(b) The examination results of 13 students in three statistics papers (a foundation paper, ST777; a more advanced paper, ST888; and a dissertation, ST999) were as follows. Note that grade of ST999 is on a pass/fail basis. Here 1 stands for pass while 0 stands for fail. ST777 (x) ST888 (y) ST999 (2) 70 88 73 99 70 89 84 77 92 73 60 88 78 54 77 0 57 83 60 79 70 1 1 1 1 1 0 60 84 52 42 1 1 01 73 65 1 1 Useful summary statistics for the data are: = 1041 = 84801 x Yi = = 856 ? = 58402 xiyi = 70203 i. Calculate and comment on the sample correlation coefficient between the marks of ST777 and ST888. Is this correlation significant at 5% level? ii. If you were told a student achieved a mark of 55 in ST777, give a point prediction for that student's mark in ST888. Please carefully state the assumptions you make here. iii. Explain why it is inappropriate to use linear regression to model the outcome of ST999 based on the marks of ST777 and ST888. iv. Finally, we would like to use logistic regression to predict the outcome of ST999 based on the marks of ST777 and ST888. Write down the algebraic form of the model. [10 marks for both parts; 20 marks in total]