I have the following sets of values for $x$ and $y$:
$x$: $0, 1.5, 2.0, 3.0, 5.0$
$y$: $0.00, 0.92, 1.41, 2.60, 5.59$
I am to find a correlation between the two sets of values. A graph of them gets:
and a graph of $log(x)$ and $log(y)$ finds
in other words a straight line. I now have no idea where to go next. I originally tried the model following, realising afterwards how wrong it was:
To find the correlation I tried to find a $y = kx + m$ equation for the graph, using the values I'd found for $log(x)$ and $log(y)$:
$k_1 = 0.667$
$k_2 = 0.663$
$k_3 = 0.674$
In other words, with some margin of error $k$ is around $0.668$.
$y = kx + m \iff m = y - kx$
$m = 0.9555 - 1.0968\times 0.668 = 0.223$
$y = 0.668x + 0.223$
Testing these values for another $x$ and $y$ shows:
$0.668\times 0.6931 + 0.223 = 0.686$
where it should have resulted in $0.3436$.