 This video is going to talk about modeling. When we talk about modeling, you need to refer to your worksheet. And we're going to be doing regressions to find equations for these models. And it tells you here exactly how to do it. Now I'm going to go step by step, but I want you to see that first we're going to enter the data, then we're going to look at the scattergram, and then choose the type of regression to find the equation. But all the steps are listed here for you. And if you need to refer back to that, it's there for you. So let's get started. Our first problem says the total value of goods and services produced by nation is called its gross domestic product, or GPD. I know you can read all that. So let's just talk about what we're going on here. It's showing us here over here in the X column that we want to start in the year 1970, and that will be year zero. So when we go over to our calculator, then first thing we need to do is hit the stat key over here by the arrows, and then we want to press enter. Now I've already entered all my data in. So this time I'll just use the data that I have. And next time I'll show you how to clear it out and put it in. So we have all this data here. And the first thing it asks us to do is to draw a scatter plot. Well, the calculator will do that. And then we could just sketch it to do that. You go to Y equal, and then you see this plot one up here at the top. We need to arrow up there. And then we want to press enter and that will highlight it for us. Now I want to do one extra thing for you. You can follow it along in this video. If you do it once, you shouldn't have to do it again. And that is to do second Y equal. And that's just going to set up the plot. You'll see here it says the plot one is on, but we want to enter there. Because what you need to see is this type here tells that I have highlighted here. The very first one says that it's going to be independent dots. And that's the best way to look at a scatter plot. And then the other important part here is this X list and Y list. There are L1 is going to be the X values and L2 is the Y values. It might not be set up that way. So if you just take a look at it real quick, you'll know that it's set up that way and then you never have to change it. And I personally like to use a box for my mark just so I can see the difference between it and if I happen to graph a line on top of it. But you can do any mark you want. That's not necessary. So let's go back to Y equals. See that the plot is turned on. Then we want to hit zoom nine and it automatically sets a window for us. And we have this graph here. So I'm just going to sketch that real quick. Oh my, it looks like I have something that looks pretty linear. Okay. It doesn't have to be perfect. I'm just going to kind of guesstimate. So as it says, the side of the association is positive or negative. Remember that positive goes up from left to right and negative goes down from left to right. So this one's going up. So it's going to be a positive association. And then we want to find the linear regression. So we go back over to stat and then over here at calculate, you need the arrow over, right arrow to calculate. And then we choose four, which is linear regression. The most common ones we'll use will be linear regression four and five, which is quadratic regression. But we just had to hit the number four and then press enter because that's the kind of regression we want. And it's going to give us our equation here and say that that's Y equal AX plus B. So A is 1.0. So Y is equal to 1.027XAX plus B. And B is positive. So it's plus 3.0928. So 093. And then you may or may not have these Rs in here. It's just statistical. It tells us how close we are. The closer to this number is to 1, then we know that that's very accurate. And this is very, very close to 1. So we would say that this is a very strong correlation. If you need to know how to put that one on there because I don't think I put this on the sheet, you would go to second 0. It says catalog above that. And then see this alpha up here. It means that the letters are on. So I can just put D because what I want to go to is diagnostics. I'll have to arrow down that to get there. Iagnostic on is what you would want. So you press enter. Mine are already on. But you would just press enter to see that that's what you want. And then press enter again. You notice above it it said diagnostics off. If you don't like those R values and you aren't going to need them for something else, you can go in and turn them off just the way we turn them on. Let's do our second example here. Leonardo da Vinci's famous diagram. That's what the man with all the lines on it. The illustration of the human body shows proportions. And that's what we're going to look at. We're going to look at the wingspan. The comparison of a person's height to the wingspan, which is just the let's put this stuff in here. I'm going to show you how to clear it out. So go to stat, edit, press enter. Now I want to clear this data out. So I'm going to arrow up to L2 and then press clear. It says on your paper, don't hit delete because then you'll totally lose the column when I press clear and enter. I still have my L2 column. I just don't have anything in it anymore. And I can arrow over to L1 and highlight that go up and highlight it clear and enter. And now I have two fresh columns to work with. And I can enter in this information that we have in our table here. So I'm going to just press 61 and then enter. And then 61.5 and enter and so on. All my X's are going to go into L1 and I enter after each one. So you go ahead and take the time to do that while I do. Take a real quick look and make sure that it looks like you would probably enter the numbers correctly and then arrow over to L2 and enter all that in. It looks like those look pretty good. Everything matches up here at the bottom with 52 and the 51.5 match up. So I know I have even columns and I want to look again at the scatter gram. My plot is already on. So I don't have to worry about that again. But I'm just double checking. I'll do zoom nine. It sets the window and then allows us that's much better to graph here. And I don't even think that these aren't really my axes. I don't think that we just need a scatter gram just because we really just want to know what kind of shape does it look like it is. Okay. Mine's not perfect. It doesn't look exactly like what you see, but you kind of get the idea. So we want to know if it's linear or nonlinear. And we would call this linear. I could see that we could get a line may become something like this. Somewhere in there that would be a possible line. And is it positive or negative? Again, it's increasing. It's going up from left to right. So it's a positive association. And then we need to find the regression again. So stat over to calculate. We're going to do linear. So that's four and enter. And now we have y is equal to point. I'm just going to go two decimal places this time. So nine five nine would be point nine six X plus one point five five four would be one point five five. And then it asks us to find the wingspan of a student that is height of 65 inches. Well, I want to do this a quick and easy way. I'm going to plug it into my calculator point nine six X plus one point five five. And then I'm going to do second window. And then that would let me do my table setup. And I want to start at 65 because that's the value I want. These are X values that I'm plugging in. So I want to plug in an X X is equal to 65. So I want to plug in 65 and then I just do second graph to look at the table. And it tells me that when X equal 65 Y is equal to 63 point nine five. And that feels like about the same. Most cases it's a little bit smaller than the actual height of the person. And that's what happens here. So we can say that feels pretty good.