What Makes the Most Popular Country for Studying Abroad?
Richard Mu and Xinyao Chen
Introduction¶
Studying abroad has appeared to be increasing in popularity in recent years both in the Univeristy of Maryland and in other Universities across the United States. University of Maryland alone offers semester exchange program to over 60 countries around the world.
While we are excited to see that students have become more enthusiastic and understanding on the purpose and benefits of studying abroad, we also wanted to examine various attributes of the countries to see which ones may be the most suitable for studying abroad. We understand that selecting a country to study abroad in is a decision that each student make base on various factors, such as personal sentient and ethnic background. However, we are also curious about how the characteristics of each country, such as crime rates, may relate to the number of students studying abroad there.
1. DATA COLLECTION¶
There are several Python libraries that will be helpful in the process of our analysis. We will explain their functionality throughout this tutorial as they appear. Here are some documentation pages that we found convenient for referencing:
import pandas as pd
import matplotlib
import matplotlib.pyplot as plt
import warnings
import requests
import re
from bs4 import BeautifulSoup
import seaborn as sns
import folium
from sklearn import linear_model
from sklearn.preprocessing import PolynomialFeatures
from sklearn.svm import SVR
# Import all necessary libraries
pd.set_option('display.max_rows', 200) # Set full visualization of dataframes
warnings.filterwarnings('ignore') # Ignore Warnings
After several attempts, we realized that there is not a collective source that contains all the information we would like to analyze, so we decided process data from multiple sources and combine them to create the most all-round dataset.
First, we found a dataset that listed the number of students in the United States that studied abroad at each country in the 2017-2018 school year. The data was downloaded as an excel sheet (or .xlsx) format so we simply used a Pandas function to read it into a Pandas DataFrame.
travel_data_2017 = pd.read_excel(open('D3A1FE70.xlsx', 'rb'),
sheet_name = "data")
travel_data_2017.head(10)
In addition, we decided to choose three attributes that each will represent a different perspective of each country to help us give characterization.
First Attribute: Peacefulness
As students studying in a foreign country, we may often find ourselves worried of places with high crime rates or recent violent uprisings. We found a Global Peace Index dataset on kaggle that measures the peacefulness of a country from 2008 - 2019. As students studying abroad for the 2017-2018 semester should have mostly decided their destination in 2017, we only extract data relating to the year 2017.
$*$note: lower peace score reflects a higher peacefulness rating$*$
peace_index = pd.read_csv('gpi-2008-2019.csv')
peace_index = peace_index[['Country','2017 rank', '2017 score']]
peace_index.head(10)
Second Attribute: Cost of Living
Studying abroad can often be seen as expensive because of the initial traveling costs, application fees, and etc. Furthermore, the financial complications continue after students arrive in their host country and remains throughout their time abroad. We visited the webpage Numbeo for cost of living index data of each country in the year 2017. Since the page did not offer any exporting option, we used a get request and scraped the table from the resulting html.
r = requests.get('https://www.numbeo.com/cost-of-living/rankings_by_country.jsp?title=2017')
root = BeautifulSoup(r.content)
# Find table from html
table = root.find("table", {"id": "t2"})
# Convert to dataframe
cost_living = pd.read_html(str(table))
cost_living = cost_living[0]
cost_living = cost_living[['Country', 'Cost of Living Index']]
cost_living.head(10)
Third Attribute: Happiness Score
Finally, we collected the happiness score of each country from the World Happiness Report. These scores are reflected from "how happy the citizens perceive themselves to be". While there are many aspects of the local citizen's lives that are distinct from the lives of foreign students, we think that the happiness scores display, to some degree, the living conditions of each country. Since it is exported as a CSV file, we used the read_csv function from the Pandas library.
happiness_df = pd.read_csv('2017-happiness.csv')
happiness_df = happiness_df[['Country','Happiness.Score']]
happiness_df = happiness_df.rename(columns={'Happiness.Score':'Happiness Score'})
happiness_df.head(10)
Extra Information
We also imported the geographic coordinate of each country for convenience of creating a map-based visualization later. Having a dataframe with the Longitude and Latitude information can be very helpful when using the folium library.
centroids = pd.read_csv('country_centroids_az8.csv')
centroids = centroids[['sovereignt','Longitude','Latitude']]
centroids.head(5)
2. PROCESSING AND TIDYING¶
After reading in datasets from various sources, we now have 5 different DataFrames storing data we will be using. Since our goal is to visualize and process attributes of each country, creating one complete table with all the information combined would be much more convenient. We decided to merge the different tables together with the country's name. Unfortunately, because these datasets all originated from different sources, not every country will be represented in every dataset. We performed an "inner-join" on each step of the merging process and dropped the rows with a country name that was missing from any dataset, as it is necessary that we do not have any data with missing values.
