Linear regression and correlation
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Estimating the line of best fit
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Correlation and Causality
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Squared Error of Regression Line
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Proof (Part 1) Minimizing Squared Error to Regression Line
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Proof Part 2 Minimizing Squared Error to Line
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Proof (Part 3) Minimizing Squared Error to Regression Line
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Proof (Part 4) Minimizing Squared Error to Regression Line
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Regression Line Example
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Second Regression Example
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R-Squared or Coefficient of Determination
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Calculating R-Squared
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Covariance and the Regression Line
Correlation and Causality Understanding why correlation does not imply causality (even though many in the press and some researchers often imply otherwise)
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- I have this article right here from WebMD
- And the point of this isn't to poke holes at WebMD.
- I think they have some great articles, and they have some great information on their site.
- But what I want to do here is to think about
- what a lot of articles you read, or a lot of research you might read, are implying
- and to think about whether they really imply what they claim to be implying.
- So this is an excerpt of an article, and the title of the article says:
- "Eating breakfast may beat teen obesity."
- So they're already trying to create this cause and effect relationship.
- The title itself says: 'If you eat breakfast, then you are less likely,
- or you won't be obese, you are not going to be obese.'
- So the title right there sets up this, that eating breakfast may beat teen obesity,
- and then they tell us about the study.
- In the study, published in 'Pediatrics', researchers analyzed the dietary and weight patterns
- of a group of 2,216 adolescents over a five-year period
- from public schools in Minneapolis, St. Paul, Minesota.
- and I won't talk too much about -this looks like a good sample size,
- it was over a large period of time, I'll just give the researchers the benefit of the doubt,
- assume that it was a broad audience, and that they were able to control for a lot of variables,
- but then they go on to say that the researcher's right,
- that teens who eat breakfast regularly had a lower percentage of total calories from saturated fat
- and ate more fiber and carbohydrates.
- - than those who skipped breakfast-
- and to some degree this first sentence is obvious
- breakfast tends to be things like cereals, grains, um, you know,
- you eat syrup, you eat waffles,
- that all tends to fall in the category of carbohydrates and sugars,
- and frankly, that's not even necessarily a good thing,
- not obvious to me whether bacon is more or less healthy than downing a bunch of syrup
- or fruit loops, or whatever else, but we'll let that be right here
- 'In addition, regular breakfast eaters seemed more physically active than their breakfast skippers'
- So over here they're once again trying to create this other cause and effect relationship
- 'Regular breakfast eaters seemed more physically active than their breakfast skippers'
- So the implication here is that breakfast makes you more active
- And then this last sentence over here, they say:
- 'Over time, researchers found teens who regularly ate breakfast tended to gain less weight,
- and had a lower body mass index (BMI) than breakfast skippers'
- So they're telling us that breakfast skipping -this is the implication-
- breakfast skipping is more likely, or can be a cause, of making you overweight,
- or maybe even making you obese.
- So the entire narrative here, from the title all the way to every paragraph,
- is: 'look, breakfast prevents obesity,'
- 'breakfast makes you active',
- 'breakfast skipping will make you obese'
- so you say, 'boy, I HAVE to eat breakfast'
- - you should always think about the motivations and the industries around things like breakfast -
- But the more interesting question is:
- Does this research really tell us that eating breakfast can prevent obesity?
- Does it tell us that eating breakfast will cause some to become more active?
- Does it really tell us that breakfast skipping can make you overweight, or make you obese?
- Or, what's more likely, are they just showing that these two things tend to go together?
- And this is a really important difference
- And let me kind of state, slightly technical words here
- and they sounds fancy, but they really aren't that fancy,
- Are they pointing out 'causality', which is what it SEEMS like they're implying?
- 'Eating breakfast CAUSES you to not be obese'
- 'Breakfast CAUSES you to be active'
- 'Breakfast skipping CAUSES you to be obese'
- So it looks like they're kind of implying causality,
- they're implying cause and effect,
- but really what the study looked at is 'correlation'
- So, the whole point of this is to understand the difference between causality and correlation
- 'cause they're saying very different things.
- '... causality versus correlation...'
- And, as I said, causality says: 'A causes B'
- while correlation just says: 'A and B tend to be observed at the same time'
- 'Whenever I see B happening, it looks like A is happening at the same time,'
- 'whenever A is happening, it looks like it also tends to happen with B.'
- And the reason that it's super important to distinguish the distinction between these
- is you can come to very, very, very different conclusions.
- So the one thing that this research does do, assuming that it was performed well,
- is it does show correlation.
- so this study does show correlation.
- it does show, if we believe all of their data, that breakfast skipping correlates with obesity,
- and obesity correlates with breakfast skipping
- we're seeing it at the same time
- activity correlates with breakfast, and breakfast correlates with activity
- and all of these correlate
- What they don't say, and there's not data here that lets me know one way or another
- 'What is causing what?'
- or maybe you have some underlying cause that is causing both.
