I am trying to understand the correlation, given by my data, between numbers and percentages.
I have four numbers : 1, 2, 3 and 4. And there percentages are respectively: 0, 0.3333, 0.6667 and 1. By using a rule of 3, i'm getting : 0.25, 0.5, 0.75 and 1.
What i know from the start is that my lowest number's percentage is 0 and my highest number's percentage is 1.
If i add a number 5, i'll get the following percentages : 0, 0.25, 0.5, 0.75 and 1.
What can replace a rule of 3 to get the right percentages ? Thank you
The correlation is $1$: all the points lie on an upward sloping straight line as shown here.
In statistics you could use simple linear regression to find the line and the correlation, but this example is easier than that since the observations are colinear. Each step of $1$ to the right takes you up by $\frac13$ so the slope is $\frac13$; a step back from $(1,0)$ then takes you to $(0,-\frac13)$ so the vertical intercept is $-\frac13$. That gives the equation of the line as $$y=\frac13 x - \frac13$$ which you can also write as $y=\frac{x-1}{3}$.
If you knew that the line passes through $(a,0)$ and $(b,1)$ then the equation would be $y=\frac{x-a}{b-a}$, i.e. $y=\frac{1}{b-a}x -\frac{a}{b-a}$, with $a=1$ and $b=4$ in your example.