Estimates of regression coefficients are most commonly obtained using OLS, ordinary least squares. Assume that we are interested in the relationship between Y and X and study this relationship by estimating the regression
Yi = ?0 + ?1Xi + ?i.
We denote the OLS estimators of ?0 and ?1 as ?0 and ?1. We can use these to define the predicted value of Yi which we write
Yi = ?0 + ?1Xi.
a) Define the residual, ei, for individual i with the help of Yi and Yi. You don’t have to but you may do it in a graph. Give an intuitive interpretation of ei.
b) The OLS estimate of ?0 and ?1 are the values that minimizes the sum of the squared residuals. Why is minimizing the sum of squared residuals intuitively appealing?