- Data representations | Lesson
- Data representations | Worked example
- Center and spread | Lesson
- Center and spread | Worked example
- Random sampling | Lesson
- Random sampling | Worked example
- Scatterplots | Lesson
- Scatterplots | Worked example
- Interpreting linear models | Lesson
- Interpreting linear models | Worked example
- Correlation and Causation | Lesson
- Correlation and causation | Worked example
- Probability | Lesson
- Probability | Worked example
Sal Khan works through a question on scatterplot from the Praxis Core Math test.
- [Instructor] We are asked, which of the following best describe the trend shown in the scatterplot above? And here the scatterplot is to the left. Pause this video and see if you can figure this out. It says, choose all answers that apply. Let's just look at what they say. They say there's a positive linear relationship between x and y. What is a positive linear relationship look like? In a positive linear relationship, that means that as x increases, y would increase, so that would be the positive part, and the linear would mean that it looks like the dots that are being plotted are roughly along a line. Let me do what a positive linear relationship might look like in red. If it looks something like this, and something like this, that's what a positive linear relationship would look like. Because it looks like you could fit a line to that data. Now if you look at the data in question over here, it doesn't look exactly like that. You have a positive relationship in this part of the data, whereas x increases, it looks like, in general, y is increasing. But then, at this part, you have a negative relationship, and this part looks a little bit flatter. In general, it's not always positive, and it also doesn't look linear. It looks like more of a curve. Some would say this looks parabolic. So this does not look linear, nor does it look positive. So I would rule this one out. There is a nonlinear relationship between x and y. Yes, in general, you could view a nonlinear relationship as a relationship where it would be hard to fit a line to that data. And it would be hard to fit a line over here. If you tried to make a line go like this, it would miss all of that data. If you tried to make the line go like this, then all of this data seems off. If you tried to make a line go like that, then really nothing seems to fit that data. So I like this. This is a nonlinear relationship between x and y. As x increases, y increases, then decreases. So as x increases, y does increase in this part of the data. And then eventually, as x increases, then y decreases. So I would say that this one is true as well.