 Okay, we're going to look at an example of multivariate regression, and I'm going to read in a data set here. This is a data set that contains the average temperature of the Northern Hemisphere land regions over the past century, and so let's start out by plotting out the data so we can see what it looks like, and there it is. And we are going to look at three potential quantities that may explain some of the variations that we see in this temperature series. So the temperature series is our dependent variable, and we're going to now look at three different independent variables. One of these independent variables is a simulation that I've done using a sort of climate model called an energy balance model that we'll be talking about in the next 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, and what I'll do is I'll select the alternative axis B so that both series are aligned on the same scale with the energy balance model values on the right-hand side and the temperature anomaly from the instrumental observations on the left-hand side. I'll change the scale just a little bit here, so you can see that in fact the energy balance model simulation, the red curve, does capture a lot 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.