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SARA ELLISON: OK, so last time right at the end of the lecture, I had introduced a more general linear model, the multivariate linear model. And I had just gone through the first couple of these slides, saying let's analyze this model using a different notation, in particular matrix notation, because the summation notation was just too clunky. It wasn't up for the job. And so let me just go through quickly. Let's see. This was, I think, the next to last slide I had up. So if we let y be the column vector of all of the observations on the dependent variable, then let epsilon be the column vector of all of the errors, and then let x be the matrix, where across the rows of the matrix, we have first the column of ones, and then a column of each of the explanatory variables. And then sort of down the matrix, we have observations on each of the-- well, we have each of the observations. Each observation corresponds to a row. So if we define this matrix and vectors th...

[SQUEAKING] [RUSTLING] [CLICKING] SARA ELLISON: OK, so a little bit of a review. I want to put what Esther has been doing the last few lectures into a little bit broader context. And that's going to be a sort of a nice segue into talking about linear regression. So what did we do for the first sort of half of the semester? We established a foundation in probability, and we proceeded to talk about how to estimate unknown parameters, OK. Most, if not all of that discussion, was focused on estimating parameters of a univariate distribution, OK. So we were talking about estimating the mean or estimating the variance or something like that. Some other parameter that characterizes sort of a univariate distribution. But so much of what we care about in social science and in lots of other settings, I mean, maybe most other settings, involves joint distributions, though. And so we really have to be concerned with how to estimate parameters characterizing either joint distribut...

[SQUEAKING] [RUSTLING] [CLICKING] SARA ELLISON: OK, where were we? Well, so this is our summary to date that I had up right before the midterm. So let me just remind you what we had just finished up. So we talked about a general discussion of estimation and also a discussion about the sample mean. We talked about criteria for assessing estimators. And we talked about frameworks for deriving estimators. And that's where we left off right before midterm. So we've seen various estimators. And we've made observations about their distributions. We've discussed how we might derive them, either by just being clever and thinking of them off the top of our head, or using maximum likelihood estimation, or using method of moments estimation to derive estimators. And then we also discussed the criteria that we might use to choose among them. That's fine. That's all useful. But when we actually have to report estimates, when we're confronted with a real dat...