# Interpreting Non-Linear Relationship from Scatter Plot

The scatter plot that I have seems very likely to have a non-linear relationship. I would like to know what is the best way to explain the relationship between both variables in the scatter plot below without performing any kind of transformation on the data. I am thinking of such explanation.

A best fit curve can be drawn on the graph, and most of the data points will lie very close to the curve. Therefore, fuel consumption has a strong non-linear relationship with the speed of the car.

I am not sure whether or not it is acceptable to indicate they have a positive or negative relationship. Plus, I am not able to explain correctly how do the y value change as the x value increases. How do I explain the change of y from x? Is my explanation above enough to summarise the scatter plot below?

• You may say something like:* looking at the figure we can observe a decrease in the fuel consumption up to speeds around $70 km/h$ and an increase in fuel consumption from that point onward*. If you want to talk about a curve fit, then you should make it explicit. Is it a polynomial fit or do you use other functions? The fit should not have many parameters because the number of points is not large. And what about the quality of the fit, can you report the value of $R^2$? – Ertxiem - reinstate Monica Oct 15 '19 at 13:45
• I see. So, saying that a curve can be drawn is not enough. Transformation and model fitting is necessary to explain whether the points lie close to a curve. – dee cue Oct 15 '19 at 13:57