The linear correlation doesn't necessarily establish cause and effect, because a third factor could, in theory, cause both an increase in carbon dioxide and an increase in global temperature. Also the fit of a linear regression equation, its correlation coefficient, is a measure of the probability that increase of carbon dioxide in the atmosphere is related to an increase in global temperature. The higher the correlation coefficient, and its square, the coefficient of determination, the more likely it is that higher global temperatures are the result of higher carbon dioxide concentrations, and the less likely that the higher temperatures are due to chance or some other unknown cause. Reliable measurements taken over a long period of time measured in centuries produce a large dataset from which to make statistical evaluations and give confidence to statistical conclusions. Statistics, while compelling in its findings, is one of a number of scientific efforts to establish the connection between atmospheric gases, and other factors like solar activity, and cannot stand alone in making judgments.