# Can a relationship between x and y be modeled, if all the data points fill the area under a curve?

I'd like to derive an equation that enables me to calculate y based on x.

I'm having troubles figuring out how to do this as my data doesn't form a line/curve, but rather creates an edge (image below).

My background in statistics is a second year university level course.

Edit: Thank you for the comments. I created the following log-log graph, which allowed me to generate a trend line: $$\text{log}_{10}y = -m*\text{log}_{10}x+k$$. The data is from a survey. I'm plotting the acceptable error margin on the y-axis and the population size on the x-axis.

• What is your goal to estimate the area under the curve at some x value or to describe the relationship between x and y? – RAND Aug 17 '19 at 3:40
• It would help to use an effective graphic. This one is ineffective--and potentially deceiving--because the cloud of points does not reveal crucial information about where the individual points lie and in what amounts. You need a better visualization tool to display these points, one that can use (say) smaller point symbols, partial transparency, or methods to represent their spatial densities (hexagon plots, sunflower plots, etc.). It would also help us to know what the x and y points are showing and their units of measurement. – whuber Aug 17 '19 at 14:34
• To me the question seems clear. The OP is used to relationships that follow a line (with some additional scatter), but now he/she is confronted with data points that fill an entire surface instead of a line and he wonders whether there are ways to express such types of data. (I agree that it is broad and unclear what direction the solution needs to be going for the specific case. But, the key point seems to me mostly that the OP is wondering about the principle in general that the data is not close to a line, but instead filling an entire area.) – Sextus Empiricus Aug 17 '19 at 15:12
• @elliotdelaunay you would make it a lot easier to answer this question and understand the problem when you explain the context of the problem. The scatter in a surface rather than around a line can be caused in many different ways. it is difficult to explain all of them and it will be much easier to explain the situation when your specific case is clear. So while your question is clear, your use-case is not. (e.g. just for a start, what do the x-axis and y-axis represent?). – Sextus Empiricus Aug 17 '19 at 15:18
• also, I imagine it might be good to plot the data on a log-log plot, instead of linear. In addition, you could use a smaller point size or make the colour of the points slightly transparent such that the density distribution of the points is easier to observe. – Sextus Empiricus Aug 17 '19 at 15:21