We will assume that we can solve this question using technology. We can use a graphing calculator to check the scatter plot to see the possible relationship between these two variables.
We can graph the following scatter plot with these two variables:
If we observe the graph, we can see that both variables have a linear relationship. The phenomenon y is related to phenomenon x in a possible linear relationship.
To find the line that best represents this relationship, we can use technology using a graphing calculator. If we do that, we can obtain the following graph:
We can see that the line has a negative slope, and the equation for this line is:
The graphing calculator used the formulas for the regression line available on the internet, and in books. The process to obtain it manually is time-consuming.
The correlation coefficient for this case is equal to r = -0.9527, which means that the negative correlation is very strong between these two variables (as was mentioned in the question).
In summary, the equation of the regression line that predicts the value of the phenomenon y knowing that of the phenomenon x is:
[This is the slope-intercept form of the line. The slope, m = -0.948276, and the y-intercept, i. e., the point where the line passes through the y-axis, is equal to b = 18.1345.]