We also decided to primarily use the "scores" instead of "rankings" for each attribute. We found that rankings are only meaningful when compared to with other entries in the same dataset, but the scores, or indexes, are more relevant when used for analysis of multiple attributes.
Note that the "Country Name" column of each DataFrame may be named differently. Choosing to display a section of each DataFrame using the head() function can be useful in helping us see the names of columns and the corresponding data. After creating a DataFrame by combining the columns of previously collected data, we also sorted the DataFrame from least popular countries to most popular countries.
fulldata = pd.merge(left = travel_data_2017,right = peace_index, left_on="Destination", right_on="Country")
fulldata = fulldata[['Destination','2017/18', '2017 score']]
fulldata.columns = ['Country','Student Count','Peace Score']
fulldata = pd.merge(left = fulldata, right = happiness_df, left_on="Country", right_on="Country")
fulldata = pd.merge(left = fulldata, right = cost_living, left_on="Country", right_on="Country")
fulldata = fulldata.sort_values('Student Count').reset_index(drop=True)
Outliers_removed= fulldata.iloc[:100]
fulldata.head(10)
3. EXPLORATORY ANALYSIS AND VISUALIZATION¶
In this section, we work towards creating meaningful visualizations that will either help us better examine the information we have or inspect how they relate to each other.
Top 50 Distribution through Bar Graph¶
First, we are interested in finding out the distribution of United States students in each country. After some experimenting, we realized that both vertical and horizontal bar graphs appear overcrowded when attempting to input over 100 entries. Since the DataFrame was sorted with student counts in ascending order, we decided to graph the last 50 rows of the DataFrame in order to see how the most popular country compares to others.
mostPopular50 = fulldata.iloc[-50:] #selecting the bottom 50 rows
matplotlib.rcParams['figure.figsize']=[15, 7] #changing size of plot
sns.set_style("whitegrid")
plt.xticks(rotation='vertical') #rotating labels
bar_count = sns.barplot( x = "Country", y = "Student Count",data = mostPopular50, orient='v')
plt.xlabel('Country Names')
plt.ylabel('Number of Students')
plt.title('Number of United States Students Studying Abroad in 2017: Top 50 Most Popular Countries')
plt.show()
We can see that there exists a large gap between countrie's popularity distribution. Even after we isolated the top 50 most popular country, the distinction between the number of United Students who studies abroad in the top 3 countries and other countries in the top 50 is very visible. The fourth most popular country - France, had about 17,000 students, while the third most popular country - Spain had over 30,00 students.
Outliers¶
For the purpose of better picturing the disparity between popularity of countries', we also used all student counts from 103 different countries to create a box-and-whiskers-plot. As we can see in the plot below, the outlier-excluded-maximum of student count is around 5,000 students, and the medium of student count appears to be less than 1,000. There are quite a few outliers representing countries that are much more popular among the students, and within these outliers we see 3 countries standing much further out compared to others - United Kingdom, Italy, and Spain (names found in bar graph above). We will pay special attention to these three countries and see how their attributes may differ from others.
plt.clf()
plt.xlabel('Number of Students')
plt.title('Country Popularity With Number of United States Study Abroad Students')
sns.boxplot(x=fulldata['Student Count'], color = 'darkorange')
plt.show()
Student Count and Country Attribute Relationship.¶
To visualize the relationship between the different attributes of a country and the number of students that study abroad there, we implement a scatter plot using matplotlib, a 2D plotting library, and seaborn, a data visualization library based on matplotlib. Specifically, we create an lmplot with the attributes as the x axis and the student count as the y axis.
