Question 4.28 The effectiveness of a tablet containing x mg of drug I and x2 my of drug 2 was being tested. In trials the following results were obtained: % effectiveness, y 92.5 50.9 20.8 94.9 54.1 16.9 89.3 47.3 25.2 94.1 45.1 49.7 98.9 37.6 95.2 [y = 469.7 [x1 =235 [x2 = 207.8 x =11,202.68 x3 =12,886.42 [ yxi = 22,028.78 _ xx2 = 19,870.22 xx2 =8,985.96 (i) Using the multiple linear least square regression model: y =a+ By+ Buzzte (a) Show that the least squares estimates of o, , and B2 satisfy: [ vi = na + B, Ex + BZ )$12 (b) Hence, using the above data, find their numerical values. [7] (ii) Predict the percentage effectiveness for a tablet containing 51.3 mg of drug x and 18.3 mg of drug x2- [2] [Total 9]Question 5.15 A revolutionary study programme has been developed to help students memorise facts before exams. The authors of the programme state that if you study their material for several days, your performance in standardised tests will improve. A publishing company wants you to investigate the authors' claims, and has provided you with the following information, which shows the average scores obtained by eight random samples of five students, with each sample being given a different number of days to study the materials: Number of days spent studying (x) 1 2 3 4 5 6 7 8 Average score (% ) in test (y) 25 28 35 48 50 61 71 79 You are given the following information: [x=36, [ y =397, Ex? = 204, [ y? = 22,441, [ xy = 2,123 (i) Plot a scatter diagram of the data. Comment on the appropriateness of using a linear regression model here. [3] (ii) One of the authors has claimed that the correlation coefficient is more than 0.9. Test this claim at the 5% level. [5] (iii) Find the equation of the least squares linear regression line. [2] (iv) Find a 95% confidence interval for the slope parameter B . [3] (v) Find a 99% confidence interval for the mean score you could expect in the test if you studied the material for 4 days. [3] (vi) Comment on the claim "Study this material for a fortnight and you'll perform really well in tests". [1] [Total 17]