Suppose there is a set of points $[(x_1, y_1),(x_2, y_2), ..., (x_n, y_n)]$.
I want to figure out whether $y$ will grow with $x$. If yes, I want to automatically find the best growth (linear growth, quadratic growth, exponential growth, or others) to fit it.
I know that pearson correlation can be used to judge whether $y$ and $x$ have a linear correlation. However, is there a threshold $t$ ? For example, if $PearsonCorr(x,y) > t$, we can conclude that $y$ and $x$ have a linear correlation.
Linear/polynomial regression can also be used to fit the points, and there are measurements such as $R^2$ and $F$ test. However, I do not know how to use them to determine the best fit, especially when $n$ is small (say 10).
Any suggestions will be appreciated!