A serious problem with his analysis, besides his having no actual expertise in statistical analysis, is that his regression model assumes a linear trend in temperature over that interval, a very strong assumption. I shall present here an analysis which doesn't make that assumption and which shows a clearly increasing global temperature from the middle of 2009 in both the RSS and UAH data.
So far we have an increase in .8 degrees Celsius from 1880. Fitting a linear trend from the middle of 2009 to April 2015 the RSS data projects a decadal increase of .2726 degrees, and the UAH data .6347 degrees. Thus by 2035, the RSS data suggests 1.34 Celsius global temperature, and the UAH a 2.07 Celsius.
The LOESS regression used here employs a somewhat arbitrary smoothing parameter and as a result our conclusions are tentative. But the evidence is very strong that in fact global temperatures are increasing since somewhere in 2009, and that we can expect an increase of somewhere between one and two degrees increase by 2035. These results are sobering.
A regression of the RSS data from December 1996 through May 2015 on a trend variable indeed shows no increase in temperature over that period of time.
Assuming a linear trend over this time is a very strong assumption. In fact, it is not hard to see that temperatures have been increasing since 2009 which is glossed over in the linear assumption. Another kind of regression, a LOESS, or locally weighted regression, allows us to see a nonlinear underlying trend:
This plot reveals a clear increase in temperatures from about the middle of 2009 on. Temperatures were increasing from 1997 to somewhere in the middle 2004, and then decreasing from there until somewhere in 2009.
The linear trend in the UAH data shows a clear increase in temperatures over the entire period:
This undeniable increase in temperatures is in conflict with the results of the RSS data and Monckton's claim of no increase. It is still a small increase, 0.1034 degrees per decade.
The LOESS regression, however, is more revealing:
The UAH data shows no decline in the middle of the 2000's, but confirms a strong increase up to 2004 and another increase from 2010 and on.
The conclusion that temperatures are presently on the rise is unavoidable. Monckton's claim of no change over 18 years and 5 months is strongly dependent on that change being strictly linear. By allowing a modification of that assumption we see a slowing or possibly a decrease in the middle of the 2000's, a marked increase before, and a clearly accelerating increase after.
These results are suggestive rather than definitive, but the implications of the kind of increases in global temperature shown in the analysis cannot be ignored. It would be a singular irresponsibility to fail to take action in the face of these trends.