I have a database like:
Site X Y
S1 1 1.5
S1 1 1.3
S1 2 1.7
S1 1 1.1
S1 4 5.9
S2 3 4.0
S2 2 2.5
S2 4 9.1
S2 4 9.2
S2 1 2.3
I need to find if $Y$ increases as $X$ increases for every site. In other words, Bigger $X$ corresponds to bigger $Y$.
I know linear regression might suit this problem. But please take a look at the following graph:
Figure 1 is not what I want because small $X$ corresponds to big $Y$. However, Figure 2 is what I want. When I use a linear regression model and RMSE as a measure, it cannot tell the difference between Figure 1 and Figure 2.
Another thing about my database is: $X$ are like levels, which are the same to all the sites. But the $Y\text{'s}$ of every sites are different. For example, for one site, $X=1$ and $Y=20$ means $20$ is a small value because it corresponds the lowest level of $X$. But for another site, $Y=15$ and $X=6$ means $15$ is the highest value because $X$ is the highest level.
So, my problem is: for every site, I need to use a linear model or any other algorithms to judge if $Y$ increases as $X$ does. Then, I need to use a measure to select some sites.