 Well, now we're going to look at a somewhat different situation where our independent variable is no longer time, but it's some quantity. It could be temperature, it could be an index of El Nino, the North Atlantic Oscillation Index. So let's look at an example of that sort. We are going to now look at the relationship between El Nino and December temperatures in State College, Pennsylvania, and we can plot out that relationship as a scatter plot. So on the vertical axis we have December temperature in State College. On the horizontal axis, our independent variable is the NINU 3.4 index. Negative values indicating La Niñas, positive values indicating El Ninos, and the strength of the relationship between the two is going to be determined by the trend line that describes how winter temperatures in State College, December temperatures in State College, depend on El Nino. And so by fitting the regression, we obtain a slope of .7397. That means for each unit change in El Nino, in NINU 3.4, we get a .74 unit change in temperature. So for a moderate El Nino event where the NINU 3.4 index is in the range of plus 1, that would imply December temperatures in State College. That year our .74 degrees Fahrenheit is the scale here, .74 degrees Fahrenheit warmer than usual. And for a modestly strong La Niña, where the NINU 3.4 is on the order of minus one or so, State College December temperatures would be about .74 degrees colder than normal. Now the correlation coefficient associated with that linear regression in this case is .174. Now we have 107 years here, our dataset as before goes from 1898 to 1994. So that's 107 years, we've got a correlation coefficient of .174. So if we use our table and we take N equal .107, R of .174, we find that the one-tailed value of P is .0365, the two-tailed value is .073. So if our threshold for significance were P of .05, the 95% significance level, then that relationship correlation coefficient of .174 with 107 years of information would be significant for a one-tailed test, but it would not pass the .05, the 95% significance threshold for a two-tailed test. So we have to ask the question, which is more appropriate here, a one-tailed test or a two-tailed test. Now if you had reason to believe that El Nino events warm the northeastern U.S., for example, then you might motivate a one-tailed test since only a positive relationship would be consistent with your expectations. But if we didn't know beforehand whether El Nino's had a cooling influence or a warming influence on the northeastern U.S., you might argue for a two-tailed test. So whether or not the relationship is significant at the P equal .05 level is going to depend on which type of hypothesis test we're able to motivate in this case.