So suppose that we have TruSpace here. Here's y, and here's x. Now y and x are two variables and I think that they are related. So it could be the amount of tomato plants that are growing and the amount of rain that the tomato plants are receiving, or it could be your earnings with respect to your education. I mean two things, two variables that I think are related. So, we put these together and we get we a scatter plot of the data that looks something like this. Now you'll notice that these data are a little different than the demand schedule that I showed you previously. The demand schedule, everything was in a really nice straight line. These data are not in a straight line. I can estimate a line that is straight, but I need to engage in a technique, and the technique is called ordinary square or minimum sum of squares. What's happening here is that, I want to draw a line of best fit, such that there is a very specific mathematical calculation that's taking place. So if I were to draw a line here, I think this line is a pretty good line of best fit, something like this. This is a line of best fit, if, for every value of x, right? So here's a value of x right here. Here's a value of x. This line is going to predict a value of y, okay? Right here. We'll call that y-hat. So, this value of x is predicting a y-hat, and that's what that line is representing. What's the value of y given the value of x? Now, there is a real value of y, and we can see it above here this guy right there and circle it. That's the real value of y given this value of x. So there's a difference between the real value and the predicted value of y given a value of x. Well, if I take that difference, y minus the predicted value of y, y-hat, and I square it, and I sum it, for every single observation, and I take the minimum of that value, I will get my line of best fit. So, sometimes you will hear your professor is referring to this line as ordinary least squares, so the least is the minimum and the squared is the squared difference of the predicted and the actual. So like the error term, okay? Sometimes we will refer to this as the minimum sum of squares. That's right. Because what I'm doing is by calculating this line I'm minimizing the sum of the squared error terms between the predicted value of y and the actual value of y. So, don't get frazzled when you hear your professor is talking about OLS, minimum sum of squares, ordinarily squares. What they're doing is they're saying we're going to create a line. We're going to estimate a line of best fit between these data that have this very specific mathematical calculation behind it. It's very unlikely that you're going to actually have to do this mathematical calculation. Excel will do it for you. Any number of programs will do it for you, as long as you just say, "Hi, I'm going to run a regression, this is what's behind it. All right, getting back to our Excel, okay we've got this little regression tab that has been pulled up and we get this little workbook if you will, that allows you to put information into the y range, information into the x range, and as some other little tabs, labels, constant zero, outputs, residuals. So we are going to do is we're going to highlight some of our information when our cursor is placed in either one of these things for our x range and for our y range. So we're going to start with our y range. So on this chart we've got price on the y axis. So I am going to highlight this information. When my cursor is put in this area right here, input y range, I'm going to highlight that right there. Then I'm going to click on the input y range. So there's my cursor and then I'm going click, highlight the information on my quantity. Then I'm going to click labels. The reason I'm clicking labels is because you'll notice that each one of my columns has a label up here. The default is that I'm going to have output put it into a new worksheet. So we're going to leave the default as is. So then I'm going to click OK. When I click OK, you'll notice that there's a new output that has appeared here and it's labeled as Sheet2. Now I'm going to make this a little bit larger here so you can see this. So now, notice this, right down here, I've got a column that is labeled coefficients. I have underneath coefficients, I have a row that's labeled intercept. So the coefficient of the intercept says 12. The coefficient of the quantity says negative 0.33333. This should look familiar. Notice that right here, on this chart, I've got a line, and my line has this characteristic, y equals negative 0.333x plus 12. Let me see if I can copy this chart over to my second so you can look at these guys right next to each other, here. So you'll notice that this chart, this linear relationship, this slope intercept form of a line, has the same characteristics as these coefficients right there. Intercept coefficient is 12, right? My slope intercept form of a line, this is the y-intercept is 12. So we call that an intercept coefficient. This, negative 0.3333333, that's the slope of the line. That's the coefficient of quantity in this equation. So, the information that is grabbed from my regression equation here, the coefficients of intercepts and the coefficient of quantity are the same information from my slope intercept form of a line. What's going to happen is that, when we're dealing with data, data from industries, we're never going to get a really beautiful, really super pretty picture like this. The data are going to be very scattered. So, we might have to run a regression, using the second tool, rather than just a simple scatter plot and a very very beautiful pretty line like this. So understanding how to interpret this information becomes very very valuable when you're actually looking at industrial situations. So, your takeaways from this first part are, we've got information, we can create a scatter plot, we can create a trend line, from that we can pull up the slope intercept form of a line and we've seen that before. We also have this regression tool, the regression tool is trying to identify the line of best fit between two sets of information. The line of best fit isn't being fit randomly, it takes on a very specific mathematical quality, this ordinary least squares. The regression tool can be downloaded from your Excel options. Using this tool, you can basically create this information about the line here. You have to know how to interpret it, but it's all right there. So, I want you to try to grab this data, this information here, this little demand information is available to you, and try to replicate everything that I have on this screen. Then we're going to go on.