We label the three top outliers, United Kingdoms, Italy, and Spain, for each graph, to see just how different they are compared to the others, as well as notice any trends. We also plot a line to show where the United States stand, as that is where the students are all traveling from, to visualize comparative trends.
Student Count vs Peace Score¶
plt.clf()
peace = sns.lmplot(x='Peace Score', y ="Student Count", size=6, aspect = 2,
scatter_kws={"s":75,"alpha":0.6,"color":'mediumseagreen'},
line_kws={"color":'darkgreen'},data = fulldata)
ax = peace.axes[0,0]
ax.set_title('Student Count vs Peace Score')
dataCoords = list(zip(fulldata['Peace Score'], fulldata['Student Count']))
for i in range(len(dataCoords)):
point = dataCoords[i]
if point[1] > 37000: #United Kingdom
ax.text(point[0]+0.035, point[1]-400, 'United Kingdom', color = 'darkslategray')
elif point[1] > 35000: #Italy
ax.text(point[0]+0.035, point[1]-400, 'Italy', color = 'darkslategray')
elif point[1] > 30000: #Spain
ax.text(point[0]+0.035, point[1]-400, 'Spain', color = 'darkslategray')
#graphing line for United States
USPeace = peace_index.loc[peace_index['Country'] == 'United States']['2017 score']
plt.axvline(USPeace.values[0],0,0.965)
ax.text(USPeace.values[0] + 0.035, 31000, 'United States', color = 'steelblue')
plt.show()
From this graph, we can see a slight trend that countries where more students study at tend to have a lower peace score, as well as more countries in general having a lower peace score. As lower peace score means that a country is more peaceful, this means that students are more likely to study at more peaceful countries. The outliers do follow this trend, and a majority of the countries visited tend to be more peaceful than the United States.
Student Count vs Happiness Score¶
plt.clf()
happiness = sns.lmplot(x='Happiness Score', y ="Student Count", size=6, aspect = 2,
scatter_kws={"s":75,"alpha":0.6,"color":'lightcoral'},
line_kws={"color":'maroon'},data = fulldata)
ax = happiness.axes[0,0]
ax.set_title('Student Count vs Happiness Score')
dataCoords = list(zip(fulldata['Happiness Score'], fulldata['Student Count']))
for i in range(len(dataCoords)):
point = dataCoords[i]
if point[1] > 37000: #United Kingdom
ax.text(point[0]+0.045, point[1]-400, 'United Kingdom', color = 'darkslategray')
elif point[1] > 35000: #Italy
ax.text(point[0]+0.045, point[1]-400, 'Italy', color = 'darkslategray')
elif point[1] > 30000: #Spain
ax.text(point[0]+0.045, point[1]-400, 'Spain', color = 'darkslategray')
#graphing United States
USHappiness = happiness_df.loc[happiness_df['Country'] == 'United States']['Happiness Score']
plt.axvline(USHappiness.values[0],0,0.90)
ax.text(USHappiness.values[0] + 0.035, 31000, 'United States', color = 'steelblue')
plt.show()
From the scatter plot of student count and happiness, there does seem to be a trend where countries with a higher happiness score tend to have more students studying abroad there. The United States does have a high Happiness Score, so the majority of countries that students go to do have a lower score. The main outliers, while of lower happiness score than the United States, still score higher than average when compared to the rest of the countries.
Student Count vs Cost of Living¶
plt.clf()
cost = sns.lmplot(x='Cost of Living Index', y ="Student Count", size=6, aspect = 2,
scatter_kws={"s":75,"alpha":0.6,"color":'orchid'},
line_kws={"color":'rebeccapurple'},data = fulldata)
ax = cost.axes[0,0]
ax.set_title('Student Count vs Cost of Living')
dataCoords = list(zip(fulldata['Cost of Living Index'], fulldata['Student Count']))
for i in range(len(dataCoords)):
point = dataCoords[i]
if point[1] > 37000: #United Kingdom
ax.text(point[0]+1, point[1]-400, 'United Kingdom', color = 'darkslategray')
elif point[1] > 35000: #Italy
ax.text(point[0]+1, point[1]-400, 'Italy', color = 'darkslategray')
elif point[1] > 30000: #Spain
ax.text(point[0]+1, point[1]-400, 'Spain', color = 'darkslategray')
USCost = 100
plt.axvline(USCost,0,0.965)
ax.text(USCost + 0.8, 31000, 'United States', color = 'steelblue')
plt.show()
The scatter plot of student count and cost of living also shows that the number of students that study at the country increases with a countries cost of living. However, nearly all countries have a lower cost of living than New York, which is what the cost of living index is based around. As there was no cost of living data for the United States with the dataset found, we will use this as the placeholder for the United States. The outliers do generally have a higher cost of living, but still fall below the United States.
