Applied Statistics Question 4 A hotel manager is reviewing the efficiency of his workers. He collects the following data from the cleaning department. X represents the working experience of a worker in the cleaning department (recorded in months) and Y represents the number of minutes the worker uses to finish cleaning the hotel's common area. X 14 12 26 12 20 18 260 240 223 211 227 237 X 48 27 18 40 45 25 196 188 208 200 191 161 (a) Calculate the coefficient of correlation of the above data. (1 mark) (b) The manager believes that the longer the working experience in the cleaning department, the faster should the worker finish the cleaning. Does the data support him? (Answer: Yes/No) (1 mark) (c) Find the values of a and b in the regression line y = a + bx of the above data. (2 marks) (d) Interpret the value of a and b in the regression line in part (c). (2 marks) (e) Peter has been working in the cleaning department for 20 months. Use the regression line in part (c) to estimate how long does it take him to finish cleaning the hotel's common area. (2 marks) (f) Is the estimation in part (e) reliable? Explain your answer with reason. (2 marks) (Total: 10 marks)