# How does one qualitatively describe the cubic increase of experimental data [duplicate]

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?

• hmmm ... the math forum seems apropos for this one. – lbf Jul 21 '18 at 18:11
• I'm voting migrate this question to MATHMATICS – lbf Jul 21 '18 at 18:14
• lbf Apologies I'm fairly new to this. Is there a convenient way for one to move a question to a more appropriate forum? Many thanks. – Bob1986 Jul 21 '18 at 18:14
• A moderator can move post or you can navigate to the math forum, join and post again there. – lbf Jul 21 '18 at 18:25
• Many thanks for the advice. I will repost on the math forum as advised. – Bob1986 Jul 21 '18 at 18:27

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.

• Polynomial although true is not a very interesting or useful way to describe the relationship unless you wish to contrast it with non-polynomial, such as exponential. In many contexts one is interested in the dominant term, in this case, the cubic term. – JeremyC Jul 21 '18 at 21:22
• @JeremyC fair point. In some limit cases we might use order of growth notation (like 'big-oh'), but I don't think it's appropriate as this doesn't seem to be a limit case (X seems to take values on a bounded domain). – JJJ Jul 21 '18 at 21:34