Plotting all attributes in relationship to each other¶
To better visualize how all the country attributes relate to each other instead of just how they affect the amount of students that study abroad at said country, we created a scatter plot with the peace score as the x-axis, the cost of living as the y-axis, and the happiness score as the size and color of the point. The greater the happiness score, the larger and darker the point is.
# Categorizing Happiness Score
category = []
for index, row in fulldata.iterrows():
if row[3] >= 2 and row[3] < 3:
category.append('2 to 3')
if row[3] >= 3 and row[3] < 4:
category.append('3 to 4')
if row[3] >= 4 and row[3] < 5:
category.append('4 to 5')
if row[3] >= 5 and row[3] < 6:
category.append('5 to 6')
if row[3] >= 6 and row[3] < 7:
category.append('6 to 7')
if row[3] >= 7 and row[3] < 8:
category.append('7 to 8')
fulldata['Happiness Category'] = category
plt.clf()
palette = {"2 to 3":"#FFF8EF","3 to 4":"#F7E3CA", "4 to 5":"#E2D1E6", "5 to 6":"#ca8bd2",
"6 to 7":"#894d94", "7 to 8":"#4D235D"}
sizesdict = {"2 to 3":2,"3 to 4":4, "4 to 5":6, "5 to 6":8,
"6 to 7":10, "7 to 8":12}
plt.title('Peace Score vs Cost of Living vs Happiness Score')
hap_sort = fulldata.sort_values("Happiness Score", ascending = False)
hap_peace = sns.scatterplot(x="Peace Score", y="Cost of Living Index", hue="Happiness Category",
size = "Happiness Category",
sizes = (50,300),
palette=palette,
data = hap_sort)
USCost = 100
plt.axhline(USCost,0,1)
ax.text(1.0, USCost+0.8, 'United States', color = 'steelblue')
USPeace = peace_index.loc[peace_index['Country'] == 'United States']['2017 score']
plt.axvline(USPeace.values[0],0,1)
ax.text(USPeace.values[0] + 0.035, 90, 'United States', color = 'steelblue')
hap_peace
At a glance, we can see that the traits follow the same trends as their individual plots with student count. A lower peace score, or a more peaceful country, tends to have a higher cost of living as well. We also see how a large concentration of darker and larger points gather at higher cost of living and lower peace score, showing that all these three traits do seem to have some sort of relationship with each other.
World Map¶
To visualize on a map how many students decided to study at each country, we created a choropleth map that shaded countries darker if more students decided to study abroad there. This was done through folium, a library that helps create leaflet maps. Due to the large range, to have a non cluttered index, we used multiple layers. By keeping the outliers distinct from the rest, we can have smaller ranges between each cutoff to have a more distinct visualization to compare the countries.
country_geo = 'world-countries.json'
palette = sns.cubehelix_palette(8, start=0.5, rot=-.75)
travel_data_2017 = travel_data_2017.sort_values('2017/18').reset_index(drop=True)
tdata_1 = travel_data_2017.iloc[-3:]
tdata_2 = travel_data_2017.iloc[:216]
map = folium.Map(location=[35, 0], zoom_start=1.7)
map.choropleth(geo_data=country_geo, data=tdata_2,
columns=['Destination', '2017/18'],
key_on='feature.properties.name',
fill_color='Oranges', nan_fill_color = 'cornsilk',
fill_opacity=0.7,
line_opacity=0.2,
legend_name='Number of U.S. Students',
threshold_scale=[0,1000,3000,7500,12500,17500])
map.choropleth(geo_data=country_geo, data=tdata_1,
columns=['Destination', '2017/18'],
key_on='feature.properties.name',
fill_color='Purples', nan_fill_color = 'cornsilk',
fill_opacity=0.7, nan_fill_opacity=0.0,
line_opacity=0.2,
legend_name=' ',
threshold_scale=[30000,30000,30000,30000,30000,40000])
map
We can see from this map that the countries with the largest number of students that study abroad there are heavily concentrated in Europe. All three major outliers are also found there. The area that sees the least number of students seem to be in the areas of Africa and the Middle East.
