Episode 6: Graph Review
NARRATOR: Ah, graphs - love 'em or hate 'em, they will be an absolutely essential tool for analyzing economic behavior in this class. If you're already a graph meister, feel free to turn this thing off right now. I just want to go through very basic review.
OK, repeat after me: "Graphs are easy. I can do this. All I need to do is count." No, really! After all, what's a basic number line, except the graph? Of course, we will want to look at relationships between things, so we need to be able to count two things at the same time. I can do this by adding a second number line.
The good news is typically we won't even need all of this -- since we very rarely deal with negative numbers, we can leave these areas out, so that we soon have a more familiar looking set of lines, one horizontal, and one vertical. These two lines -- the axes -- will allow us to measure what's happening between two variables (I'll call them something generic right now, like X and Y).
It's possible the X and Y will exhibit what's known as a positive, or direct, relationship. If they do, then X and Y will move together -- that is, both of them increase, or both of them decrease, together.
Let me give you an example: instead of "X", what if I have "The number of A's that Dr. McGlasson gives this semester"? Instead of "Y," I have "the number of students who enroll for the class next semester." If I never give an "A," people aren't going to be very anxious to sign up for my class, and I have very low enrollment. If I give lots of "A's," however, the class gets to be very popular, and lots of students enroll. So I see that there is a positive, or direct, relationship between the number of A's that are given, and the number of students who enroll for the class in the future. Alternatively, X and Y may exhibit a negative, or indirect, relationship. If they do, then X and Y will move in opposite directions; that is, as one rises, the other falls.
For example, instead of the number of A's on horizontal axis, I put the number of F's given by Dr. McGlasson, and then on the vertical axis, I'm going to keep the number of students enrolling in the class. If I fail practically everyone in the class, why would anyone want to take my class in the future? I find that a large number of F's translates to a fairly low number of students enrolling.
If I hardly ever fail anyone, lots of students are going to take my class so very small number of F's translates to a fairly high level of enrollment. So I'm finding that there's a negative, or inverse, relationship between the number of F's that I give and future enrollment in my class. This negative or inverse relationship exhibited between the two variables has a negative slope.
There is one final possibility: X and Y could exhibit a constant, or independent, relationship. Let me give you an example where I have two completely unrelated variables that are going to illustrate this. What if, on the horizontal axis, I have the number of students enrolled in my class; on the vertical axis, the number of dogs in the McGlasson household (I happen to have two)? Now, whether I have no students, 50 students, 150 students -- I'm going to have two dogs. So if no students enrolled? Two dogs. 50 students enrolled? Two dogs. 150 students enrolled? Two dogs. I find with the constant or independent relationship, I have a straight horizontal line that's not showing either positive or negative slope; it's got a slope of zero. The number of dogs is completely unchanging as the number of students changes.
Over the course of the semester, I'll ask you whether you can identify a relationship as being a positive relationship or negative relationship, so you may want to see if you can think of some examples of each to give yourself some practice.
NEXT TIME: How do you use graphs to illustrate scarcity and choice?