Mostly Harmless Econometrics

02Understanding Regression: Building and Interpreting Models

You're looking to buy a house. You've got a list of factors that you think will affect the price: location, size, age, and so on. But how do you figure out how much each of these factors contributes to the price? Enter regression, a statistical tool that helps us understand the relationship between different variables. In our house-buying scenario, the price of the house is what we're trying to predict or explain. This is our dependent variable. The factors that we think will affect the price, like location, size, and age, are our independent variables. Think of regression like baking a cake. The type of cake (chocolate, vanilla, red velvet) you end up with depends on the ingredients you use and their quantities. Similarly, the price of the house depends on the factors we've identified and their 'quantities' or values. Now, how do we build a regression model? First, we need to decide which variables to include. In our house price example, we might start with location, size, and age. But we could also consider other factors, like the number of bathrooms or proximity to schools. Next, we need to decide on the form of the relationship. For instance, does the price increase linearly with size, or does it increase at a decreasing rate (a quadratic relationship)? To estimate the parameters of our model (how much each factor contributes to the price), we use a method called least squares. This method minimizes the difference between the actual prices and the prices predicted by our model. It's important to remember that building a regression model isn't just about crunching numbers. We also need to use theory and prior empirical evidence to guide our choices. Once we've built our model, we need to interpret it. The coefficients in our model tell us the average change in the house price for a one-unit change in an independent variable, holding all other variables constant. For instance, the coefficient on size might tell us that for each additional square foot, the price increases by $200. We also need to consider statistical significance. This tells us whether the observed relationship between the house price and our factors is real or just due to chance. But regression isn't perfect. It relies on several assumptions, like a linear relationship between the dependent and independent variables, and no correlation between the independent variables. If these assumptions are violated, our results might be misleading. For instance, if larger houses are more likely to be newer, then size and age are correlated, which can distort our results. We need to be aware of these issues and know how to diagnose and address them. In conclusion, understanding, building, and interpreting regression models is a powerful tool for making sense of the world around us. Whether you're buying a house, running a business, or conducting research, regression can help you uncover the relationships that matter. So go ahead, take these concepts and apply them in your own field of interest. You might be surprised at what you discover.

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