In this section, we want to start talking about the relationship that exists or if any relationship exists between two variables so to start that conversation, we want to introduce a new type of graph, which is called a scatter plot so scatter plots are used to graph paired data or dependent data, so the thing to keep in mind is for a scatter plot will always need two separate data sets, so we’re going to graph that pair data on a single coordinate plane, so unlike histogram’s that only graph one variable at a time, a scatter plot is going to depict both of those variables plotted at the same time, so one variable will be represented by the X-axis, while the other is represented by the Y-axis. So what’s going to happen is our paired points are going to turn into. XY coordinates, meaning those are points that we can plot and scatter plots are going to help us understand what we refer to as the Association or again, the relationship between two variables so Association just meaning relationship and again, if any exists, there may be an association. There may be no association between these two variables, so scatter plots are going to help us understand that by examining the trend of the scatter plot, the shape and the strength of any Association that we might see. So we have a few different scatter plots depicted here below so again. What’s happening is our horizontal axis or X axis is representing values for one variable and the vertical axis. The Y axis is representing values for our second variable. The paired points get turned into these coordinate pairs, which we can then plot as points and now we can talk about these three different descriptors, trend, shape and strength. So in this case, we can see that as we read the graph from left to right, Our points are increasing so we could describe the trend as an increasing trend. The shape in this case is approximately linear because our points are following a straight line pattern, more or less and then in terms of strength, we want to talk about, Basically how close those points fit to that shape that we identified so in this case we’re saying it’s a linear pattern and in this case, the strength of that. Association seems to be very strong because the points closely. Follow that straight line pattern. So that’s an example of an increasing trend. If we jump down to the second row, we have an example of a decreasing trend. So in this case, our points are headed down as we read the graph from left to right. We still have a linear shape and again we have a relatively strong strength or a strong Association. Since again, they follow pretty tightly to that straight line pattern. So other cases we might see would be in our second graph here. We still have an increasing trend. We have a linear shape, but we have not necessarily a weak Association, but not quite as strong because the points, there’s a little bit more scatter in our graph, so we might refer to this as a moderate or fairly strong Association. First graph on the second line is again a decreasing trend. The shape is still more or less linear and again we have more of a moderate strength to that Association because our points aren’t following that straight-line pattern quite as closely as they did. In this other example For our last two. We’ve got a graph here where the points are sort of scattered around. There’s no particular straight line pattern. No kind of shape really occurring here. So in a case like this, we would simply say that it looks like there’s no. Association the points don’t seem to be following any specific pattern. They’re just sort of scattered or spread around, and then our last example we still have sort of a bit of scatter, not exactly a linear pattern, but if we sort of trace the pattern that these points are going, we would trace out sort of a parabola shape, so in terms of shape we could refer to this as a changing shape. We could refer to the shape as a parabola or a curve and again we’ve got a relatively moderately strong. Association the points follow pretty closely to that pattern, but there are a few points that kind of spread away from that. So in that last example, again, what we have is a case of changing trend, not just in the first few examples where we saw specifically just an increasing or excuse me increasing or decreasing trend for our purposes, What we’re going to mostly be interested in finding are variables that follow a linear shape, so either of these first four examples, there are statistical processes for looking at scatter plots and variables that follow other types of shapes, Parabolas different types of curves, but for our purposes we’re going to be mostly concerned with identifying when two variables have a linear shape and then talking about whether that’s an increasing decreasing trend and how strong that correlation or how strong that Association is so in our first example, let’s take a look at given some data actually constructing a scatter plot and then describing the trend shape and strength of that graph, so with our data in statcrunch, we can select graph and then scatter plot will select our first variable and second variable. We have some other options here, but for now, that’s all. We really need to indicate and click compute that will generate this scatter plot for us and we can start to discuss the trend and shape of that graph, so what we could say in this case is there is a fairly strong, positive linear. Association, so these points more or less. Follow a straight line pattern. I think it’s fairly strong because we do have some points that are a little bit further away from maybe where that straight line would fall, but a fairly strong, moderately strong, positive linear Association. Since as we read from left to right, the graph is increasing, so there’s a fairly strong, positive linear association between these variables in the context of the data. What that would mean is countries with more rollercoasters tend to contribute more to tsunami aid. So if we see a positive correlation or a positive association, what that’s telling us is that as one variable increases, so does the other. So as we see countries with larger numbers of rollercoasters, those same countries tend to have larger amounts of money that they contribute to tsunami aid.