Mapping the Other Attributes¶
With the same reasoning of mapping the student count on a world map, we mapped each attribute with a choropleth map to visualize each attribute geographically as well to visualize any geographic trends.
# Creating Maps for each attribute
peace_data_2017 = peace_index.sort_values('2017 score').reset_index(drop = True)
peace_map = folium.Map(location=[35, 0], zoom_start=1.7)
peace_map.choropleth(geo_data=country_geo, data=peace_data_2017,
columns=['Country', '2017 score'],
key_on='feature.properties.name',
fill_color='Greens', nan_fill_color = 'cornsilk',
fill_opacity=0.7,
line_opacity=0.2,
legend_name='Peace Score by Country')
happiness_data_2017 = happiness_df.sort_values('Happiness Score').reset_index(drop = True)
happiness_map = folium.Map(location=[35, 0], zoom_start=1.7)
happiness_map.choropleth(geo_data=country_geo, data=happiness_data_2017,
columns=['Country', 'Happiness Score'],
key_on='feature.properties.name',
fill_color='Reds', nan_fill_color = 'cornsilk',
fill_opacity=0.7,
line_opacity=0.2,
legend_name='Happiness Score by Country')
cost_data_2017 = cost_living.sort_values('Cost of Living Index').reset_index(drop = True)
cost_map = folium.Map(location=[35, 0], zoom_start=1.7)
cost_map.choropleth(geo_data=country_geo, data=cost_data_2017,
columns=['Country', 'Cost of Living Index'],
key_on='feature.properties.name',
fill_color='Purples', nan_fill_color = 'cornsilk',
fill_opacity=0.7,
line_opacity=0.2,
legend_name='Cost of Living Index by Country')
Peace Score by Country¶
display(peace_map)
Taking into mind that a more peaceful country would instead mean a lighter color, by comparing this map with the student count map, we can see how the areas that tend to have more students study abroad there (Europe) are more peaceful than average, but generally not the most peaceful of all. The less peaceful areas as seen in parts of Africa and the Middle East tend to receive less students studying abroad.
Happiness Score by Country¶
display(happiness_map)
Mapping the happiness score continues to confirm the trends that we have already gathered. Countries with a higher happiness score have a higher number of students studying abroad there, and the general area of these countries tend to be happier as well. Similar to the map of the peace score, it is not the happiest country that receive the most students.
Cost of Living Index by Country¶
display(cost_map)
The map of the cost of living for each country is missing much more data, as well as being fairly less diverse in terms of how it differs between each country. Regardless, we continue to see the trend that most of the geographic areas that receive more students have around the same cost of living, while not having the highest cost of living.
One observation that has kept popping up to keep in mind is how the countries with the most students studying abroad there generally do not have the highest (or lowest) value of a certain attribute. This is visible not just in the maps, but on the previous scatter plots as well.
4. Further Analysis and Machine Learning¶
For this phase in the Data Science Lifecycle, we will be conducting a polynomial regression analysis on the data in order to predict the number of students that would study abroad at a country based off the country's happiness score, peace score, and cost of living.
Why Polynomial¶
As observed before during the visualization of our data, it is clear that each attribute is not perfectly linear. Taking into account the outlier positions, as well as the positions of other countries with higher student count, a polynomial fit may be better to consider as the data shows that it isn't as simple as a one to one relationship throughout. The maps and scatter plots all complemants this observation, as the countries with the most students are generally not the highest or lowest of that attribute.
Polynomial Line of Best Fit¶
We graph the same plots using each attribute vs student count, but we use the parameter of order = 3 to visualize an estimated polynomial regression instead.
