Instructions. Answer ALL 3 questions in your exam Answer Booklet. Detailed answers are required to obtain full marks. 1. A stockbroker believes that the share price of publicly-listed shares in which the average family invests is highly related to consumer confidence as reflected in average retail sales. The stockbroker collects a sample of blue-chip stocks, including SIA, DBS, OCBC, and Singtel, averages their share price at the end of trading day and then compares this price against an index of retail sales ranging from 1 to 100 (where the higher the index is, the higher the retail sales). Retail Index(X) Average share price ($) (Y) 56 12 76 13 23 10 76 15 43 14 67 15 a) Construct a scatter plot. [2 marks] b) Use the least-squares method to find the regression equation. [4 marks] c) Interpret the meaning of bo and bi- [2 marks] d) Using the model from b), predict the mean value of the share package if the retail index is 60. [2 marks] e) Calculate the value of retail index if the mean value of the share package is 14. [2 marks] f) Compute the correlation coefficient between the 2 variables. [3 marks] g) Given the value calculated in f) above, describe the relationship between the retail index and the average share price. [3 marks] h) State two (2) assumptions relating to the errors of the Linear Regression. [2 marks]