You must provide clear working, notation and answers. You may use a calculator or other means to perform calculations, however you must show clearly all your working - full marks will only be given with correct and clear working. YOU MUST NOT USE 'R' FOR QUESTION 1. 1. A group of students completed a piece of homework. Their marks as a percentage, along with the number of study hours spent outside of class over a three-week period are given in the following table: Stud hours 20 16 34 23 27 32 18 22 Homework mark (21) 64 61 84 70 88 92 72 77 (3) Plot a fully-labelled scatter diagram for the above data and make a comment on what it appears to show. [5 marks] (b) Calculate r, the correlation coefcient, and interpret this value. [10 marks] (0) Obtain the least-squares regression line for this data and interpret the values of the two constants. [10 marks] (d) Calculate the least-squares estimate of the variance of the residuals, 6'2. [10 marks] (e) Obtain a 95% condence interval for the mean response when the number of study hours is 25 and then perform a similar calculation for a 95% prediction interval. [15 marks]