Please do not use the "Im" command in R to run the regression, use the OLS formula instead! Both your detailed solution and your R code need to submitted in elearning. 1. (Univariate OLS) In order to study the effect of education (educ) on Earning (earning), we have a data set called PS2Earning.txt, which contains information on 935 individuals. Read in the data set in R and do the following. (a) Using the formulas on slide 22 of Lecture Note 3 to estimate the coefficient a and b in the following model, earning; = a + b educ; + What is the covariance between educ and the estimated residual? What can you say about the normal equation (see slide 24 of Lecture Note 3)? (b) Now use the the formula dito estimate the coefficient d in the following model, i=1 earning; d educi + ui (c) Is the mean of the estimated residuals zero, and why? Does the normal equation still hold now? What can you say about the covariance between educ and the estimated residual again? Is it a good idea to get ride of the intercept term?