 We're going to take a look at an example of multivariate regression, and I'm going to read in a data set here. This data set contains the average temperature of the Northern Hemisphere land regions over the past century. So let's start out by plotting the data so we can see what it looks like. And there it is. We're going to look at three potential quantities that may explain some of the variations that we're going to see in this temperature series. So the temperature series is our dependent variable. And we're going to look at three different independent variables. One of these independent variables is a simulation that I've done using a climate model called an energy balance model that we'll be talking about in a future lesson. And I've subjected this theoretical climate model to both human impacts, estimated radiative forcing by greenhouse gases, and anthropogenic sulfate aerosol emissions, as well as radiative forcing by natural causes, including volcanoes, explosive volcanic eruptions, and estimated changes in solar output over time. So let's take a look at what that simulation looks like. So let's click year and EBM. So we have both series here. We have the temperature anomaly in blue and the EBM output in yellow with the values on the right-hand side. So you can see that, in fact, the energy balance model simulation, the yellow curve, does capture quite a bit of the variation in the blue curve, the instrumental surface temperature data. But there's still quite a bit of variation that's left unexplained, and we will now look at two other factors that are internal to the climate system rather than external in nature that might explain some of that residual variability.