X

Let X be a 5 x 3 design matrix [, 1] [, 2] [,3] [1,] 1.8 0.9 2.1 [2,] 2.9 1.4 3.3 [3,] 0.9 1.8 2.7 [4,] 0.3 1.1 2.4 [5,] 0.3 0.3 2.1a. What will be the ratio of the distance between two observations if: . The matrix is recorded in centimeters for all 5 variables. . The matrix is recorded in kilometers for all 5 variables. Is this the same for all Minkowski distances? b. Let X and Y be jointly (bivariate) normal, with Var(X) = Var(Y). Write out both the joint and marginal distributions. Hint: If you are missing any values, then just leave them as unknown values. c. Let the points A, B, ..., E lie on a straight line where d( A, B) = 1, d(B, C) = 2, ., d( D. E) = 4 and each point is to the right of the previous point. Show that both the single linkage agglomeration and single linkage divisive methods produce the same clusters. d. Describe the situation when the distance from the origin to a point in p dimensional space is the same for: euclidean, manhattan, and chebychev distances. e. Given a dataset with 2 binary categorical variables, show that the use of any of the three main distance measures for continuous data do not make sense. Provide examples