Please provide all code in R. Thanks!
3. Here we'll look at the relationship between undergraduate GPA and LSAT scores amongst individuals applying to law school. (a) The law data is stored in the bootstrap package in R. To load and plot it, enter the following commands: install.packages ("bootstrap') library (bootstrap) data(law) plot (law) Does there appear to be a strong relationship? Calculate the correlation. (b) Take B = 1000 bootstrap replicates of the data to get 1000 bootstrap estimates of correlation. Create a histogram of the bootstrap correlations. Insert a red vertical line in the histogram showing the correlation calculated on the original data. (c) Calculate the bootstrap percentile confidence interval for correlation and insert blue vertical lines in the histogram from part (b) at the upper and lower limits. Based on this, could we reject the null hypothesis that the true correlation is equal to 0.5? (d) Calculate the bootstrap estimate of bias as well as the (standard) bias corrected boot- strap percentile confidence interval. Insert additional green vertical lines in the histogram showing the bounds for this new interval. According to this, could we reject the null hypothesis that the true correlation is equal to 0.5? (e) Based on these confidence intervals, you should see strong evidence that the true correlation is not equal to 0. Design a permutation test to explicitly test this. 3. Here we'll look at the relationship between undergraduate GPA and LSAT scores amongst individuals applying to law school. (a) The law data is stored in the bootstrap package in R. To load and plot it, enter the following commands: install.packages ("bootstrap') library (bootstrap) data(law) plot (law) Does there appear to be a strong relationship? Calculate the correlation. (b) Take B = 1000 bootstrap replicates of the data to get 1000 bootstrap estimates of correlation. Create a histogram of the bootstrap correlations. Insert a red vertical line in the histogram showing the correlation calculated on the original data. (c) Calculate the bootstrap percentile confidence interval for correlation and insert blue vertical lines in the histogram from part (b) at the upper and lower limits. Based on this, could we reject the null hypothesis that the true correlation is equal to 0.5? (d) Calculate the bootstrap estimate of bias as well as the (standard) bias corrected boot- strap percentile confidence interval. Insert additional green vertical lines in the histogram showing the bounds for this new interval. According to this, could we reject the null hypothesis that the true correlation is equal to 0.5? (e) Based on these confidence intervals, you should see strong evidence that the true correlation is not equal to 0. Design a permutation test to explicitly test this
