Interpreting Graphs, Correlation, Causation, and Omitted Variables - Online Tutor, Practice Problems & Exam Prep

Interpreting Graphs (Part One)

Alright, so now let's do a quick review on interpreting graphs. Alright? 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? So things are thought to be correlated if we are able to make predictions based on this information. And our next term here, causation, it's a relationship where one event triggers another one. So this is one thing causes another thing. This is basically a 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 going to 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? 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, 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, 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 y value going down and the opposite, right. X going down and y going up. So let's think of an example of a 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, let's do a little one. Maybe we've got, you know, number of missed 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 0 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.

Interpreting Graphs (Part Two)

Alright. So now let's discuss some of the problems we might run into when interpreting graphs. Let's look at this left graph first. We've got wages and education, so education is on our x-axis and wages on our y-axis, 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, and the idea is that yes, 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. So the idea here is that sometimes a graph might omit a variable. So we call this the omitted variable bias, alright? This omitted variable, and the idea here is while education is important for determining your wage, so is 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 going to be. Alright, so that is one way that a graph can omit some information, right? We're omitting a variable here; 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 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. 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 a 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 are a lot of police officers in that city. So since there are a lot of police officers, that must be why there's a lot of crime. 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 police officers cause crime rather than crime causing police officers.

Cool. So those are our 2 types of pitfalls that we might run into: an omitted variable and reverse causality. Cool? So let's move on to the next video.