Lack of correlation disproves causation. Correlation only suggests it. Lack of correlation between CO2 and temperature shows CO2 does not cause rising temperatures.
Correlation measures how well 2 quantities are linked.
A correlation
 of around 1 indicates things move together
 of around 0 indicates things are not linked
 of around 1 indicates things move in opposite direction
It is very important to remember whilst 2 quantities may have a correlation close to 1, this may arise by coincidence. Hence the mantra
Correlation is not causation
Which students are encouraged to repeat when they say their prayers.
But perhaps not climate scientists.
Using HADCRUT4 temperature anomalies and CO2 levels from Mauna Loa there are 2 periods between 1960 and 2014 where CO2 levels are not correlated with temperature anomalies and one where CO2 levels and temperature anomalies are reasonably well correlated.
So if CO2 levels cause rising temperatures did someone switch this off from 1960 to 1976 and again from 2004 to 2014?
19601976

0.02

19762004

0.78

20042014

0.02

This graph of CO2 Levels and temperature anomalies illustrates this
The three periods clearly have very different trends
However the plot of net change in CO2 from the same month the previous year appears to follow changes in temperature much more closely.
This was pointed out by Prof Murray Salby
The following graph compares observed CO2 levels with those where the current months CO2 level, C, is calculated from
 The current months temperature anomaly T
 The CO2 level in the same month the previous year Cl
 2 numbers A and B
using the formula
C = A + Cl + T x B
A = 1.22 ± 0.03
B = 1.66 ± 0.09
So the first year is used to provide the annual shape
Each year there is an increment of a constant 1.22 ppm
For each month in the year add 1.66 x that months temperature anomaly and the CO2 level for the same month in the previous year.
It seems to be to simple to be true and no iterative models or supercomputers
Until you remember CO2 levels show a more or less linear increase with each year and the shape within each year is roughly the same.
The correlation between observed and calculated levels is 0.99971717
Correlation is not causation
But this method matches the entire period which is not true for CO2 drives temperature theory.
As Prof Murray Salby pointed out this method has a simple physical model
CO2 levels are the integral of past temperatures + annual constant increase
It is just about impossible (for me at any rate) to see how this can be true and simultaneously CO2 causing temperature rise
So I conclude rising CO2 levels do not cause temperature rise
And thus all the money being spent on renewable energy, and knocking down flood defences is being completely wasted.
Oh – it’s our money by the way.