1.ABC crop wants to examine the ability of certain factors to explain or predict the number of units sold of its product(Y) over the past quarter by its sales force. Its market research department extract a random sample of n=20 sales man from this record and Identifies the following p = 4 variables an possible regression or predictor: Number of 'cold' calls (visits) made (X1): number of follow up calls (visits) made (X2); average amount of time (in minutes) spend with client (X3); and number of month of sales experience (X4). This observation appear in following table. In what follows the aforementioned variable will be coded as such: units (Y); cold (X1); Fall(X2); clt(X3) and exp(x4). Units (Y) Cold (X1) Fall(X2) Cit(x3) Exp(x4) 12 14 62 10 20 21 120 12 27.25 45 100 16 20 27 24.25 13 50 8 25 10.5 85 16 19 30 20.75 20 130 16 46 24.5 20 115 17 24.25 50 15 80 14 28 15 125 22 20 65 30.75 14 59 10 21 15.75 53 13 - 15 25 16.5 50 13 14 25 17.5 60 13 10 20 21 111 19 17 55 23.25 16 89 10 30 20 20 126 22 58 30.5 15 77 15 29 18.25 60 9 26 20.25 21 119 18 45 31.75 22 110 15 51 36.25 a) Obtain Hat matrix. b) Verify properties i) n = + (x-x)'(x,'x.) (x - x) H) Eh, No. of parameters. lil) 0 hu 1 and iv) -0.5 hy 0.5. c) Check whether outline present or not in Y space. d) Check whether outline presentor not in X space. e) Identify influential case. 1.ABC crop wants to examine the ability of certain factors to explain or predict the number of units sold of its product(Y) over the past quarter by its sales force. Its market research department extract a random sample of n=20 sales man from this record and Identifies the following p = 4 variables an possible regression or predictor: Number of 'cold' calls (visits) made (X1): number of follow up calls (visits) made (X2); average amount of time (in minutes) spend with client (X3); and number of month of sales experience (X4). This observation appear in following table. In what follows the aforementioned variable will be coded as such: units (Y); cold (X1); Fall(X2); clt(X3) and exp(x4). Units (Y) Cold (X1) Fall(X2) Cit(x3) Exp(x4) 12 14 62 10 20 21 120 12 27.25 45 100 16 20 27 24.25 13 50 8 25 10.5 85 16 19 30 20.75 20 130 16 46 24.5 20 115 17 24.25 50 15 80 14 28 15 125 22 20 65 30.75 14 59 10 21 15.75 53 13 - 15 25 16.5 50 13 14 25 17.5 60 13 10 20 21 111 19 17 55 23.25 16 89 10 30 20 20 126 22 58 30.5 15 77 15 29 18.25 60 9 26 20.25 21 119 18 45 31.75 22 110 15 51 36.25 a) Obtain Hat matrix. b) Verify properties i) n = + (x-x)'(x,'x.) (x - x) H) Eh, No. of parameters. lil) 0 hu 1 and iv) -0.5 hy 0.5. c) Check whether outline present or not in Y space. d) Check whether outline presentor not in X space. e) Identify influential case
