Please write the code in R. Don't post the previous wrong answer. Will give thumbs up for the correct and complete answer. The file (T9-12.DAT )contains this data.

93.0 96.0 97.8 9 12 9 20

88.8 91.8 96.8 7 10 10 15

95.0 100.3 99.0 8 12 9 26

101.3 103.8 106.8 13 14 12 29

102.0 107.8 103.0 10 15 12 32

95.8 97.5 99.3 10 14 11 21

95.5 99.5 99.0 9 12 9 25

110.8 122.0 115.3 18 20 15 51

102.8 108.3 103.8 10 17 13 31

106.8 120.5 102.0 14 18 11 39

103.3 109.8 104.0 12 17 12 32

99.5 111.8 100.3 10 18 8 31

103.5 112.5 107.0 16 17 11 34

99.5 105.5 102.3 8 10 11 34

100.0 107.0 102.8 13 10 8 34

81.5 93.5 95.0 7 9 5 16

101.3 105.3 102.8 11 12 11 32

103.3 110.8 103.5 11 14 11 35

95.3 104.3 103.0 5 14 13 30

99.5 105.3 106.3 17 17 11 27

88.5 95.3 95.8 10 12 7 15

99.3 115.0 104.3 5 11 11 42

87.5 92.5 95.8 9 9 7 16

105.3 114.0 105.3 12 15 12 37

107.0 121.0 109.0 16 19 12 39

93.3 102.0 97.8 10 15 7 23

106.8 118.0 107.3 14 16 12 39

106.8 120.0 104.8 10 16 11 49

92.3 90.8 99.8 8 10 13 17

106.3 121.0 104.5 9 17 11 44

106.0 119.5 110.5 18 15 10 43

88.3 92.8 96.8 13 11 8 10

96.0 103.3 100.5 7 15 11 27

94.3 94.5 99.0 10 12 11 19

106.5 121.5 110.5 18 17 10 42

106.5 115.5 107.0 8 13 14 47

92.0 99.5 103.5 18 16 8 18

102.0 99.8 103.3 13 12 14 28

108.3 122.3 108.5 15 19 12 41

106.8 119.0 106.8 14 20 12 37

102.5 109.3 103.8 9 17 13 32

92.5 102.5 99.3 13 15 6 23

102.8 113.8 106.8 17 20 10 32

83.3 87.3 96.3 1 5 9 15

94.8 101.8 99.8 7 16 11 24

103.5 112.0 110.8 18 13 12 37

89.5 96.0 97.3 7 15 11 14

84.3 89.8 94.3 8 8 8 9

104.3 109.5 106.5 14 12 12 36

106.0 118.5 105.0 12 16 11 39

1. A firm is attempting to evaluate the quality of its sales staff and is trying to find an examination or series of tests that may reveal the potential for good performance in sales. The firm has selected a random sample of 50 sales people and has evaluated each on 3 measures of performance: growth of sales, profitability of sales, and new-account sales. These measures have been converted to a scale, on which 100 indicates 'average' performance. Each of the 50 individuals took each of 4 tests, which purported to measure creativity, mechanical reasoning, abstract reasoning, and mathematical ability, respectively. The n=50 observations on p=7 variables are listed in the eclass named as T9-12.DAT.

(a) Assume an orthogonal factor model for the standardized variables. Obtain the (unrotated) principal component solution and the (unrotated) maximum likelihood solution for m=2 and m=3 common factors. Given these four solutions, obtain the rotated solutions. For all eight of these fits, list (i) the proportions of variance accounted for by each of the m factors, (ii) estimated communalities, (iii) specific variances, and (iv) the sum of squares of the residuals for the m=2 and m=3 solutions. When I run your R program I should see eight pieces of output displayed, each similar to the following. rotated pc solution, m=2 :

prop. variance =0.450.41 ss.resids =0.24