 Okay, we're going to look at an example here. I'm loading in December average temperatures for state college Pennsylvania for a hundred and seven year period from 1888 to 1994. So let's plot out the data. That's what they look like. That's a scatter plot, or if we like, we can view them in terms of a line plot. If we look at the statistics tab, it tells you that the average of the temperature is 30.9 just under 31 degrees Fahrenheit. So the average December temperature in state college Fahrenheit Pennsylvania is about a degree Fahrenheit below freezing. The standard deviation 3.95 just under four degrees Fahrenheit. So the fluctuation from year to year in the average December temperature in state college is a fairly sizable four degrees Fahrenheit. One year it might be 30, the next year it might be 34, the next year it might be 31, the next year it might be 27. That gives you some idea of the fluctuations, and of course we can see those fluctuations here in the plot. Now we can calculate a trend line. Let's go to the linear regression tool. That calculates the linear trend in the time series. It tells us that there is a trend of .025 degrees Fahrenheit warming per year, or if we want to express that in terms of a century, 2.5 degrees Fahrenheit warming per century. That's the warming trend in state college Pennsylvania. Now the correlation coefficient for that regression is r equals .193. If we look that up in the statistics table, put in 107 years for the length of our series, put 193 for the correlation, and we calculate the significance, tells us that the p-value is .023 for a one-tailed test, .046 for a two-tailed test. So in either case the correlation, the regression, the trend in the series would be significant at greater than the p-equal .05 level, it would be significant at the 95% confidence level. Arguably we should go with the one-tailed test since we're really testing the hypothesis that there's a warming trend in state college. Since we know the globe is warming, our hypothesis was unlikely to be that state college showed a cooling trend. We were interested to see if state college showed the warming trend that we know is evident in temperature records around the world, so one could, in fact, one would typically motivate a one-tailed or a one-sided hypothesis test. And so the trend passes that test at the .02 level, it's fairly significant. We go back again. We can see the standard error in the slope is .012. So if we were to take the value .025 and add plus or minus 2 times this number here of .012, it would give us the range, the 95% confidence range in the trend, in the slope of this warming trend.