PYTHON PROGAMMING

 

This is a tutorial assignment on Cluster & Multivariate Analysis.

Run the Python code provided and write a brief paragraph regarding the results.

#

-*- coding: utf-8 -*-

# K-means Cluster Analysis (Python)

from __future__ import division, print_function

# import packages for this example

import pandas as pd

# DataFrame operations

from collections import OrderedDict # to create DataFrame with ordered columns

# special plotting methods

from pandas.tools.plotting import scatter_matrix

import numpy as np # arrays and math functions

import matplotlib.pyplot as plt # static plotting

from sklearn import preprocessing

from sklearn.cluster import KMeans

from sklearn import metrics # for silhouette coefficient

# previously obtained data from public-domain source at Stanford University

# 240 student participants’ self-ratings on 32 personality attributes

# a review of these data suggests that student survey participants were

# given an adjective check-list with instructions to self-rate such as:

# “Rate the extent to which each adjective describes you. Use a

# 1-to-9 scale, where 1 means ‘very much unlike me’ and

# 9 means ‘very much like me.’ ”

# source: http://www.stanford.edu/class/psych253/data/personality0.txt

# create Pandas DataFrame from the student data

# define a pandas DataFrame

student_data=pd.read_csv(‘C:/Users/Jahee Koo/Desktop/MSPA/2018_Winter_410_regression/HW04_Cluster/student_data.csv’)

# for fun, add your own data to the student_data

# data frame by self-rating the 32 adjectives on a 1-to-9 scale …

# this would provide 241 observations

# for example…

# my_data_dict = {“distant”:1, “talkative”:5, “careless”:1, “hardworking”:8,

# “anxious”:2, “agreeable”:6, “tense”:1, “kind”:7, “opposing”:3, “relaxed”:5,

# “disorganized”:4, “outgoing”:5, “approving”:3, “shy”:1, “disciplined”:5,

# “harsh”:1, “persevering”:9, “friendly”:7, “worrying”:3, “responsive”:6,

# “contrary”:2, “sociable”:6, “lazy”:1, “cooperative”:8, “quiet”:3,

# “organized”:6, “critical”:5, “lax”:2, “laidback”:5, “withdrawn”:1,

# “givingup”:1, “easygoing”:6}

# my_data_frame = pd.DataFrame(my_data_dict, index = [0])

# student_data = pd.concat([student_data, my_data_frame])

print(”)

print(‘—– Summary of Input Data —–‘)

print(”)

# show the object is a DataFrame

print(‘Object type: ‘, type(student_data))

# show number of observations in the DataFrame

print(‘Number of observations: ‘, len(student_data))

# show variable names

variable = student_data.columns

print(‘Variable names: ‘, variable)

# show descriptive statistics

pd.set_option(‘display.max_columns’, None) # do not limit output

print(student_data.describe())

# show a portion of the beginning of the DataFrame

print(student_data.head())

print(”)

print(‘—– K-means Cluster Analysis of Variables —–‘)

print(”)

# it is good practice to standardize variables prior to clustering

# work with standard scores for all cluster variables

# standard scores have zero mean and unit standard deviation

# here we standardize each student’s data

standardized_student_data_matrix = preprocessing.scale(student_data)

# transpose of matrix needed for clusters of variables

variable_cluster_data = student_data.T

# specify the number of clusters in order to perform

# K-means cluster analysis on the variables in the study

# there is much psychological research about what are called

# the big five factors of perosnality:

# extraversion, agreeableness, conscientiousness, neuroticism, openness

#

# some personality researchers have focused on only two factors:

# extraversion/introversion and neuroticism

# suppose we think five factors (and five clusters) will be sufficient

# here we use our knowledge of the big-five personality factors

# assuming that there may well be five clusters to identify

kmeans = KMeans(n_clusters = 5, n_init = 25, random_state = 1)

kmeans.fit(variable_cluster_data)

cluster = kmeans.predict(variable_cluster_data) # cluster ids for variables

# create pandas DataFrame for summarizing the cluster analysis results

#variable_kmeans_solution = pd.DataFrame(OrderedDict([(‘cluster’, cluster),(‘variable’, variable )]))

variable_kmeans_solution = pd.DataFrame(OrderedDict([(‘cluster’, cluster),(‘variable’, variable ) ]))

print(variable_kmeans_solution)

# print results of variable clustering one cluster at a time

for cluster_id in sorted(variable_kmeans_solution.cluster.unique()):

print()

print(variable_kmeans_solution.loc[variable_kmeans_solution[‘cluster’] == \

cluster_id])

