Bass Diffusion Model, Cluster Analysis and Factor Analysis Submit both a link to a word document and your google sheets link (or excel)

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Month Adopters 1 1 2 5 3 9 4 18 5 42 6 74 7 89 8 91 9 159 10 46 11 94 12 81 13 73 14 69 15 73 16 57 17 60 18 61

Principal Components Analysis 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 __________________________________________________________________________ ____________________________ 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 __________________________________________________________________________ ________________________________ 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 %)