4. This exercise refers to the following model: wage; = Bo + Bigrade, + wi, where the wage of individual i is regressed on his/her highest grade completed and a constant term. You are asked to compute the intercept and slope estimates in a variety of ways, and compare your results in each case. First, use the command keep if !missing (wage, grade) to drop people with missing wage or grade from the dataset. (a) How many observations were dropped? (b) Use the regress command to estimate the coefficients Bo and 31. What is the value of Bo? What is the value of B1? (Hint: type regress wage grade, the constant term will be added automatically to the regression. To find Bo, check the row labeled by _cons and the column labeled by Coef.) (c) You are now asked to compute the same estimates using a different procedure: . Compute the sample covariance between wage and grade, and the sample variance of grade, and save them in two scalars, cov_wg and var_g. (Hint: you can compute the variance-covariance matrix using the corr command, with the option covariance. For instance, if you type corr wage grade, covariance, the output will be a matrix containing the variance of wage, the variance of grade and the covariance between wage and grade. On a related note, the three values will be stored in r(Var_1), r(Var_2) and r(cov_12), respectively. You can check the list of stored objects by typing return list just after running the corr command.) . Generate the scalar beta_1 equal to cov_wg / var_g and display it by typing display beta_1. What is the relation between this estimate for , and the one in 4(b)