- So, for example, they're saying breakfast causes activity,
- or they're implying breakfast causes activity, they're not saying it explicitely,
- but maybe activity causes breakfast,
- maybe, people who are more active are more likely to be hungry in the morning
- '...maybe activity causes breakfast ...'
- And then you start having a different takeaway.
- Maybe you say, 'wait, maybe if you're active and you skip breakfast'
- - and I'm not telling you that you should-
- 'maybe you'll lose even more weight, maybe it's even a healthier thing to do'
- we're not sure, so, they're trying to say
- 'look, if you have breakfast, it's gonna make you active, which is a very positive outcome'
- but maybe you can have the positive outcome without breakfast
- who knows?
- Likewise, they say breakfast-skipping, or they're implying,
- that breakfast-skipping can cause obesity,
- but maybe it's the other way around
- maybe people who have high body fat, maybe for whatever reason
- they're less likely to get hungry in the morning
- so maybe it goes this way, maybe there's a causality there
- or what's even more likely, maybe there's some underlying cause which causes both of these things
- to happen
- and you can think of a bunch of different examples of that
- one could be the physical activity
- so physical activity - and these are all theories, I have no proof for them -
- but I just wanna give you different ways of thinking about the same data
- and maybe not just coming to the same conclusion that this article
- -it seems like- is trying to lead us to conclude that we should eat breakfast
- if we don't want to become obese.
- So maybe if you're physically active, that leads to you being hungry in the morning,
- so you're more likely to eat breakfast,
- and, obviously, being physically active makes it so that you burn calories,
- you have more muscle, so that you're not obese
- so notice: if you view things this way, if say that physical activity is causing BOTH of these,
- Then all of a sudden you lose this connection between breakfast and obesity
- Now you can't make the claim that if somehow breakfast is the magic formula
- for somebody to not be obese
- So let's say that there is an obese person,
- Let's say that this is the reality, that physical activity is causing both of these things,
- and let's say there is an obese person, what will you tell them to do?
- will you tell them 'eat breakfast and you won't become obese anymore'?
- well, that might not work, especially if they're not physically active
- I mean, what's gonna happen if you have an obese person who's not physically active,
- and then you tell them to eat breakfast?
- maybe that will make things worse,
- and, based on that, that the advice or the implication of the article is the wrong thing,
- physical activity may be his thing, that he should be focused on
- maybe it's something other than physical activity
- maybe you have sleep
- maybe people who sleep late and they're not getting enough sleep
- maybe that leads to obesity
- and obviously because they're not getting enough sleep they wake up as late as possible
- and they have to run to the next appointment
- - or they have to run to school, in the case of students -
- and maybe that's why they skip breakfast
- so, once again, if you find someone's obese, maybe the rule here isn't
- to force some breakfast down their throats,
- maybe it'll become even worse, because maybe it is their lack of sleep
- that's causing their metabolism to slow down, or whatever
- so it's very very important, when you're looking at any of these studies,
- to try to say 'is this a correlation? or is this causality?'
- If it's correlation, you cannot make the judgement that,
- 'hey, eating breakfast is necessarily gonna make somebody less obese,'
- all that tells you is that these things move together.
- A better study would be one that is able to prove the causality.
- And then we can think of other underlying causes that would kind of
- break down the narratives that this piece is trying to say
- -I'm not saying it's wrong!
- maybe it's absolutely true that eating breakfast will fight obesity
- But I think it's equally or more important to think about what the other causes are,
- not to just make a blanket statement like that.
- So, for example, maybe poverty causes you to skip a breakfast, for multiple reasons,
- maybe if both of your parents are working, there's no one there to give you breakfast,
- um, maybe there's more stress in the family, who knows what it might be,
- and so, when you have poverty, maybe you are more likely to skip breakfast,
- and maybe when there's poverty, maybe you have two
- - the parents are working, and the kids have to make their own dinner, and whatever else-
- maybe they also eat less healthy, so eat less healthy at all times of the day,
- and that leads to obesity.
- So, once again, in this situation, if this is the reality of things,
- just telling someone to also eat breakfast regardless of what that breakfast is,
- even if it's fruit loops or syrup,
- that's probably not going to help the situation
- Maybe eating unhealthy dinners is the underlying cause
- '... unhealthy dinner...'
- And if you eat an unhealthy dinner,
- maybe by breakfast time, you're not hungry still,
- 'cause you binged so much on dinner, so you skip breakfast,
- and this also leads to obesity.
- but once again, if this is the actual reality,
- doing the advice that that article is saying may actually be a bad thing.
- If you eat an unhealthy dinner, and then force yourself to eat a breakfast when you're not hungry,
- that may make the obesity even worse.
- So the whole point of this video isn't to say that the implications from that article are necessarily
- wrong
- But the important thing is to just realize that it might be wrong,
- and just because you saw this correlation with the data,
- it doesn't mean that eating breakfast is somehow magically going to fight obesity
Be specific, and indicate a time in the video:
At 5:31, how is the moon large enough to block the sun? Isn't the sun way larger?
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