Query: Soares finds lack of correlation between CO2 and temperature

Relevant passages:
Correlation does not imply causation <=SEP=> In statistics , many statistical tests calculate correlations between variables and when two variables are found to be correlated , it is tempting to assume that this shows that one variable causes the other . That `` correlation proves causation , '' is considered a questionable cause logical fallacy when two events occurring together are taken to have established a cause-and-effect relationship . This fallacy is also known as cum hoc ergo propter hoc , Latin for `` with this , therefore because of this , '' and `` false cause . '' A similar fallacy , that an event that followed another was necessarily a consequence of the first event , is the post hoc ergo propter hoc ( Latin for `` after this , therefore because of this . '' ) fallacy .   For example , in a widely studied case , numerous epidemiological studies showed that women taking combined hormone replacement therapy ( HRT ) also had a lower-than-average incidence of coronary heart disease ( CHD ) , leading doctors to propose that HRT was protective against CHD . But randomized controlled trials showed that HRT caused a small but statistically significant increase in risk of CHD . Re-analysis of the data from the epidemiological studies showed that women undertaking HRT were more likely to be from higher socio-economic groups ( ABC1 ) , with better-than-average diet and exercise regimens . The use of HRT and decreased incidence of coronary heart disease were coincident effects of a common cause ( i.e. the benefits associated with a higher socioeconomic status ) , rather than a direct cause and effect , as had been supposed .   As with any logical fallacy , identifying that the reasoning behind an argument is flawed does not imply that the resulting conclusion is false . In the instance above , if the trials had found that hormone replacement therapy does in fact have a negative incidence on the likelihood of coronary heart disease the assumption of causality would have been correct , although the logic behind the assumption would still have been flawed . Indeed , a few go further , using correlation as a basis for testing a hypothesis to try to establish a true causal relationship ; examples are the Granger causality test and convergent cross mapping .

Cross-correlation <=SEP=> In signal processing , cross-correlation is a measure of similarity of two series as a function of the displacement of one relative to the other . This is also known as a sliding dot product or sliding inner-product . It is commonly used for searching a long signal for a shorter , known feature . It has applications in pattern recognition , single particle analysis , electron tomography , averaging , cryptanalysis , and neurophysiology .   For continuous functions f and g , the cross-correlation is defined as :     where denotes the complex conjugate of , and is the displacement , also known as lag , although a positive value of actually means that leads .   Similarly , for discrete functions , the cross-correlation is defined as :   The cross-correlation is similar in nature to the convolution of two functions .   In an autocorrelation , which is the cross-correlation of a signal with itself , there will always be a peak at a lag of zero , and its size will be the signal energy .   In probability and statistics , the term cross-correlations is used for referring to the correlations between the entries of two random vectors X and Y , while the correlations of a random vector X are considered to be the correlations between the entries of X itself , those forming the correlation matrix ( matrix of correlations ) of X . If each of X and Y is a scalar random variable which is realized repeatedly in temporal sequence ( a time series ) , then the correlations of the various temporal instances of X are known as autocorrelations of X , and the cross-correlations of X with Y across time are temporal cross-correlations .   Furthermore , in probability and statistics the definition of correlation always includes a standardising factor in such a way that correlations have values between − 1 and +1 .   If and are two independent random variables with probability density functions f and g , respectively , then the probability density of the difference is formally given by the cross-correlation ( in the signal-processing sense ) ; however this terminology is not used in probability and statistics . In contrast , the convolution ( equivalent to the cross-correlation of f ( t ) and g ( − t ) ) gives the probability density function of the sum .

Pearson correlation coefficient <=SEP=> In statistics , the Pearson correlation coefficient ( PCC , pronounced -LSB- ˈpɪərsən -RSB- ) , also referred to as the Pearson 's r , Pearson product-moment correlation coefficient ( PPMCC ) or bivariate correlation , is a measure of the linear correlation between two variables X and Y . It has a value between +1 and − 1 , where 1 is total positive linear correlation , 0 is no linear correlation , and − 1 is total negative linear correlation . It is widely used in the sciences . It was developed by Karl Pearson from a related idea introduced by Francis Galton in the 1880s .