Diffusion and Segmentation.

Include answers to questions and images of completed excel sheet in response. Data set, r output and questions are below.

Data set:

Month	Adopters
1	1
2	5
3	9
4	18
5	42
6	74
7	89
8	91
9	159
10	146
11	94
12	81
13	73
14	69
15	73
16	57
17	60
18	61

Call: principal(r = Data[, 2:16], nfactors = 15, rotate = "none") Standardized loadings (pattern matrix) based upon correlation matrix PC1 PC2 PC3 PC4 PC5 PC6 PC7 PC8 PC9 PC10 PC11 PC12 PC13 PC14 Form of letter of application 0.45 0.61 0.38 -0.10 0.10 0.44 0.10 0.09 0.21 0.01 -0.05 -0.06 -0.01 0.02 Appearance 0.58 -0.05 -0.03 0.29 0.75 -0.03 -0.01 -0.01 -0.04 0.01 0.04 0.00 0.09 -0.02 Academic ability 0.11 0.34 -0.52 0.70 -0.18 0.16 0.18 -0.02 -0.03 0.12 0.07 0.05 -0.01 0.00 Likeability 0.62 -0.19 0.56 0.38 -0.11 0.08 -0.08 -0.17 -0.19 0.07 -0.16 0.01 0.02 0.04 Self-confidence 0.80 -0.36 -0.29 -0.19 0.00 0.01 0.08 0.22 0.06 0.10 -0.17 0.11 0.00 -0.10 Lucidity 0.86 -0.19 -0.18 -0.08 -0.18 0.12 -0.30 0.01 0.06 0.11 -0.01 0.00 0.13 0.03 Honesty 0.43 -0.58 0.34 0.46 -0.05 -0.21 0.09 0.19 0.21 0.00 0.02 -0.05 -0.06 0.06 Salesmanship 0.89 -0.04 -0.22 -0.22 0.03 -0.08 0.01 -0.08 -0.04 0.21 0.07 -0.20 -0.09 -0.01 Experience 0.37 0.79 0.10 0.07 -0.09 -0.26 -0.07 0.33 -0.18 -0.01 -0.03 -0.04 0.04 0.01 Drive 0.86 0.07 -0.10 -0.17 -0.17 -0.18 0.29 -0.14 0.08 -0.09 0.01 -0.02 0.17 0.06 Ambition 0.87 -0.10 -0.25 -0.22 0.14 0.08 0.12 0.02 -0.17 -0.09 -0.07 0.06 -0.11 0.13 Grasp 0.91 -0.03 -0.14 0.08 -0.07 0.10 -0.24 0.06 0.04 -0.14 0.18 0.05 -0.03 0.04 Potential 0.91 0.03 -0.09 0.21 -0.11 0.04 -0.01 -0.08 -0.03 -0.24 -0.07 -0.09 -0.04 -0.14 Keeness to join 0.71 -0.12 0.56 -0.22 -0.10 0.05 0.15 0.03 -0.14 0.06 0.21 0.09 0.00 -0.08 Suitability 0.65 0.60 0.11 -0.02 0.07 -0.29 -0.10 -0.21 0.18 0.06 -0.03 0.12 -0.09 -0.01 PC15 h2 u2 com Form of letter of application -0.01 1 3.3e-16 4.1 Appearance 0.00 1 2.4e-15 2.3 Academic ability 0.01 1 4.4e-16 3.1 Likeability -0.06 1 1.4e-15 3.7 Self-confidence -0.06 1 1.1e-16 2.3 Lucidity 0.09 1 4.4e-16 1.8 Honesty 0.03 1 -8.9e-16 4.7 Salesmanship -0.03 1 1.1e-15 1.6 Experience 0.00 1 2.3e-15 2.3 Drive -0.03 1 1.3e-15 1.8 Ambition 0.06 1 6.7e-16 1.7 Grasp -0.10 1 1.6e-15 1.5 Potential 0.05 1 1.7e-15 1.4 Keeness to join 0.04 1 1.9e-15 2.8 Suitability 0.02 1 2.3e-15 3.1

PC1 PC2 PC3 PC4 PC5 PC6 PC7 PC8 PC9 PC10 PC11 PC12 PC13 PC14 PC15 SS loadings 7.51 2.06 1.46 1.20 0.74 0.49 0.35 0.31 0.26 0.18 0.15 0.10 0.09 0.06 0.04 Proportion Var 0.50 0.14 0.10 0.08 0.05 0.03 0.02 0.02 0.02 0.01 0.01 0.01 0.01 0.00 0.00 Cumulative Var 0.50 0.64 0.74 0.81 0.86 0.90 0.92 0.94 0.96 0.97 0.98 0.99 0.99 1.00 1.00 Proportion Explained 0.50 0.14 0.10 0.08 0.05 0.03 0.02 0.02 0.02 0.01 0.01 0.01 0.01 0.00 0.00 Cumulative Proportion 0.50 0.64 0.74 0.81 0.86 0.90 0.92 0.94 0.96 0.97 0.98 0.99 0.99 1.00 1.00

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Principal Components Analysis Call: principal(r = Data[, 2:16], nfactors = 4, rotate = "varimax") Standardized loadings (pattern matrix) based upon correlation matrix RC1 RC2 RC3 RC4 h2 u2 com Form of letter of application 0.12 0.83 0.11 -0.14 0.73 0.27 1.1 Appearance 0.44 0.15 0.40 0.23 0.43 0.57 2.8 Academic ability 0.06 0.13 0.01 0.93 0.88 0.12 1.0 Likeability 0.22 0.25 0.87 -0.08 0.87 0.13 1.3 Self-confidence 0.92 -0.11 0.16 -0.06 0.88 0.12 1.1 Lucidity 0.86 0.10 0.26 0.00 0.82 0.18 1.2 Honesty 0.22 -0.24 0.86 0.00 0.85 0.15 1.3 Salesmanship 0.91 0.22 0.10 -0.04 0.89 0.11 1.2 Experience 0.09 0.85 -0.05 0.21 0.78 0.22 1.2 Drive 0.80 0.35 0.16 -0.05 0.79 0.21 1.5 Ambition 0.92 0.16 0.10 -0.04 0.88 0.12 1.1 Grasp 0.81 0.25 0.33 0.14 0.85 0.15 1.6 Potential 0.75 0.33 0.41 0.22 0.89 0.11 2.2 Keeness to join 0.44 0.36 0.53 -0.52 0.89 0.11 3.7 Suitability 0.38 0.80 0.08 0.08 0.79 0.21 1.5

RC1 RC2 RC3 RC4 SS loadings 5.77 2.73 2.39 1.35 Proportion Var 0.38 0.18 0.16 0.09 Cumulative Var 0.38 0.57 0.73 0.81 Proportion Explained 0.47 0.22 0.20 0.11 Cumulative Proportion 0.47 0.69 0.89 1.00

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clusteranalysis <- kmeans(pc4$scores, centers =5, iter.max = 10, nstart = 2) clusteranalysis

K-means clustering with 5 clusters of sizes 7, 2, 16, 13, 10

Cluster means: RC1 RC2 RC3 RC4 1 1.1583789 -0.7798782 -1.1450024 0.6610491 2 -1.8921510 2.1361827 -2.3991022 0.6277571 3 0.6959956 0.6733108 0.3945668 -0.2589635 4 -0.7228193 -0.2245969 0.6666492 0.8782616 5 -0.6063629 -0.6666430 -0.2166288 -1.3156843

Within cluster sum of squares by cluster: [1] 12.5593286 0.3996124 16.0740310 20.7003423 16.0724001 (between_SS / total_SS = 65.0 %)