# Question Video: Understanding Correlation Mathematics • 8th Grade

Suppose variable 𝑥 is the speed of a train and variable 𝑦 is the time for the train to get to the station. You suspect that the more the train increases its speed, the less time it takes to get to the station. Does this follow a positive correlation, negative correlation, or no correlation?

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### Video Transcript

Suppose that variable 𝑥 is the speed of a train and variable 𝑦 is the time for the train to get to the station. You suspect that the more the train increases its speed, the less time it takes to get to the station. Does this follow a positive correlation, a negative correlation, or no correlation?

First, let’s consider what we mean by a positive correlation, a negative correlation, or no correlation. The 𝑥- and 𝑦-variables will have a positive correlation if as one of the variables increases, so does the other. A negative correlation, on the other hand, is when one of the variables is increasing as the other variable decreases. In this image, as 𝑥 increases, 𝑦 is decreasing. And we would say there’s no correlation if the pattern does not fit into either one of these other categories if there’s no relationship between the increase of one variable and its outcome on the other.

So let’s consider our scenario. Along the 𝑥-axis is the speed of a train. Along the 𝑦-axis is the time it takes to get to the station. If we say, for some speed 𝑎, it will take 𝑏 amount of time to get to the station, for some faster speed 𝑐, we expect that the time it would take to get to the station would be less than the time it took at the slower speed. We’re saying the faster the train goes, the less time it will take to get to the station, which means as 𝑥 increases, 𝑦 decreases. And we can expect a negative correlation between these two variables.