What type of linear correlation might exist between the number of hours spent on social media and the number of hours spent doing homework?
Let’s think about this term, linear correlation. Linear correlation refers to a straight-line relationship between two variables. If two variables have a linear, positive correlation, then we can say that as one variable increases, so does the other. And we’re therefore able to draw a line of best fit on the scatter diagram that represents both of these variables, as shown.
If the two variables have linear negative correlation, we say that as one increases, the other decreases. Once again, we can draw a line of best fit on the scatter graph that represents these variables. But this time, the line of best fit will have a negative slope. It will slope downwards.
Now, of course, it’s also important to realize that some variables will have no correlation at all. In these cases, the scatter graphs might look a little bit like this. And we see that there’s no real way to draw a line of best fit on this diagram. So we’re thinking about the number of hours spent on social media and the number of hours spent doing homework. We want to work out if there is a linear positive correlation and linear negative correlation or no correlation at all.
So, let’s imagine what a school day for an average student might look like. That student might spend six hours at school. They might spend around nine hours sleeping, possibly more. And they might spend a couple of hours just doing the day-to-day things, like eating and showering and so on. That leaves us with seven possible hours in our day. So, these are the hours we’re interested in. These are the possible hours that we could spend doing homework or looking at social media.
Let’s say then that we choose to spend one hour looking at social media. That could leave us a total of six hours to complete our homework. Now that is an awful lot of homework, but we are thinking about a mathematically perfect scenario. We might also choose to look at social media for two hours. Now that leaves us five possible hours to do homework. If we look at social media for three hours, we have four hours to do homework. And we could continue this table in this manner.
We now might notice that as our hours on social media increase, our hours spent doing homework decreases. And in fact, these do this at the same rate. Now, we said that when this was the case, we were dealing with a negative linear correlation. And so, we can say that the type of linear correlation that might exist between the number of hours spent on social media and the number of hours spent doing homework would be a negative correlation.