# The silhouette coefficient is a useful general-purpose index

# for evaluating the strength of a clustering solution. The original

# reference is

# Peter J. Rousseeuw (1987). “Silhouettes: a Graphical Aid to the

# Interpretation and Validation of Cluster Analysis”.

# Computational and Applied Mathematics 20: 53–65.

# doi:10.1016/0377-0427(87)90125-7.

# larger positive values of the silhouette coefficient are preferred

# these indicate dense, well separated clusters

# evaluate the clustering solution using the silhouette coefficient

print(‘Silhouette coefficient for the five-cluster k-means solution: ‘,

metrics.silhouette_score(variable_cluster_data, cluster,

metric = ‘euclidean’))

# a low silhouette coefficient suggests that we may want to try

# kmeans with alternative values for the number of clusters

# or perhaps this problem is not particularly well suited for cluster analysis

print(”)

print(‘—– Selected K-means Cluster Analysis for Student Segments —–‘)

print(”)

# here we are working in much the way we would in a market research

# study looking for market segments… here segments/clusters of students

# it is good practice to standardize variables prior to clustering

# work with standard scores for all cluster variables across students

# standard scores have zero mean and unit standard deviation for all variables

# these were computed earlier in working on the variable clustering

student_cluster_data = student_data

# specify the number of clusters in order to perform
# K-means cluster analysis on the variables in the study

# with no preconceived notions about the number of student segments/clusters

# we search across various cluster analysis solutions defined

# each individual k-means solution is defined by the argument n_clusters

# consider selecting a solution based on the silhouette coefficient

# for more info on silhouette see

# http://scikit-learn.org/stable/auto_examples/cluster/plot_kmeans_silhouette_analysis.html

for nclusters in range(2,21): # search between 2 and 20 clusters/segments

kmeans = KMeans(n_clusters = nclusters, n_init = 25, random_state = 1)

kmeans.fit(student_cluster_data)

segment = kmeans.predict(student_cluster_data) # cluster ids for variables

print(‘nclusters: ‘, nclusters, ‘ silhouette coefficient: ‘,

metrics.silhouette_score(student_cluster_data, segment,

metric=’euclidean’))

# results suggest that a two-cluster/segment solution is best

print(”)

print(‘—– Solution for Two Student Segments —–‘)

print(”)

kmeans = KMeans(n_clusters = 2, n_init = 25, random_state = 1)

kmeans.fit(student_cluster_data)

segment = kmeans.predict(student_cluster_data) # cluster index

# create pandas DataFrame for summarizing the cluster analysis results

# using OrderedDict to preserve the order of column names

student_kmeans_solution = pd.DataFrame(OrderedDict(

[(‘student’, range(0,len(student_cluster_data))),

(‘segment’, segment)]))

print(student_kmeans_solution)

# to interpret the results of the segmentation

# we can review the original ratings data for the two clusters/segments

# merge/join the segment information with the original student data

student_segmentation_data = student_kmeans_solution.join(student_data)

# try printing the means for attributes within each segment

for segment_id in sorted(student_segmentation_data.segment.unique()):

print()

print(‘Attribute means for segment: ‘, segment_id)

this_student_segment_data = student_segmentation_data[ \

student_segmentation_data.segment == segment_id]

attributes = this_student_segment_data.ix[:,’distant’:’easygoing’].mean()

print(attributes)

centers = kmeans.cluster_centers_

plt.scatter(centers[:,0],centers[:,1], c=’black’,s=200,alpha=0.5)

#make blobs

#a different example where the data is generated

from sklearn.datasets.samples_generator import make_blobs

X,y_true = make_blobs(n_samples=300,centers=4,cluster_std=.60,random_state=0)

plt.scatter(X[:, 0],X[:, 1], s=50);

print(X)

kmeans.fit(X)

y_kmeans = kmeans.predict(X)

plt.scatter(X[:,0],X[:,1], c = y_kmeans, s=50, cmap = ‘viridis’)

centers = kmeans.cluster_centers_

plt.scatter(centers[:,0],centers[:,1], c=’black’,s=200,alpha=0.5);

