I have generated some data Y and would like to describe its variation as a function of some variable X. Using MS Excel, I obtained the trendline shown in the figure below which suggests that Y varies approximately cubically with X. However, I would like to omit the trendline itself (leaving only the data points marked by the blue diamonds) and describe the data qualitatively in an increasing sense. To that end, would it be accurate for me to use the following statement: the data Y increases approximately cubically with X?
Polynomial, according to Merriam Webster:
a mathematical expression of one or more algebraic terms each of which consists of a constant multiplied by one or more variables raised to a nonnegative integral power (such as a + bx + cx2)
I would say the relationship is not just cubic, because there are other terms. Instead, polynomial fits perfectly (it fits your approximation, perhaps not your actual data, but that you would have to judge for yourself, perhaps have a look at Cross Validated).
In your situation, you could say the following:
The relationship between X and Y is polynomial.
Searching Google Scholar for the terms polynomial and correlation shows the term polynomial correlation is used quite often (though not always in this specific context).
Attribution: "Polynomial." Merriam-Webster.com. Accessed July 21, 2018. https://www.merriam-webster.com/dictionary/polynomial.