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An insurer has collected data on average alcohol consumption (units per week) and cigarette smoking (average number of cigarettes per day) in eight regions in the UK. Region. i 1 2 3 4 5 6 7 8 Average Alcohol unis per week, 5 15 25 21 29 13 18 21 17 19.875 Cigarettes per day, Mi 4 8 8 10 6 9 7 5 7.125 For these observations we obtain: Exx;=1,190; 247 =3,355; Ex? =435 Calculate the coefficient of correlation between alcohol consumption and cigarette smoking. 141 (ii) Calculate a 95% confidence interval for the true correlation coefficient. You may assume that the joint distribution of the two random variables is a bivariate normal distribution. (6] (iii) Fit a linear regression model to the data, by considering alcohol consumption as the explanatory variable. You should write down the model and estimate the values of the intercept and slope parameters [3] (iv) Calculate the coefficient of determination R2 for the repression model in part [iii). (v) Give an interpretation of R- calculated in part (iv) [1] [Total 15]