# Correlation formula for a Quadratic

I have used quadratic regression on a dataset to find the graph of best fit, that is, finding the coefficients a, b and c in the general formula of y = ax^2 + bx + c.

Having done that I would now like to find the correlation coefficient of that fit to the data. Can anybody help with either the formula for the correlation coefficient or the coefficient of determination for a quadratic?

• This is just multiple regression on the variables $x$ and $x^2,$ so go ahead and use the standard formulas. – whuber Mar 26 at 13:27
• Welcome to CV havelly. It is somewhat unclear what you mean by correlation coefficient for a quadratic. Pearson's correlation coefficient assumes a linear, not quadratic relationship between $x$ and $y$. Spearman's correlation coefficient assumes a monotonic relationship between $x$ and $y$. I assume you are not asking about Pearson's (or Spearman's) correlation coefficient between $x^{2}$ and $y$, since that seems very obvious. – Alexis Mar 26 at 16:14
• Thank you for the welcome. Perhaps I will re-frame the question as it can be confusing. I have used quadratic regression on a dataset with two variables and from that the a, b and c coefficients have been determined so I have an equation like y = 5x^2 + 2x + 7. Now this is not a perfect match to the data, that is, the graph does not exactly go through all the data points but will be fairly close to them. How can I now calculate the correlation coefficient for this quadratic equation to the dataset? – havelly Mar 27 at 2:01
• Nope. That does not clarify. See my first comment. – Alexis Mar 27 at 15:16