Interpreting Graphs, Correlation, Causation, and Omitted Variables
1. Reading and Understanding Graphs
Interpreting Graphs, Correlation, Causation, and Omitted Variables - Video Tutorials & Practice Problems
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Interpreting Graphs (Part One)
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Alright, so now let's do a quick review on interpreting graphs, right? We've been making them up to this point. Now let's analyze them a little bit. So first let's define these two points. These two terms, we've got correlation which is the relationship between two variables that allows us to predict outcomes, right? Um So things are thought to be correlated if we are able to make predictions based on this information and our next uh term here causation, it's a relationship where one event triggers another one. So this is one thing causes another thing. This is basically cause and effect relationship. Right? So causation cause and effect. So let's look at an example here, we've got a graph here with outside temperature on the X axis and ice cream sales on the Y axis. So what I'm trying to point out is that as the temperatures rise, people are gonna buy more ice cream. So we might see a graph something like this, right? Where as the temperature is rising. So are the sales of ice cream? Cool. Um And the idea here is right, we see outside temperature going up, sales going up this relationship. What we see when they go up together or down together. This is called a positive correlation, positive correlation. Um And it's also sometimes called a direct relationship. So this is when we see something like the X values going up, then the Y value is also going up or when the X value goes down, same thing. The Y value is also going to go down, right? So up together or down together is a positive relationship compared to what we call a negative relationship or an inverse relationship. Um That's when they move opposite. So that would be something where we see the X value going up, keep it consistent with the colors there. We'll see the Wye Valley going down and the opposite, right? X going down and why going up? So, let's think of an example of and uh negative or an inverse relationship. Let me get out of the way. We'll put a little graph right here. So, maybe a negative relationship might be something. Uh let's do a little one. Maybe we've got, you know, uh number of miss classes or let's say, absences over here, absence from class. And over here we'll put your grade, right? So the idea is while absences are low, so if you've got zero absences, you might have a really high grade. And as the absences go up, your grade falls. Right. So this is a negative relationship. The absences are going up and your grade is going down. Cool. So now, in the next video, we'll do a little more discussion about interpreting graphs and some of the pitfalls that you might run into
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Interpreting Graphs (Part Two)
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3m
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Alright. So now let's discuss some of the problems we might run into when interpreting graphs. So let's look at this left graph first. We've got wages and education. So education on our X axis and wages on our Y axis. Um And you might expect to see something like this where as education goes up so do our wages, right? That's probably why a lot of you are studying right now. Um And the idea is that yeah, your wages will go up in the future as you are more educated. Cool. But what are we missing here? Right. There's another factor to the compensation equation that we might be leaving out. Um So the idea here is that sometimes a graph might omit a variable. So we call this the omitted variable bias. Alright, omitted variable. Um And the idea here is that although education is important for your for your to determine your wage. So is um your experience. Right? So experience in this case is going to be our omitted variable. Right? I would imagine that there is some correlation between the amount of experience you have and what your wage is gonna be. Alright. So that is one way that a graph can omit some information. Right? We're emitting a variable here. Um It's not showing us the full picture. I'm going to get out of the picture now to use this right graph to explain what we call reverse causality, reverse causality. So remember causation is where one thing uh One thing comes before the other right? It's a cause and effect relationship. So reverse causality you can imagine is where you take the effect and you think that the effect causes the cause, right? You're looking at it backwards, not the cause causing the effect. Where you're looking at the effect causing the cause. So it's reverse causality. So the idea here is something like this where we have police officers on the X axis and crime on the Y axis. And the idea here is that it's saying that as police officers increase in the city, so does the crime, right? And that seems kind of backwards, Right? So the idea is like you look at a city with a lot of crime and you're like, hey there's a lot of police officers in that city. So since there's a lot of police officers, that must be why there's a lot of crime um instead of thinking of it the other way around, right? So a city with a lot of crime has a lot of police officers, so they're kind of mixing up the variables here. The idea being that the graph is showing that um police officers cause crime rather than crime causing police officers. Cool. So those are two types of pitfalls that we might run into an omitted variable and reverse causality. Cool, so let's move on to the next video