you're predicting house prices, you're going to use things like the size, the location, the location and age of the house. Now, obviously, with a house, if you're trying to think the price of a house, how much should you sell it for or how much should you buy a house for? We always hear the mantra location, location, location, right? But that's really only one factor because the size of the house is going to be a factor as well. And the age of the house is going to be a factor. So when you're trying to come up with a model to predict the price of a house, then it's going to get quite complex quite quickly. And your model is probably not going to be perfect due to the fact that every house is unique, you know, right? Every house has its own location, has its own age and size and so on. So you can try to come up with models that give you predictive power and you can come up with complex models based on on multiple regression analysis. But again, as you do that, obviously your models are going to get much more complex. Okay, so correlation does not equal causation. There's our common phrase used often as a mantra. Why is this important? Misunderstanding, misinterpreting correlation can lead to wrong calculations and misguided actions. So it became becomes quite important because when people see a correlation, we want to as human beings determine that there's a cause and effect relationship. And if we do that and get it wrong, then we're going to be taking action on the wrong data. So remember that if there is a cause and effect relationship, we should have a correlation, right? There should be a correlation if there were a cause and effect relationship. But if there is a cause and effect or if there is a correlation, it doesn't necessarily mean that there's a cause and effect relationship. It's kind of the first step that we would do mathematical calculation to see correlation to then make the prediction as to or try to give validation to a hypothesis that we might have had already, that there's a cause and effect relationship, right? But it's not the final factor. So species correlations, relationships that seem meaningful, but are not due to coincidence or external that are due to coincidence or external factors. So if you're looking at a whole bunch of data sets, it's possible that you find correlate, you will find correlations that just happened basically randomly, right? There's no reason that the things should be moving in alignment with each other, but they are. And when you find those and you realize that they're that they're species, it's kind of funny, because then you can come up with like scenarios. Well, how would that be that this these two things will line up because obviously they don't. That's why it's funny. But so relationship between ice cream sales and shark attacks, for example, if you just looked at all the data and for some reason, you're look at these two data sets. And as ice cream sales go up, shark attacks go up. Well, probably they're probably not related. Now you could imagine a scenario, maybe they're somehow related in some way because ice cream sales went up because it's hotter. And they're it's hotter. And they're more people are at the beach or so I don't know. You could you can kind of try to figure out if there is some kind of link between the two. But the point here is that there might not be a link between the two that might be a completely useless exercise because maybe there is no cause and effect relationship. It just happened to randomly come up that these two things that are totally not related. I mean, you might be talking about like ice cream sales somehow in the middle of the country, not anywhere by the ocean or in the middle of any landmass versus shark attacks, which you would think would only happen at the beach. How would that be correlated can't possibly be correlated. But they're I mean, it can't possibly be a cause and effect relationship, even though you might have this random correlation kind of thing. Number of people who drowned by falling into pool and films Nicholas cage appeared in. So again, those things would be completely not correlated. If you looked at those data sets, you know, like pool drowned in somehow or correlated mathematically to the number of films that Nicholas Cage has appeared in. Does that I mean, could maybe does does Nicholas Cage cause people to not swim well or want to want to jump in a pool even though they can't really know that doesn't make any sense, right? So but but again, if you just looked at enough data randomly, you will find correlations like that. So that's why the phrase comes into play. Correlation does not necessarily equal causation, even though correlation is an important step to try to determine if there is causation. By the way, the next question, of course, if we determine that there is causation is to make sure that we have the causal factor correct because the next question would be, what is the causal factor and the cause and effect relationship and the other common problem and sometimes manipulation that people make when they're being dishonest is to reverse the cause and effect relationship between the data points. And if you're acting on something based on the concept or idea that there's a mathematical relationship or correlation and that there's an assumption that that's due to a causation, but then you flipped. What's the causal factor in that relationship that could lead to the wrong action, right? You want you need to get the causal factor correct as well.