ed

organized

lax

7

5

2 7 9 5 5 8 9 9 9 5 9 7 9 9 5 5 5 7 5 5 8

3 8 2 7 5 8 4 8 5 7 5 8 7 6 7 3 7 7 5 7 5 8 2 7 6 6 4 3 7 2 2 7
6 6 2 5 1 8 2 9 2 8 7 6 7 5 5 2 5 8 3 9 2 8 5 8 7 4 5 5 7 6 2 8
3 7 6 7 8 8 2 8 3 7 2 5 6 4 6 2 8 8 3 8 2 6 3 8 4 7 6 6 6 4 3 7
7 3 3 5 8 6 7 2 3 3 5 2 5 8 7 5 6 2 8 7 3 2 6 6 7 5 5 3 3 7 5 5
7 6 7 6 7 8 7 8 5 5 6 5 6 8 5 3 6 7 7 7 5 4 5 7 8 6 6 4 4 6 4 7
3 6 8 6 6 7 3 5 3 7 7 8 7 5 7 2 4 8 6 2 2 9 6 6 4 4 6 9 9 2 3 8
7 6 2 9 7 8 6 7 2 4 4 6 5 4 8 6 8 6 5 8 5 7 4 8 6 6 4 3 2 5 6 6
2 6 2 8 2 7 4 7 4 8 3 8 7 3 6 4 8 8 2 8 3 8 3 8 5 7 7 3 6 3 1 7
4 7 3 6 3 7 3 7 5 6 3 5 7 5 7 6 7 6 4 7 4 7 3 7 5 6 5 3 4 4 2 5
3 5 2 8 3 7 3 5 4 5 2 5 4 7 8 7 8 7 3 8 5 7 4 7 7 8 7 5 5 6 2 7
3 4 6 4 7 4 7 4 6 5 5 3 4 7 4 6 4 4 7 5 6 4 5 4 7 5 5 5 5 7 7 4
2 5 4 7 8 8 7 8 3 4 3 5 6 6 7 2 7 7 8 6 2 6 5 8 8 6 3 3 3 5 4 4
7 3 2 8 5 8 3 7 4 7 5 3 5 6 8 2 7 8 7 8 3 5 3 6 7 4 5 3 7 6 3 7
7 3 5 6 6 7 6 6 3 5 3 4 6 6 5 3 7 6 6 7 4 4 5 6 5 6 4 5 6 6 4 6
6 3 2 8 4 6 5 8 3 6 1 6 5 7 8 2 8 7 6 8 3 7 1 7 7 8 5 1 6 5 1 6
4 5 4 8 7 6 7 7 4 4 2 6 5 5 6 1 9 8 9 9 3 5 5 9 5 9 9 7 3 5 1 6
6 5 2 9 6 5 6 6 4 4 1 6 7 5 9 3 9 7 8 9 6 6 3 5 5 9 6 1 5 6 2 6
2 7 2 7 3 6 6 7 2 6 6 8 6 2 6 2 7 7 2 9 3 7 4 7 2 6 3 2 7 2 2 7
6 4 3 5 6 6 5 8 2 4 4 4 6 7 6 2 6 6 4 6 5 6 7 8 6 6 6 5 5 6 4 6
5 5 2 8 6 5 6 8 4 2 1 4 5 5 7 4 9 7 8 8 6 5 2 5 4 8 6 3 1 6 6 5
1 8 1 7 2 8 1 8 3 8 2 8 8 1 4 1 8 9 2 7 1 8 4 7 3 7 3 6 6 1 1 7
7 7 5 6 7 7 7 6 4 2 6 5 5 5 7 5 4 6 7 5 4 6 7 4 7 5 7 3 4 3 4 4
5 5 2 8 5 7 7 7 3 6 1 3 5 4 9 6 7 6 4 7 5 5 6 6 6 9 5 5 6 7 3 4
5 6 3 8 8 4 6 7 6 4 4 4 6 6 8 7 7 7 5 7 6 4 5 6 6 7 7 5 5 6 5 7
6 3 5 8 6 7 6 7 6 4 1 5 6 6 8 6 7 6 6 8 5 5 2 4 7 9 6 3 5 4 2 5
3 2 2 7 4 6 4 7 3 7 3 2 6 6 6 1 7 7 7 7 3 6 5 7 8 7 4 6 4 4 2 5
7 6 3 8 5 8 6 7 8 7 6 3 7 6 9 4 4 7 2 8 6 6 3 6 6 6 3 6 7 6 2 7
5 3 3 7 5 6 5 7 6 6 3 5 5 5 7 2 8 8 5 8 3 5 2 6 4 7 6 2 5 3 2 7