Student Count vs Peace Score¶
plt.clf()
peace = sns.lmplot(x='Peace Score', y ="Student Count", size=6, aspect = 2,
scatter_kws={"s":75,"alpha":0.6,"color":'mediumseagreen'},
line_kws={"color":'darkgreen'},order = 3, data = fulldata)
ax = peace.axes[0,0]
ax.set_title('Student Count vs Peace Score')
dataCoords = list(zip(fulldata['Peace Score'], fulldata['Student Count']))
for i in range(len(dataCoords)):
point = dataCoords[i]
if point[1] > 37000: #United Kingdom
ax.text(point[0]+0.035, point[1]-400, 'United Kingdom', color = 'darkslategray')
elif point[1] > 35000: #Italy
ax.text(point[0]+0.035, point[1]-400, 'Italy', color = 'darkslategray')
elif point[1] > 30000: #Spain
ax.text(point[0]+0.035, point[1]-400, 'Spain', color = 'darkslategray')
#graphing line for United States
USPeace = peace_index.loc[peace_index['Country'] == 'United States']['2017 score']
plt.axvline(USPeace.values[0],0,0.965)
ax.text(USPeace.values[0] + 0.035, 31000, 'United States', color = 'steelblue')
plt.show()
Student Count vs Happiness Score¶
plt.clf()
happiness = sns.lmplot(x='Happiness Score', y ="Student Count", size=6, aspect = 2,
scatter_kws={"s":75,"alpha":0.6,"color":'lightcoral'},
line_kws={"color":'maroon'},order = 3,data = fulldata)
ax = happiness.axes[0,0]
ax.set_title('Student Count vs Happiness Score')
dataCoords = list(zip(fulldata['Happiness Score'], fulldata['Student Count']))
for i in range(len(dataCoords)):
point = dataCoords[i]
if point[1] > 37000: #United Kingdom
ax.text(point[0]+0.045, point[1]-400, 'United Kingdom', color = 'darkslategray')
elif point[1] > 35000: #Italy
ax.text(point[0]+0.045, point[1]-400, 'Italy', color = 'darkslategray')
elif point[1] > 30000: #Spain
ax.text(point[0]+0.045, point[1]-400, 'Spain', color = 'darkslategray')
#graphing United States
USHappiness = happiness_df.loc[happiness_df['Country'] == 'United States']['Happiness Score']
plt.axvline(USHappiness.values[0],0,0.90)
ax.text(USHappiness.values[0] + 0.035, 31000, 'United States', color = 'steelblue')
plt.show()
Student Count vs Cost of Living¶
plt.clf()
cost = sns.lmplot(x='Cost of Living Index', y ="Student Count", size=6, aspect = 2,
scatter_kws={"s":75,"alpha":0.6,"color":'orchid'},
line_kws={"color":'rebeccapurple'},order = 3,data = fulldata)
ax = cost.axes[0,0]
ax.set_title('Student Count vs Cost of Living')
dataCoords = list(zip(fulldata['Cost of Living Index'], fulldata['Student Count']))
for i in range(len(dataCoords)):
point = dataCoords[i]
if point[1] > 37000: #United Kingdom
ax.text(point[0]+1, point[1]-400, 'United Kingdom', color = 'darkslategray')
elif point[1] > 35000: #Italy
ax.text(point[0]+1, point[1]-400, 'Italy', color = 'darkslategray')
elif point[1] > 30000: #Spain
ax.text(point[0]+1, point[1]-400, 'Spain', color = 'darkslategray')
USCost = 100
plt.axvline(USCost,0,0.965)
ax.text(USCost + 0.8, 31000, 'United States', color = 'steelblue')
plt.show()
These estimates seem to be much better at taking into account that the countries with the highest student count aren't necessarily the highest or lowest of whatever attribute is being estimated.
