Answer Happy

marks 2. (15 marks) The world's 10 largest companies yield the following data: 3 4 5 8 10 Company X1 =sales X2 =profits ei (x1, x2) 1 144.25 32.18 2 152.36 16.59 95.04 10.91 95.41 65.45 14.14 65.97 62.97 9.52 63.31 6 263.99 25.33 264.81 7 265.19 18.54 285.06 15.73 285.47 9 92.01 8.10 165.68 11.13 166.00 * 265.73 92.27

These data give x= 159.20 16.28 S 7227.6 287.9 287.9 57.0 and ey is an eigenvector of the sample covariance S that is associated with the largest eigenvalue. (a) Detect if there exist some outliers in the data by standardized values of data, and give the reason. (5 marks) (b) Calculate e1(21, X2)' for the first two companies. (5 marks) (c) according to the following table, test if e; (x1, x2)' follows a normal distribution by using the QQ plot correlation test at the significance level .10. (The critical value at the significance level .10 and the sample size 10 for the QQ plot correlation test for normality is .9351) (5 marks) .05 .15 .25 .35 .45 .55 .65 .75 .85 .95 Probability level (j – 1/2)/n Standard normal quantile -1.645 -1.036 -.674 -.384 --125 .125 .385 .674 1.036 1.645

a (c) according to the following table, test if e: (21, x2)' follows a normal distribution by using the QQ plot correlation test at the significance level .10. (The critical value at the significance level .10 and the sample size 10 for the QQ plot correlation test for normality is .9351) (5 marks) .05 .15 .25 .35 .45 .55 .65 .75 .85 .95 Probability level (j – 1/2)/n Standard normal quantile -1.645 -1.036 -.674 -.384 -.125 .125 .385 .674 1.036 1.645