Use the data "catholic p5numpla p5hmage p5hdage w3daded_hsb w3momed_hsb w3momscr w3dadscr w3income w3povrty p5fstamp c5r2mtsc 0 1 47 45 0 0 53.5 77.5 62500.5 0 0 60.043 0 1 41 48 0 0 34.95 53.5 45000.5 0 0 56.28 0 1 43 55 0 0 63.43 53.5 62500.5 0 0 55.272 1 1 38 39 0 0 53.5 53.5 87500.5 0 0 64.604 0 1 47 57 0 0 61.56 77.5 150000.5 0 0 75.721 0 1 41 41 0 0 38.18 53.5 62500.5 0 0 54.248 0 1 31 32 1 1 34.95 29.6 32500.5 0 0 40.064 0 1 38 41 0 0 63.43 33.42 37500.5 0 0 46.097 0 1 26 28 1 1 35.78 29.6 45000.5 0 1 53.336 " for the following assignment. The data is from a longitudinal study that focused on children's early school experiences beginning with kindergarten through third grade. Analyze the effect of going to Catholic school, as opposed to public school, on student achievement. Because students who attend Catholic school on average might be different from students who attend public school, we will use propensity score matching to get more credible causal estimates of Catholic schooling. For this assignment, we'll assume that the covariates listed below are the only variables that matter and there are no unmeasured confounders. Data Description: Each row represents information collected on a unique child. Outcome variable: c5r2mtsc: child's math test scores Treatment variable: catholic: 1 = child went to catholic school (treatment group); 0 = child went to public school ( control group) Covariates: p5numpla: # of places child has lived for at least 4 months since 1st grade p5hmage: age of mother p5hdage: age of father w3daded_hsb: 1 = father's education level is high school or below, 0 = some college or above w3momed_hsb: 1 = mother's education level is high school or below, 0 = some college or above w3momscr: mother's occupational prestige score w3dadscr: father's occupational prestige score w3income: family income w3povrty: poverty score dummy p5fstamp: food stamp dummy Answer the following question using the propensity score matching technique using R code. 1) Examine initial covariate balance before matching. Create table1 with standardized differences. 2) Estimate the propensity score (the probability of being Treated given a set of pre-treatment covariates) for each student, and plot the propensity overlap plot to examine the region of common support. 3) Execute the 1-to-1 matching algorithm on the logit of propensity score. Use the caliper of 0.01. 4) Examine covariate balance after matching. Create table1 with standardized differences. 5) Estimate the treatment effect, i.e., the difference between the mean math test scores of children who went to Catholic school and those who went to Public school. Is it statistically significant? Provide appropriate conclusions.