6 3 4 6 7 4 4 6 2 5 6 3 4 8 5 3 6 6 8 5 2 5 7 6 9 5 5 5 5 6 6 5
3 5 2 7 6 7 6 8 5 4 2 4 5 6 8 3 7 7 6 6 3 4 3 8 6 9 7 4 4 5 3 3
6 7 2 7 4 3 6 4 4 3 3 7 5 1 8 2 7 6 6 8 3 3 5 6 2 7 7 2 3 4 2 6
6 6 4 8 2 6 6 7 5 4 6 4 4 4 7 6 6 5 3 8 6 5 3 5 4 5 6 3 3 5 3 4
6 6 1 9 3 5 1 8 2 8 1 7 6 6 9 3 9 7 2 9 3 7 1 7 3 8 6 1 8 5 1 7
5 5 2 8 6 8 5 7 4 6 3 7 7 2 7 2 8 8 8 9 4 7 2 7 4 8 7 5 7 3 2 8
3 6 2 6 3 7 3 6 4 7 1 3 5 6 7 4 3 7 2 7 3 6 3 7 4 7 5 4 6 5 2 6
2 5 1 7 2 6 6 5 2 4 1 6 4 6 6 5 5 6 5 8 4 7 6 6 6 9 6 3 8 3 2 7
2 5 3 5 3 7 2 6 2 8 6 6 5 5 3 6 5 7 2 6 2 8 7 7 4 4 5 5 7 2 3 8
6 6 4 7 2 7 2 9 6 8 3 7 4 5 7 3 7 8 3 8 4 7 4 7 3 7 7 4 7 4 1 8
6 5 3 7 4 8 4 6 2 6 5 5 6 4 7 3 7 7 4 4 3 7 5 7 4 4 4 6 7 3 2 6
2 7 6 7 6 6 6 7 3 5 3 3 4 7 6 6 8 7 8 8 4 6 6 6 3 7 6 3 6 3 1 6
5 6 3 7 3 5 4 6 4 7 5 6 6 4 6 2 7 7 3 7 5 7 4 6 5 6 4 6 6 4 2 5
2 9 3 8 8 7 7 7 3 2 3 8 8 3 6 4 8 9 6 7 4 8 4 6 3 9 7 4 4 4 7 8
3 6 3 7 6 7 4 8 4 5 2 7 5 3 7 5 8 7 5 7 4 7 6 8 5 8 5 4 6 6 3 6
1 6 3 4 3 5 3 5 5 8 8 3 5 7 7 4 8 6 3 5 4 7 8 7 6 2 9 7 7 2 2 7
2 6 3 6 3 6 3 7 2 6 6 7 6 3 5 2 7 8 3 7 3 6 2 7 4 5 3 5 7 2 2 7
5 5 6 7 5 6 6 5 5 5 4 5 5 8 5 5 6 7 6 8 5 5 5 7 7 5 5 5 5 5 2 6
2 5 2 8 2 7 1 7 5 5 1 7 7 2 9 5 9 8 5 9 5 8 2 7 2 9 8 5 5 1 1 5
4 5 4 8 7 6 7 5 4 3 4 3 3 3 7 6 7 6 8 8 5 6 3 5 5 3 7 3 4 4 3 4
5 7 5 7 9 7 9 7 6 4 8 7 7 6 6 3 7 6 8 6 6 6 4 7 6 2 7 5 7 6 4 5
3 8 4 6 6 4 7 6 4 2 2 5 3 4 4 4 6 6 7 8 4 4 4 4 4 8 8 2 2 3 3 3
5 6 3 8 6 7 5 8 3 4 2 8 8 3 8 5 8 7 3 7 3 8 5 6 4 8 8 3 5 4 1 4
2 8 2 8 7 6 7 7 7 3 4 9 7 3 5 4 9 8 7 7 3 8 3 6 2 5 7 4 3 1 1 2
6 4 3 8 6 5 6 6 4 4 4 4 5 7 7 4 7 5 6 7 4 4 3 5 5 6 4 3 5 5 5 5
3 8 5 7 5 7 4 8 2 6 6 8 6 4 9 3 8 8 3 5 4 7 2 7 3 4 4 7 8 3 1 8
3 8 3 6 6 7 5 6 3 3 3 8 5 2 6 3 6 8 4 5 6 8 4 5 3 1 3 2 5 2 3 6
6 7 2 8 4 7 6 8 4 5 3 8 7 1 9 2 7 8 3 9 2 6 2 7 2 8 6 3 8 2 3 8
