Let’s step back and look at an equation z equals x times y. If we knew both z and x, then we can solve for y. Similarly, if we knew both z and y, then we can solve for x. In other words, if we know any two of the three variables in this equation, we can solve for the one that’s missing. So, now let’s revisit the factor model, keeping in mind that we can think of the stock return, the factor exposure, and the factor returned as three variables. If we can calculate two of these, then we can use regression to estimate the third variable that’s missing. In the case of a time series risk model, like the Fama-French example, we get the stock return in factor returns first. So, we use regression to estimate the factor exposure Beta. For a cross-sectional risk model, we get the stock return and factor exposure Betas first. Then we use regression to estimate the factor return. Again, this might take some getting used to, because when we look at regression formulas, we’re probably used to seeing a letter y for the dependent variable, a letter x for the independent variable, and a Greek letter Beta to represent the coefficient that we’re estimating. Instead, we can shake things up and let our brains be more flexible. So, we’ll think about what data is available as inputs for the regression and what variables we don’t have, and we’ll estimate with regression.