This section we're going to be talking about regression analysis, and how to interpret regression output. Your professors in the MBA program are going to leverage the regression tool quite a bit. It's a very powerful tool, and it's used across virtually every subject area in the in the MBA space, from everything from your economics and your finance to accounting, to strategy, and marketing. So it's a tool that you're going to be seeing quite a bit in your MBA studies, and understanding what it means, how to use it, how to interpret the output of regression analysis. It's going to give you a huge step-up on your classmates and make you a much more effective and efficient student in the classroom. So what we have here on this Excel spreadsheet is a demand schedule. This is a demand schedule that we talked about in one of the earlier sections. Here I have prices and corresponding quantity demands. Now, you'll notice that the demand schedule here shows that as price goes down, the quantity demanded goes up. Now, we use these same data in the earlier sections to talk about a linear equation. We use a linear equation, the slope intercept form of a line to describe mathematically the data that we have here. Now, we're going to use regressions to reveal the exact same information. Now, I'm going to do this in several different ways. First, I'm going to show it to you as a scatter plot and then show you the line of best fit on the scatter plot. So I'm going to show you this technique. Then I'm going to show you the regression technique using the Analysis ToolPak on Excel. Now, of course, I'm using a PC. As we go, I'll be showing you how to do this on a PC, but I'll also be showing you how to download some of the tools in case you are using a Mac. So like I said, here we have a demand schedule. The regression technique is a technique in which we can understand the relationship between two variables. What we have here is we have a price and a quantity. As we discussed in one of our earlier sections, we can develop a function, say, the quantity demanded is a function of price. So let me show you this relationship using a scatter plot first. So I'm going to create a scatter plot of these data. In order to do this, I'm going to highlight the data and then identify which part of this data is going to go into which part of the scatter plot. So as we discussed before, for a demand schedule, we have the price on the y-axis, and we have the quantity on the x-axis. If I highlight the data of the price and click on a scatter plot, I get this information right here. Now, you'll notice that these data is lined up. So it starts with 12, and it goes down in this fashion right here. On the x-axis, you'll know it starts at 0 and it has 1, 2, 4, 12, all the way up to 13 because there's 13 different data points here. Well, this is not accurate in terms of the price with relationship to the quantity. So what I'm going to do is I'm going to click on this information here. I'm going to click on the chart, and I'm going to select the data, which will allow me to put in the x-values that I want, which is this quantity elements right here. When I click on "Okay", now you'll notice that my chart, my scatter plot, it has the same shape but the variables, that is the scale on the x-axis has changed from 0-13, all the way to 0 to essentially 36. So this is accurately depicting the information from my schedule. Now, the reason that we're talking about regression is because I want you to understand the mathematical relationship between these two variables. If I click on any one of these little spots here, I can add a trend line. What I'm going to do is I'm going to add a linear trend line, and I'm going to display the equation on the chart right here. Now this equation right here, you'll notice it says y is equal to negative 0.3333x plus 12. This is also in our slope intercept form of a line. Y represents our y variable over here. The x represents the x variable over here. The 12 represents the y-intercept, which is this point up here, exactly where this line is intersecting the y-axis. Negative 0.3333333 identifies the slope of this line as it stands. So this says that, if I was going to write a function that says y is a function of x, it would be y is equal to negative 0.333x plus 12. Now we've seen this before when we did the algebra section. So what is regression? Regression is a technique under which I can take these data and establish this relationship, calculate this linear relationship, but I can do it outside of this plot system that I've just showed you. In order to calculate a regression using Excel, we need to have a couple of tools uploaded. The first tool that we have to do is we have to upload what's called the Analysis ToolPak. Let me show you how to do this on Excel and from a PC, is you click on your options down here, and you go to the Add-In menu right here. When you click on that, the Analysis ToolPak are one of the first two add-ins that you can add in. One of them is the Analysis ToolPak, and the other one is the Visual Basic version of this. So let me show you how we add in the Analysis ToolPak. You can add it in from one of the options from your Excel menu here. So first we're going to click down to our options, click on "Options", then we're going to click on "Add-Ins" here. You'll notice that it says Analysis ToolPak, and then right underneath, it says Analysis ToolPak VBA. The second one, the VBA is a Visual Basic version of this. We can use this first one, the Analysis ToolPak. We're going to click on here. I'm going to click on "Go". Now, when I click on "Go", I have this toggle here, which will allow me to add in the Analysis ToolPak on my Excel, and I'm going to click on both of these right here and hit "Okay". Now, when I do this, what's going to happen is that, in my data tab up here in my Excel, I've got different ribbons. I've got Home, Insert, Page Layout, Formulas, Data. If I click on My Data tab on the far right-hand side of this, I'm now going to have a data analysis option that's available to me. So I'm going to start using this data analysis option. So if you haven't loaded in the Analysis ToolPak, I would recommend just pausing this right now, and just go through those steps, and make sure that you have the Analysis ToolPak available to you on your Excel. So using the Data Analysis tab, what I'm going to do is I'm going to click on this. When I click on this, I get some different options in terms of my data analysis, from analysis of variance to correlation, covariance, some different descriptive statistics, and what have you. The tool that we're going to be talking about here and we're going to be using is what we call regression. Scroll down here, and there's a little word right there regression. I'm going to click on that. So when I click on "Regression", it pulls up a tab that allows me to input information. Now, the regression analysis itself is a tool that's trying to identify relationships between different variables. So for a second, I'm going to back up and just tell you what these relationships are.