5 5 7 7 7 8 7 8 2 3 6 3 7 6 6 7 7 7 4 7 7 7 4 7 7 3 7 5 2 2 5 3
3 7 9 4 4 7 5 6 3 6 9 7 6 6 1 3 3 8 8 3 7 7 9 6 2 1 3 8 7 3 6 8
2 8 2 9 7 5 8 8 7 5 6 8 7 3 7 7 6 8 9 8 7 7 2 8 3 8 8 4 3 3 3 8
6 8 5 4 4 6 4 5 6 7 6 7 5 4 7 6 7 6 5 6 6 7 6 4 3 5 7 5 7 3 2 6
5 5 2 7 7 5 6 7 5 5 4 6 5 3 7 2 7 7 7 8 3 8 4 4 3 7 8 3 4 4 4 5
3 8 1 7 5 9 5 9 1 4 1 7 5 2 8 2 9 9 9 9 1 7 1 9 1 9 1 5 3 1 1 7
6 5 8 7 7 6 7 4 3 3 7 5 5 8 6 2 6 7 8 4 3 7 6 6 4 3 3 6 6 7 6 3
5 6 3 7 8 5 8 7 4 3 6 5 4 3 7 3 6 7 8 6 4 6 5 6 5 4 3 3 3 4 4 5
5 7 2 8 7 8 8 7 3 3 4 5 4 7 9 4 8 7 9 9 2 4 4 6 8 8 7 3 3 5 4 3
1 9 3 8 4 6 4 8 3 7 4 9 9 1 6 5 8 9 5 7 4 9 4 7 2 8 4 3 6 1 1 6
3 7 6 5 2 7 2 5 3 6 8 8 7 3 2 5 6 7 3 5 4 7 8 8 2 2 4 6 6 3 3 7
6 5 3 7 5 8 6 6 4 5 2 5 6 6 6 5 6 6 5 8 3 5 4 6 6 7 5 2 5 4 2 6
2 9 4 8 2 5 2 5 5 7 2 8 5 2 8 4 8 8 2 6 4 8 3 5 2 8 5 4 7 2 1 7
3 7 3 8 7 6 7 7 4 4 4 8 7 3 7 1 8 9 6 8 4 6 3 6 2 7 1 5 4 3 1 6
6 6 6 6 7 8 4 5 4 6 5 5 7 3 2 3 5 5 7 3 4 5 9 9 6 3 2 3 8 3 3 9
3 7 2 6 5 8 2 6 5 9 5 7 7 2 4 3 6 7 2 6 3 9 7 7 1 6 5 7 9 1 4 9
3 7 2 8 6 6 6 8 4 4 2 7 6 5 6 5 5 7 8 8 4 7 6 6 5 8 5 4 6 4 4 6
3 6 3 6 2 7 3 7 6 5 6 6 7 4 7 3 3 7 3 4 5 7 6 5 4 3 6 6 6 4 4 6
5 3 2 7 3 6 2 7 3 5 4 3 5 7 8 2 7 7 2 7 3 3 2 8 7 7 5 3 6 6 2 5
5 7 8 8 9 7 8 7 7 5 8 4 3 2 6 8 8 7 8 8 6 5 6 5 6 3 7 4 7 6 2 6
5 5 1 7 9 6 5 9 7 6 3 4 7 7 6 1 9 9 9 9 4 5 5 7 8 7 9 5 7 6 3 7
3 7 1 9 6 5 5 8 5 5 1 8 5 2 9 3 9 9 6 9 5 8 1 8 2 9 7 2 2 2 1 8
3 7 2 7 2 7 2 7 5 7 2 7 6 2 6 3 6 7 3 8 3 7 4 7 3 7 4 5 5 3 1 5
2 6 5 7 3 7 3 8 6 7 4 5 5 3 4 2 7 8 2 8 4 7 1 8 3 7 7 3 8 2 1 8
1 9 6 6 6 8 3 7 3 6 6 9 8 1 3 1 6 8 2 5 1 9 5 7 1 4 3 5 5 1 1 8
4 6 3 7 5 8 5 9 2 4 5 7 7 4 7 2 8 9 5 7 2 7 4 9 3 6 5 5 6 3 2 7
1 7 4 8 6 7 6 7 1 6 4 8 9 3 9 4 7 9 6 8 3 9 5 8 4 5 6 3 7 2 6 8
7 3 6 8 4 6 7 8 3 4 2 4 7 7 9 5 7 8 7 9 3 3 5 7 8 9 5 5 4 7 5 4
3 8 5 8 8 7 7 8 8 5 7 6 5 6 6 6 7 7 7 8 6 6 6 6 5 5 6 2 3 5 4 4
