Suppose variable 𝑥 is the number of hours you spent studying, and variable 𝑦 is your grade in the final exam. You suspect that the more hours you spend studying, the higher your grade is. Does this follow a positive correlation, a negative correlation, or no correlation?
When we think about the correlation of data, we’re thinking about if there’s a relationship between the 𝑥- and 𝑦-variables. In a positive correlation, both variables are increasing. As 𝑥 increases, 𝑦 increases. In the negative correlation, one variable decreases as the other increases. And we say that there is no correlation if we do not see an apparent relationship between the two variables.
If we think about our values for 𝑥 and 𝑦, the value along the 𝑥-axis represents the number of hours spent studying, and the 𝑦-axis represents the grade on the final exam. As we move to the right along the 𝑥-axis, we’re modeling more and more time spent studying for the final exam. And according to our supposition, the more time we spend, the higher the grade is. We could add a line that represents our assumption. As 𝑥 increases, 𝑦 increases, which is a model of positive correlation.