 Hi, this is Don and I want to take a few minutes to show you how to do auto regression using PHSTAT. This is a data set that I found. It has cold production for the years 1960, drag it down there, through 2007. And I've already saved a little bit of time when we do auto regression. In this case, I want to do a second order regression. So we want to go back two years, or two time periods, from the original data. And I label the original data y sub t and the second column I'm calling going one year back y sub t minus one and then y sub t minus two. All I did was to copy this data in the first column, starting there and dragging down copy and then pasting it one cell down, one year down, and then pasting it again two years down. And so you get the data to look like that. Now I went ahead and as I said, label these three columns, it can get confusing when you start doing the regressions using data analysis or PHSTAT as to where you want to select your area. So what I like to do is to go ahead and copy just the area I want. And again, we go from the end of the time t one to the beginning of the time t minus two. And I'm going to copy those, and I'm just going to paste it over here. And then I'm going to transfer these labels over. So I'll remember they are copy those and paste those. And so we have our data moved over a bit so that now we know exactly what we want to use in our regression analysis. If we're going to use PHSTAT, I'm going to add in PHSTAT and we go to regression. And unlike data analysis, which only has a single tool called a regression tool, which works for simple and multiple regression, PHSTAT has a number of tools. And because we're using more than one x value, we're using y of t minus one, one year back and two years back, that's multiple regression. If you use simple in your regression tool, you won't get the right answer for a auto regression for a second order auto regression. So I'm going to click on multiple regression. And the first thing we have to do is to identify our y cell, our outcome cell. And in this case, I'm going to click in there, or you can click on this little icon there. And I want y sub t, so I'll highlight that area, that area. And then once I've got it selected, I click on the little insert icon. Now I want to select my x variables, again, click on that icon. And this time, I'm going to select both y t minus one and y t minus two. And once I get that, again, I select that little icon and we've got our data there. I've got the default first cell and both range contains a label. I'm going to leave the confidence interval 95%. We want the regression statistics and we want the ANOVA table. And for this purposes, we don't need the rest of these options there. But I am going to go ahead and name my output, so I remember, second order. That's good enough. And click OK. All right, and we get this output here. We've got our regression information over there. But here is the ANOVA output is what we need. We've got our multiple r square or 0.972, which says 98% of the variation in the year t is due to, can be explained by the variation in the years t minus one and t minus two. And here is our output. The overall ANOVA is significant. And for our second order and our first order coefficients, we have a p-value of less than 0.05. Remember, we were going for 95%, which uses an alpha of 0.05. Both of those are significant, which means this slope from zero, because we're rejecting the null that the slope is zero. And this slope is also different from zero, because again, it's significant statistically and we're rejecting that null hypothesis that this slope was zero. So our equation is pretty straightforward there. We've got our two of coefficients and our intercept, and we can write down the regression equation pretty simply. That's how you do the auto regression in PhDAT.