3 6 4 7 3 7 2 8 3 7 4 7 5 3 6 2 8 7 2 6 3 7 5 6 3 6 4 2 6 2 2 6
2 7 5 8 5 8 6 8 4 6 5 8 8 4 8 4 8 8 4 8 4 8 6 8 5 7 6 3 8 3 3 8
1 8 6 7 5 8 3 8 4 7 6 8 6 3 5 3 7 8 6 8 4 8 5 8 5 5 6 2 7 2 2 7
1 7 6 5 6 8 2 8 4 7 6 8 6 6 4 3 5 9 7 7 4 9 7 7 6 5 5 6 6 4 3 9
6 7 2 6 5 5 3 8 5 5 6 7 5 2 4 2 7 8 5 9 5 8 4 6 5 4 5 4 4 3 2 4
2 8 6 5 3 6 2 7 6 7 6 8 5 1 3 7 6 8 3 6 6 8 4 6 2 7 7 5 8 1 3 7
3 6 3 6 3 7 3 7 4 7 3 6 6 6 6 2 4 7 2 7 3 7 6 7 5 7 2 6 7 3 4 8
6 3 3 6 7 7 6 7 4 4 7 2 3 7 5 2 5 7 8 7 2 5 6 6 8 5 6 4 5 6 4 5
2 7 4 6 5 9 6 7 3 5 3 7 8 5 6 3 6 7 5 6 3 8 3 6 3 7 3 3 7 2 2 8
3 7 3 7 5 7 4 8 7 5 2 8 6 5 6 4 8 8 6 9 6 8 5 7 5 7 6 5 5 3 2 6
7 4 3 6 6 5 4 6 7 4 6 3 3 7 6 7 6 6 6 6 7 4 5 5 6 4 7 3 5 6 5 4
2 7 1 9 1 7 1 8 5 5 1 9 9 2 9 4 9 7 2 9 5 8 1 9 3 9 7 1 4 5 1 6
5 5 5 6 3 8 1 9 5 6 6 7 5 5 4 6 9 9 3 6 4 7 5 8 5 5 7 4 7 5 1 6
5 8 3 8 4 8 5 7 4 7 9 8 7 3 8 4 9 9 7 9 4 8 2 8 4 2 5 6 3 2 1 6
2 7 4 7 7 6 5 5 4 6 3 8 5 2 7 3 7 7 6 7 5 8 6 6 3 6 6 2 6 3 2 6
7 7 2 6 5 7 6 8 2 5 4 8 8 6 5 3 7 8 7 8 3 8 6 8 5 6 7 4 3 2 4 7
1 8 4 9 5 7 4 8 4 6 2 9 6 4 8 3 9 9 5 7 3 8 2 7 3 8 4 5 3 2 1 4
2 8 4 9 6 6 5 7 5 4 6 8 7 1 8 3 7 9 6 8 4 8 3 6 2 7 7 3 3 1 2 7
1 8 5 5 9 7 7 7 5 7 6 7 7 4 6 5 7 7 6 6 5 7 7 7 4 6 8 6 6 2 1 9
3 3 2 6 8 8 7 7 3 3 2 6 8 6 6 2 5 7 9 8 4 6 2 7 6 7 6 5 3 3 1 7
7 4 3 7 7 7 7 7 3 5 2 3 7 7 7 5 8 7 8 8 2 4 4 7 7 7 5 3 5 6 2 5
3 7 3 7 7 6 4 6 3 6 3 8 6 3 5 6 7 8 3 6 3 8 7 6 4 3 4 3 5 4 3 7
3 5 1 7 6 6 5 5 3 5 3 5 4 6 7 2 7 6 7 7 3 7 3 6 5 6 6 4 5 6 3 3
4 5 5 8 8 8 9 8 6 3 4 7 5 3 7 5 7 8 8 8 3 8 3 7 3 6 6 2 3 5 5 5
5 7 7 7 4 6 2 7 5 6 2 8 6 3 7 7 7 7 3 8 3 7 2 6 2 8 6 2 6 4 2 6
3 6 2 4 2 9 4 9 1 7 5 7 7 4 4 1 5 9 3 7 1 8 4 9 4 5 3 7 7 2 1 9
5 5 3 8 7 6 7 6 6 3 6 6 6 5 6 7 6 6 6 7 5 6 5 6 5 6 6 6 5 5 4 5
3 6 5 7 4 8 2 7 1 8 6 5 4 4 4 2 4 8 4 8 2 7 5 8 4 4 2 5 2 3 4 8
6 4 2 6 2 8 2 7 3 8 2 4 7 5 7 2 6 6 6 8 3 4 5 8 6 8 3 2 4 6 3 8
