Evidence-based policy of global warming is best relying on a relevant sample of data. We choose a sample of annual data from 1959 to-date to provide some statistically robust stylized facts about the relationships between actual CO2 and temperature. Visually, there is a clear upward trend in both data. Time series analyses suggest that CO2 is difference-stationary and temperature is trend-stationary. Thus, the moments (mean, variance, etc.) of the data in levels are functions of time, which means that the correlation between the two variables may be spurious. Most importantly is that the variance of CO2 (and all greenhouse gases) are significantly smaller than the variance of temperature, hence they cannot explain the variations in temperature. We find no statistically robust evidence of correlation, long run co-variation, long run common trend, or common cycles between CO2 and temperature over a period of 60 years. Nonetheless, at most 40 percent of the variance of the Northern Hemisphere temperature is due to , 20 percent of the Southern Hemisphere, and much less of global temperature.