So let's say you've got a bunch of numbers and you put them on a scatter plot. It might look a little bit like that. Now, I haven't labelled the axes, I don't really want to do that.
Now, once you've done that, you should be able to interpret the scatter plot. You're taking all of those raw numbers, you're putting them on a graph, and then that graph should tell you something. Now, let's look at this graph here. You can see the dots are all random, it's all over the place. Sometimes the number's very large on the x-axis and very small on the y-axis.
Sometimes it's very large. on the x-axis and very large on the y-axis. We say that a scatter plot like this has no association here. Now an example of a scatter plot that has no association might be one with height on the x-axis and maths mark on the y-axis.
You wouldn't expect people that are taller to be better at maths or people that are taller to be worse at maths. So there is no association between height and maths mark. Now look at this graph. You can see that the dots go upwards.
That is, as the x-axis gets larger, as the number there gets larger, the number on the y-axis also gets larger. We call this a positive association. Now, my favorite example of positive association might be, as the temperature goes up, ice cream sales also go up.
If it's zero degrees, you wouldn't expect to sell very many ice creams. If it's up to like 30 or 35 degrees, everyone's going to come to your ice cream truck and buy. ice creams so there is a positive association.
Now hopefully you guessed we were going to have negative association as well. X-axis, Y-axis and the dots moving down. As the X-axis increases the Y-axis decreases.
So as it gets hotter the soup sales in my soup truck go down because people don't want to eat soup when it's really hot outside but they do want to eat a lot of soup when it's cold outside. Now, I am going to rub this one out, but I do want to show it to you really quickly. We can have all sorts of other associations as well.
So, for instance, time of day here, the temperature starts off cold at 5 in the morning, and then it starts to heat up as we get to midday, and then it starts to cool down again. So, we don't really call this a positive or negative association. It's got some other stuff.
You'll learn about that in another one, but I just want to show you that, hey, we can have all sorts of shapes. So, now that we've talked about that, we really need to talk about linear versus nonlinear associations. So, linear, like the word line. Something's linear if it looks like you can draw a straight line through it.
That's supposed to be straight. Okay, that's a straight line. Something's non-linear if it doesn't look like you can draw a straight line through it. If, instead of drawing a straight line, it would make more sense to do something a bit more like that. Alright, so...
Lots of linear examples that I already sort of went through where I think this would be linear and this would be linear up to a point. This one here, you've seen graphs like that before in the news recently with like COVID-19. Now, that's a special kind of nonlinear relationship called exponential.
But that's sort of a bit beyond where I want to go here. I just want you to know that there's linear ones, straight lines and nonlinear, not straight lines. And finally, we come to strength of association.
So you can see that these are really close together and you can see that the explanatory variable explains the response variable really well. They're very closely correlated. We call this a strong association. This one here, you can see they're a bit more spread out. The explanatory variable is not explaining the response variable like exactly, but it is obviously contributing there somewhat.
So we use the word moderate. And this is really hard to kind of see here, but you can see it's just kind of giving the impression that it's moving up in this direction. You can see there's not many dots here, there's not many dots here, and they're sort of following this pattern here. We call that a weak association.
Now, just so you don't get the wrong idea, these are all strong, moderate, and weak positive associations. But I can turn them around as well and have a strong negative association. A strong negative association.
Now there probably is just one more thing I need to show you here. If a dot looks like it's lost its way, if all of the other dots are in a sort of a pattern, and one of them is like way out here somewhere, or maybe way up here somewhere, we call those dots outliers. They're strange. They're different to all of the others.
So now that I've told you all of this, you should be able to look at a graph like this and interpret it. And so you would say something like, hours of homework and maths mark have a... Looks kind of like that.
So a moderate positive association and you can say something like It is noted there are two outliers. And we've got one here and one here. And we can write some more there.
We can say one of the outliers does lots of homework and doesn't do very well in maths. And one of the outliers doesn't do very much homework and does very well in maths. So outliers can lie on both sides there.
So you need to be able to look at those graphs, interpret them, and use your... mathematical words. Moderate positive association, outliers.
Okay, that is interpreting scatter plots.