 So now let's try our multivariate regression using all three predictors the energy balance model simulation El Nino in the NAO So we go to the regression model tab here And with the click of the mouse we can select all three quantities at once ebm Media 3.4 and the NAO and we're trying to predict We're trying to predict temperature So we run that model And now we can see that we explained nearly 80 percent of the variation in the temperature series We went from just under 72 percent to now essentially 80 percent of the variation using these three predictors And that's about as good as you can expect to do in a simple multivariate regression of this sort to explain Roughly four-fifths of the total variation in the data We can see also that the autocorrelation coefficient is small this row value down at the bottom It's not going to be statistically significant and we don't have to worry about autocorrelation and the residuals, which is nice So now let's go back to plot settings We're going to going to plot alongside our temperature series our model output from this simulation Let's make that line plot And put these on the same scale click over here click one Down here minus one So our model simulation result remembers includes both The energy balance simulation El Nino and NAO these two internal factors The yellow curve is our statistical model, but based on these three predictors The blue curve is the actual temperature series and we've explained a fairly impressive amount of variation in the data We can see the effect of volcanic eruptions and some of the short-term coolings that are seen in the record And then a lot of the other internal fluctuations are at least partially explained by the NAO and El Nino If we like we can recover the regression coefficients in our regression model The constant term the term multiplying the energy balance model El Nino Nino 3.4 and the NAO index The sum of these terms is our statistical model and it does quite well in this particular case Finally, we can take a look at the residuals. What's left over after all this Let's get rid of that Plot the residuals and that's what's shown here in the blue curve. There is some variability, of course It's left over that isn't explained by laugh by the factors we've considered But there isn't a whole lot of a structure in that time series suggesting that the results of this multivariate regression are probably meaningful and Telling us something about the underlying factors that explain long-term variations and year-to-year Variations, decadal variations in the Northern Hemisphere land temperatures over time. We can see our Total model values were minus one to one the residuals here are minus point four to roughly point three