The successful application of simple statistical methods in economic modelling suggest that similar methods could provide insight into global climate. We apply an autoregressive method to observed time series to determine the dependence of atmospheric CO2 concentration on carbon emissions and, in turn, the dependence of globally averaged temperature on atmospheric CO2 concentration. We ascribe physical meaning to the regression parameters in terms of first order differential equations describing the diffusion of CO2 and temperature between reservoirs, viz.: the diffusion of CO2 between the atmosphere and the deep ocean and the transport of heat from the mixed layer. A strong feature of regression models is their built-in mechanism for deciding when a model provides an adequate description of the given data. Two implications of this statistically robust approach are that CO2 diffuses from the atmosphere within a time scale of decades and that global average temperatures are unlikely to exceed 2 deg C above pre-industrial values.