1 7 1 8 7 8 5 9 2 5 1 8 6 3 7 3 8 9 6 9 1 7 2 9 3 7 3 2 2 1 1 2
5 5 2 9 6 8 7 8 3 5 4 6 6 8 7 2 8 8 7 9 4 6 2 7 8 5 7 3 5 6 2 5
2 5 1 7 1 1 5 5 2 1 1 6 2 8 2 2 7 8 8 5 4 6 6 3 5 8 4 4 5 3 8 5
3 7 4 6 4 6 2 6 2 7 3 7 5 4 7 2 8 7 5 6 3 8 4 6 5 6 2 4 5 2 1 4
3 7 5 8 6 7 6 9 3 5 6 7 8 3 5 6 7 7 6 5 3 8 4 7 4 6 5 2 7 6 4 6
5 4 5 5 6 8 4 8 4 6 6 7 7 5 4 2 5 7 4 6 5 6 5 7 6 5 4 4 6 5 4 7
6 4 7 9 6 7 5 5 3 8 5 4 6 6 9 5 7 7 6 8 6 4 7 6 6 5 6 6 6 7 2 6
5 4 2 7 2 7 2 6 5 8 3 4 5 4 5 3 7 7 2 8 4 5 3 5 6 6 5 3 8 5 2 7
7 2 7 2 8 4 8 5 7 2 8 2 3 8 1 8 2 5 8 1 6 2 9 5 7 1 7 8 2 7 7 3
6 3 4 7 6 7 3 7 3 6 3 5 6 3 7 2 6 6 7 7 3 5 6 8 8 6 5 6 5 6 6 6
2 4 3 5 3 7 4 6 3 5 6 4 7 4 6 5 6 7 4 7 2 6 2 8 6 4 4 2 5 3 2 5
6 5 4 6 5 5 5 6 5 5 6 4 5 5 7 5 7 5 5 7 5 5 5 5 5 4 6 5 5 5 3 5
6 6 4 5 6 6 7 9 4 5 5 5 8 9 7 4 9 9 7 6 4 5 6 6 7 5 4 4 4 6 2 6
7 4 3 6 6 8 3 7 2 9 7 4 5 6 4 6 6 7 3 6 3 4 3 7 2 4 6 6 9 7 5 7
2 7 2 7 3 7 3 7 3 8 6 7 6 3 6 2 7 8 3 8 3 8 3 7 2 6 5 5 7 2 2 8
4 3 2 8 7 8 6 8 4 7 3 5 5 6 5 4 6 7 7 8 5 7 5 6 7 7 6 4 7 3 3 7
5 3 2 3 6 2 4 7 2 4 3 4 3 7 7 2 7 5 7 7 3 6 2 6 5 7 3 2 4 5 1 6
2 7 4 9 5 7 3 7 2 6 3 7 5 3 9 2 8 8 7 7 2 7 2 8 3 8 6 2 5 1 1 6
4 5 2 8 6 8 5 9 2 6 2 4 6 7 8 1 6 8 6 9 2 6 5 7 7 8 3 5 6 5 3 6
1 8 5 7 4 6 4 6 6 8 5 7 6 2 6 7 5 7 3 7 4 9 2 7 2 7 6 4 6 4 3 7
3 8 1 8 5 7 5 8 6 3 1 8 8 1 6 3 7 9 4 9 6 9 1 7 2 9 8 3 7 1 1 7
2 6 2 8 2 6 5 7 5 5 2 7 3 1 7 5 7 7 2 7 5 6 1 7 2 8 8 2 5 1 1 5
6 6 7 7 5 5 3 6 3 6 6 4 5 6 6 6 7 6 4 6 5 4 5 5 6 6 6 6 6 6 4 6
4 8 3 7 4 6 3 6 4 6 2 7 6 4 6 5 5 7 3 7 4 8 2 7 2 8 6 3 6 4 3 6
5 8 3 8 7 8 5 9 3 5 1 8 6 3 8 4 7 8 4 9 4 7 2 7 5 7 5 3 3 3 2 5
6 4 2 4 6 6 4 8 6 6 6 4 6 8 4 2 7 6 6 4 3 4 6 6 8 4 4 5 6 6 2 6
7 5 6 5 5 6 6 6 6 6 6 7 7 5 5 4 7 6 5 6 6 6 6 7 7 5 7 4 4 7 4 6
3 7 4 8 6 4 6 6 4 2 6 7 7 3 6 4 7 7 6 8 4 7 2 6 2 8 6 2 3 3 2 4
