Please help me with solving questions (a) and (b). Provide all the steps to get to the final solution. THANKS a lot!

In their book "Mastering 'Metrics" (2015), Angrist and Pischke use linear regression to answer the question of whether it's worthwhile spending a lot of money each year on private university tuition, as many American students do. Using data for former students (schools that they attended, SAT-test scores they had received, gender, race etc. ), they estimate among others the following model yi = a + Bpi + yAitei, where y; is an individual i's earnings, p; is a dummy for if an individual attended a private college or university (p; = 1) or not (p; = 0) and A; symbolizes a set of additional control variables. e; is the error term. Using the table below from Angrist and Pischke (2015), answer the following questions (a) Interpret the coefficient in column (1) in the table. (b) Interpret the first coefficient in column (2) in the table. Why has the coefficient on Private school changed from column (1) to column (2)? What can you say about the control variable in this case?TABLE 2.3 Private school effects: Average SAT score controls No selection controls Selection controls (1) (2) (3) (4) (5) (6) Private school .212 .152 .139 034 .031 .037 (.060) (.057) (.043) (.062) (-062) (.039) Own SAT score + 100 051 024 .036 .009 (-008) (.006) (-006) (.006) Log parental income 181 .159 (.026) (.025) Female -.398 -.396 (.012) (.014) Black -.003 -.037 (.031) (.035) Hispanic .027 .001 (.052) (.054) Asian .189 .155 (.035) (.037) Other/missing race -.166 -.189 (.118) (.117) High school top 10% .067 .064 (.020) (.020) High school rank missing 003 -.008 (.025) (-023) Athlete .107 .092 (.027) (024) Average SAT score of .110 .082 .077 schools applied to + 100 (.024) (.022) (.012) Sent two applications .071 -062 .058 (.013) (.011) (.010) Sent three applications .093 .079 .066 (.021) (.019) (.017) Sent four or more applications 139 127 .098 (.024) (-023) (.020) Notes: This table reports estimates of the effect of attending a private college or university on earnings. Each column shows coefficients from a regression of log earnings on a dummy for attending a private institution and controls. The sample size is 14,238. Standard errors are reported in parentheses