Scree plot pca python

#This assignment is a tutorial so have a bit of fun with it

#If you would like to explore some additional options give it a try

#Goal is to provide some meaningful info to the restaurant owner

#Some notes below

#Both PCA and FA provide useful summary info for multivariate data, but

#all of the original variables are needed for their calculation, so

#the big question is can we use them to find a subset of variables to

#predict overall score?

#Also,trying to give meaningful labels to components is really hard.

#When the variables are on different scales you need to work with the

#correlation matrix. For this assignment they are on same scale so

#we will work with the raw data.

#PCA only helps if the original variables are correlated, if they

#are independent PCA will not help.

#Approach takes two steps

#First step find the dimensionality of the data, that is the

#number of original variables to be retained

#Second step find which ones, more on this below

# import packages for this example

import pandas as pd

import numpy as np # arrays and math functions

import matplotlib.pyplot as plt # static plotting

from sklearn.decomposition import PCA, FactorAnalysis

import statsmodels.formula.api as smf # R-like model specification

#Set some display options

pd.set_option('display.notebook_repr_html', False)

pd.set_option('display.max_columns', 40)

pd.set_option('display.max_rows', 10)

pd.set_option('display.width', 120)

#Read in the restaurant dataset

food_df = pd.read_csv('C:/Users/Jahee Koo/Desktop/MSPA/2018_Winter_410_regression/HW03 PCA/FACTOR1.csv')

#A good step to take is to convert all variable names to lower case

food_df.columns = [s.lower() for s in food_df.columns]

print(food_df)

print('')

print('----- Summary of Input Data -----')

print('')

# show the object is a DataFrame

print('Object type: ', type(food_df))

# show number of observations in the DataFrame

print('Number of observations: ', len(food_df))

# show variable names

print('Variable names: ', food_df.columns)

# show descriptive statistics

print(food_df.describe())

# show a portion of the beginning of the DataFrame

print(food_df.head())

#look at correlation structure

cdata = food_df.loc[:,['overall','taste','temp','freshness','wait','clean','friend','location','parking','view']]

corr = cdata[cdata.columns].corr()

print(corr)

#Use the correlation matrix to help provide advice to the restaurant owner

#Look at four different models and compare them

#Which model do you think is best and why?

#Model 1 full regression model

#Model 2 select my reduced regression model taste, wait and location

#Model 3 Full PCA model

#Model 4 Reduced PCA model with parking, taste and clean

#Model 5 FA model

#First find the PCA

#Second find the FA

#Run the models

#Compare the models and show VIF for each model

#PCA

print('')

print('----- Principal Component Analysis -----')

print('')

pca_data = food_df.loc[:,['taste','temp','freshness','wait','clean','friend','location','parking','view']]

pca = PCA()

P = pca.fit(pca_data)

print(pca_data)

np.set_printoptions(threshold=np.inf)

np.around([pca.components_], decimals=3)

#Note per Everett p209 pick the three variable