 So continuing where we left off the yellow curve is showing us the component of the variation in December state college Temperatures that can be explained by El Nino in a particularly strong El Nino year Where the Nino 3.4 indexes say as large as plus 2 we get a December temperature That's about one and a half degrees Fahrenheit above average. That is to say that 0.0 0.74 degrees Fahrenheit that we get for one unit change in Nino 3.4 for particularly strong La Nina event We get a negative 0.74 degrees effect that we get for the negative Nino 3.4 anomaly of negative two or so We had sorry a negative 1.5 Fahrenheit cooling effect for negative two or so So the influence of El Nino is small compared to the overall variability of roughly four degrees Fahrenheit in the series But it is statistically significant at least if we are able to motivate a one-sided hypothesis test If we had reason to believe That now Nino events warm state college temperatures in the winter then the regression gives us a significant result That's significant at the 0.05 level the standard threshold for statistical significance Okay, so that may not be that satisfying We're not explaining a large amount of the variation in the data But we do appear to be explaining a statistically significant fraction of the variability in the data Now finally, let's look at the residuals from that regression What I'll do is I will get rid of these other graphs Let's keep year. Let's change this to model residuals I'm just going to plot the model residuals as a function of time and that's what they look like There isn't a whole lot of obvious structure and in fact if you go back to the regression model tab You'll and we look at the value of the lag one Auto-correlation coefficient. We'll see that it's minus zero point zero nine That's slightly negative and it's quite small close to zero If we look up the statistical significance not going to be even remotely significant So we don't have to worry much about auto-correlation influencing our estimate of statistical significance We also don't have much evidence here of the sort of low frequency structure and the residuals that might cause us to worry So the nominal results of our regression Analysis appear to be valid and again if we were to invoke a one-sided hypothesis test We would have found a statistically significant albeit a weak influence of El Nino on state college December temperatures