>> Here's a table showing the amount of revenue collected by the Internal Revenue Service for the years 1960 to 2000. Let's enter the information into the calculator, and choose the model, and generate a regression equation. And actually make a prediction for the amount of revenue collected in the year 2008. A year outside of the data set. Well we begin by entering the information. I will press that and, then enter for edit, and notice that I've already entered the information. The important feature here is that zero corresponds with the year 1960. So 1960 is the basis year. And a number like, oh, 15 here means 15 years beyond 1960. Oh, that would be 1975. So the amount of revenue for 1975 is, is this value from the table. All right, so let's keep that in mind as we go through the problem. It just makes this business of, of establishing a basis year, and so forth, just allows us to make it a little bit easier to set up the window and a little bit easier to enter the information. All right, let's look at a scatter plot. Not I have already turned the plot on and, to establish an appropriate window I'll press zoom and then select item number 9, zoom stat. Pressing enter. Here is our information> Now the scatter plot seems to be rising over here. And we saw from the earlier problem that there are several models it might be appropriate for this situation. The exponential model on the earlier one was a better fit. And lets use an exponential model here, because we are studying exponential functions in this chapter. So we'll go through the stat and then we want to calculate. So I'm pressing right arrow. And I want the exponential model, let's go down here. Exponential regression here we go, and pressing enter once again. Now diagnostics is on here, and I have my R squared, my R values here. And notice that they are, they're pretty, they're pretty high values. They are pretty close to, to 1. We ought to get a very good fit here for the information. Let's press Y equals and get the calculator to input this equation forth. I'm pressing there, and then down to item 5, statistics, right arrow twice, enter. And here is the equation on board. Now by the way, I'm pressing second quit here to get back to this. The A value is 88.57. We could actually write this equation in algebraic form. You know, we could round this to the nearest hundred, we could round the B value to the nearest hundredth, maybe, or my the year new [inaudible]. And we could actually build this equation algebraically. And the question that we're asking could be calculated algebraically. It would be a fairly easy thing to do it's that way. But in digit that way we are almost forced to round this long decimal. So we get a little more accuracy, I think, by using the calculator for the entire, to answer the, the question in it's entirety. Well let's see, we're at the point where we're ready to graph, and I'm overlaying the graph with the data points. And we see that the graph is a pretty close fit with these data points.