4 5 5 9 7 7 7 8 2 5 5 3 7 7 9 4 7 7 7 9 3 2 2 8 5 6 7 7 7 4 1 8
2 7 1 8 2 5 7 7 7 6 5 8 5 2 9 5 8 7 9 8 6 7 5 6 2 5 6 5 6 2 1 8
1 5 4 9 9 4 7 8 2 7 8 9 6 2 7 6 8 9 9 8 3 7 5 5 2 6 6 5 7 3 1 2
6 7 6 8 7 8 7 5 4 5 6 6 3 5 6 6 9 6 6 7 5 5 5 7 4 4 6 3 4 5 5 5
2 8 5 8 7 8 5 7 2 4 7 7 7 3 8 2 7 9 8 7 2 9 3 8 2 3 2 2 5 1 1 6
3 7 4 7 4 6 3 7 4 6 4 7 5 3 8 4 6 6 4 7 3 7 3 7 3 7 4 5 4 2 2 4
3 5 1 8 3 6 2 7 3 6 4 7 7 4 8 3 8 7 2 9 3 7 3 8 4 8 5 3 4 4 2 4
7 6 2 8 7 4 6 6 5 3 1 7 4 2 6 6 9 8 7 8 6 8 1 6 5 8 7 5 6 2 3 8
5 6 1 7 5 9 3 9 3 9 1 9 9 2 7 3 9 9 2 9 3 8 3 8 5 9 9 9 9 2 1 9
5 4 7 7 4 3 6 4 4 4 6 5 7 7 5 4 7 7 4 7 6 5 4 7 5 3 4 2 4 6 3 6
4 5 2 8 9 7 8 8 2 3 2 5 5 6 6 2 8 8 8 8 2 4 3 7 7 8 5 2 3 6 3 4
1 6 1 9 2 5 2 8 4 8 2 6 5 2 5 1 9 8 3 9 2 6 2 7 2 6 6 2 4 1 1 4
5 6 5 3 6 8 5 7 7 6 7 6 7 3 7 6 7 7 7 8 6 7 7 7 4 5 7 4 4 5 5 8
7 7 8 7 5 6 3 6 8 7 4 6 4 5 3 7 7 8 7 5 7 6 9 8 7 5 8 7 9 7 4 8
3 7 2 7 6 8 7 6 3 5 1 8 7 3 7 3 6 9 7 7 5 8 5 7 3 9 4 5 6 3 2 7
2 6 3 6 5 7 5 7 2 5 6 6 5 5 5 3 6 7 6 7 3 7 6 7 6 5 3 5 5 3 5 5
2 7 4 7 3 7 3 8 2 5 7 6 8 5 8 3 8 8 2 7 5 7 6 7 5 4 2 7 6 3 4 6
5 8 3 5 7 5 7 7 6 6 5 8 5 5 4 6 5 8 7 7 6 8 7 5 1 6 7 4 4 2 5 6
6 5 4 3 3 7 3 7 3 7 6 4 5 6 6 3 6 6 3 7 4 5 6 6 7 4 5 6 7 6 2 7
3 8 5 6 5 7 4 6 5 7 6 8 6 3 5 4 6 6 5 6 4 7 4 6 2 7 5 5 6 3 4 6
4 6 4 7 3 6 2 7 3 5 5 6 7 6 6 2 6 7 3 7 3 7 2 7 6 7 3 3 6 3 2 7
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3 8 4 9 7 6 5 6 3 5 3 7 5 5 9 2 8 7 7 8 3 6 1 6 5 7 5 2 5 3 2 7
8 6 7 7 9 9 9 6 8 4 7 5 3 4 7 6 6 7 9 8 8 2 6 8 8 3 9 3 1 7 3 3

distant

talkative

careless

hardworking

anxious

agreeable

tense

kind

opposing

re

lax

dis

organized

outgoing

approving

shy

disciplined

harsh

persevering

friendly

worrying

responsive

contrary

sociable

lazy

cooperative

quiet

critical

laidback

withdrawn

givingup

easygoing

2

7

1

4

8

5

9

6

3