Y 17 25 52 39 37 26 34 6 57 39 26 42 26 37 49 38 22 55 35 38 55 24 21 22 14 12 31 30 43 18 27 41 43 32 17 36 23 28 36 27 29 53 41 32 50 X1 7 12 68 83 89 75 57 6 96 42 10 95 63 94 90 19 40 75 70 32 85 45 14 96 73 34 41 48 50 3 51 65 98 60 17 88 63 86 85 60 24 90 51 6 82 X2 48 86 90 99 22 37 86 1 97 29 7 18 58 38 41 88 28 75 58 85 94 90 72 19 6 3 67 53 58 8 47 39 67 17 35 12 27 21 25 44 39 38 90 25 98 X3 39 20 84 20 25 1 3 52 63 71 34 87 63 33 93 55 91 88 34 80 69 9 89 61 60 23 27 33 81 94 37 68 36 55 5 97 15 42 9 23 24 91 85 60 68 X4 32 26 87 19 58 5 52 14 64 74 95 54 46 31 88 99 20 84 48 63 83 1 25 23 18 11 84 13 96 73 11 73 9 41 51 75 2 24 85 32 77 65 57 64 56 X5 17 22 34 23 17 7 27 2 33 21 19 12 20 14 25 35 8 31 20 29 35 17 18 6 4 2 30 12 32 16 12 22 16 11 17 16 5 9 21 14 22 21 30 17 31 X6 0 2 12 16 18 16 11 2 19 8 3 19 11 20 17 4 8 15 13 4 16 10 2 19 14 6 7 9 9 1 10 12 21 13 3 17 12 17 16 10 6 19 8 0 15

10.7 Consider the data set in Table 10.20, which consists of a dependent variable Y and six predictor variables, X1, X2, X6. Analyze the data set for collinearity. In particular. (a) Compute the condition number for the X-variables. Is there any evidence of collinearity? (b) Compute all principal components (PCs) and regress Y on all PCs. Which PCs are significant? (c) Construct the scatter plot of the first two PCs. What would the slope of the least squares regression line describing the relationship between these two PCs be? Why? (d) How many sets of collinearity exist in the data? (e) Which of the variables are involved in each set? (f) What is the relationship among the variables in each set of collinear variables? (g) How many principal components would you use to deal with collinearity in this case? (h) Which model would you recommend to describe the relationship between Y and the other predictors variables? Table 10.20 A Data Set for Exercise 10.7. X2 ; Row Y X1 X5 6 8 9 10 11 1 12 14 13 14 15 16 17 18 19 20 93 55 91 88 34 80 co 69 9 20 84 3 51 51 65 17 88 63 17 16 10 23 27 29 10.7 Consider the data set in Table 10.20, which consists of a dependent variable Y and six predictor variables, X1, X2, X6. Analyze the data set for collinearity. In particular. (a) Compute the condition number for the X-variables. Is there any evidence of collinearity? (b) Compute all principal components (PCs) and regress Y on all PCs. Which PCs are significant? (c) Construct the scatter plot of the first two PCs. What would the slope of the least squares regression line describing the relationship between these two PCs be? Why? (d) How many sets of collinearity exist in the data? (e) Which of the variables are involved in each set? (f) What is the relationship among the variables in each set of collinear variables? (g) How many principal components would you use to deal with collinearity in this case? (h) Which model would you recommend to describe the relationship between Y and the other predictors variables? Table 10.20 A Data Set for Exercise 10.7. X2 ; Row Y X1 X5 6 8 9 10 11 1 12 14 13 14 15 16 17 18 19 20 93 55 91 88 34 80 co 69 9 20 84 3 51 51 65 17 88 63 17 16 10 23 27 29