Assume you are going to estimate a linear regression based on the following data. 7 Advertising Expenditure 3 5 6 3.5 4 4.5 7 7.5 8.5 ($'000s) Sales 50 250 700 450 75 150 200 750 800 1100 ($'000s) a. Estimate the slope and intercept coefficients of the linear regression model. (5 marks) b. If advertising expenditure is equal to $9,000, estimate the total Sales Income. (2 marks) Question 2 Approximately three (3) out of every four (4) Australians who filed a tax return received a refund in a particular year. If three (3) individuals are chosen at random from among those who filed a tax return that year, find the probabilities of the following events; a. All three (3) received a refund. b. None of the three (3) received a refund. (3 marks) (2 marks) c. Exactly one received a refund. (2 marks) Question 3 The number of accidents that occur on an assembly line have a Poisson distribution with an average of three (3) accidents per week. a) Find the probability that a particular week will be accident free. b) Find the probability that at least three (3) accidents will occur in a week. c) Find the probability that exactly five (5) accidents will occur in a week. (3 marks) (2 marks) (2 marks)