Speaker 1: Now a very useful and powerful tool for getting students to think about what regressions look like is Excel. Now Excel is useful simply because students are generally quite familiar with the interface of Excel and students can see what happens with data as we create new variables in Excel but also it's relatively straightforward to carry out regressions in Excel. So this example is based on an exercise that I set for students and in the exercise I asked students to estimate a relationship between the natural log of weekly wage, individuals age, the age left education, whether or not they are male or female and so on. Now the first thing that I always do with students whenever introducing them to regressions in Excel is walk them through how Excel can carry out OLS regressions for them. Now Excel has a regression capability built into it and if it's turned on it will be under the data part of the top menu. Now here we don't have anything about data analysis in this top right hand corner and the data analysis button is what we're going to need to press in order to turn on regressions. So in order to activate it you go to the file menu, click on options, then you click on add-ins and then you'll see at the bottom it says manage Excel add-ins, you click go, you need to select analysis tool pack and analysis tool pack VBA, you click OK and then a new button appears under the data menu which is called data analysis and this allows Excel to carry out regressions for you. Now this is slightly less elegant than using something like Stata in that if you want to carry out an OLS regression you need to first of all click on data analysis and then click regression and then you need to select the data which covers your dependent variable. So in this case let's use the weekly wage as the dependent variable. Now there's a whole load of options if you click labels that indicates that the first observation is a label for the data and similarly if you want to select your X data you can select that by again clicking and dragging. So now we've got our dependent variable is selected as weekly wage and we've got that column indicated as our weekly wage and our explanatory variable is just age. If you click OK you get a new worksheet created with our regression results included. Now there are some little fiddly bits that we need to be aware of when we're using Excel to carry out regressions. The first thing is that if you want to include multiple explanatory variables, the explanatory variables that you want to include need to be next to each other in the sheet. So we couldn't include age and the private sector dummy here without also including the age left education or we would need to delete that column. So you can include multiple explanatory variables but you need to make sure that they are next to each other within the data set. So for instance if we wanted to carry out a regression with not just age but also age left education we could change this input X range so that we select both column B and column C down to C101 and now we're going to have both the age and the age left education as explanatory variables in our model. But if we'd wanted to do that for instance with the private sector dummy so let's see what happens if we try and do that just based on the two columns. Say we select this column for age and then press control and try and select the column for private sector as well. We now get an error message coming up. Excel cannot cope with columns that aren't next to each other. But in a way this is a good thing because it means that students think about the regression specification that they're running. The data looks like the regression specification that they're running. They have to do that by design. The other thing that I find Excel particularly good for is for illustrating to students the idea of perfect multicollinearity. In that if we've got two variables which are perfectly collinear for instance male and female and if we try to introduce both of these explanatory variables we can see the relationship that exists between the two variables and it's very obvious to students when they see data in this format what that relationship is.