Linear Regression¶
To further confirm that Linear Regression may not be the best choice, we will be creating a linear model using scikit-learn's LinearRegression() and finding the R^2 value, which shows the accuracy of the linear fit. Scikit-learn is a machine learning library that features various forms of classification, regression, and clustering algorithms. We will also be plotting a graph of the residuals.
plt.clf()
plt.title('Linear Regression Residuals')
plt.xlabel('Countries')
features = fulldata[['Peace Score','Happiness Score', 'Cost of Living Index']]
results = fulldata[['Student Count']]
X = features
y = results['Student Count']
lm = linear_model.LinearRegression()
model = lm.fit(X,y)
axis = list(range(0,103))
predicted = model.predict(X)
fdc = fulldata.copy()
counter = 0
for index, row in fulldata.iterrows():
regression = row[1] - predicted[counter]
fdc.at[index, 'residuals'] = regression
counter = counter +1
fdc
residualplot = sns.scatterplot(x=axis, y="residuals", color='crimson', alpha=.6, s=60,
data = fdc)
print("R^2 Value: "+ str(lm.score(X,y)))
From the graph of residuals between predicted and actual values, we can see that the model has differences in the thousands. The x-axis of this graph is an arbitrary value to represent each country, but are plotted from the countries that receive the lowest amount of students to the highest. For the countries with higher student counts, they are vastly underestimated by the linear model, which makes sense given the vast difference between countries of lower and higher student count. The lower countries, while not to an as harsh degree, are generally overestimated as well.
We can also see that the R^2 is terrible, at a value of around .099988. From these two factors, a better model than a linear function should be used.
Polynomial Regression¶
plt.clf()
plt.title('Polynomial Regression Residuals')
plt.xlabel('Countries')
polynomial_features= PolynomialFeatures(degree=3)
x_poly = polynomial_features.fit_transform(X)
model = lm.fit(x_poly, y)
predicted = model.predict(x_poly)
counter = 0
for index, row in fulldata.iterrows():
regression = row[1] - predicted[counter]
fdc.at[index, 'residuals'] = regression
counter = counter +1
fdc
residualplot = sns.scatterplot(x=axis, y="residuals", color='seagreen', alpha=.6, s=60,
data = fdc)
print("R^2 Value: "+ str(lm.score(x_poly,y)))
While the R^2 has increased, it is still quite bad. This is likely heavily related to the outliers, which differ by far too large of a proportion. The graph of residuals holds the same pattern, and doesn't change much as far the higher countries are considered, though the lower countries due have a slightly more accurate prediction, albeit still quite unreliable.
One thing to try is to remake the model with the 3 main outliers removed.
Polynomial Regression (Big 3 Outliers Removed)¶
plt.clf()
plt.title('Polynomial Regression Residuals (3 Outliers Removed)')
plt.xlabel('Countries')
features = Outliers_removed[['Peace Score','Happiness Score', 'Cost of Living Index']]
results = Outliers_removed[['Student Count']]
X = features
y = results['Student Count']
polynomial_features= PolynomialFeatures(degree=3)
x_poly = polynomial_features.fit_transform(X)
model = lm.fit(x_poly, y)
axis = list(range(0,100))
predicted = model.predict(x_poly)
counter = 0
for index, row in Outliers_removed.iterrows():
regression = row[1] - predicted[counter]
Outliers_removed.at[index, 'residuals'] = regression
counter = counter + 1
fdc
residualplot = sns.scatterplot(x=axis, y="residuals", color='darkorange', alpha=.6, s=60,
data = Outliers_removed)
lm.score(x_poly, y)
However, even with the major outliers removed, the R^2 value is still incredibly low. The residual plot follows the same exponential pattern, though much less harsh as the three major countries with differences in the 30000s are no longer considered. We can see that the predictions for the lower countries are still becoming slightly more accurate.
A number of factors could be impacting this, such as the low amount of data of only a single year that we have to work with. Furthermore, we at the moment have only three features, and despite the relationship they have with student count, it is possible that it is not enough to explain the very large differences of the number of students studying abroad at these countries. The maps have also shown that large geographic areas tend to follow certain trends for the attributes, and taking into account the continent or some other geographic attribute may help improve the model, though it is not as viable due to the limited data we have.
SVR (Support Vector Regression) Model¶
Given the unreliability of the predictions that the linear and polynomial regression models have given us, perhaps using a different model (as a polynomial regression is still an offshoot of linear regression) such as a Epsilon-Support Vector Regression could provide us with something interesting. We decided on the SVR model based off the attributes of our data as explained from the link https://towardsdatascience.com/choosing-a-scikit-learn-linear-regression-algorithm-dd96b48105f5.
plt.clf()
plt.title('SVR Residuals')
plt.xlabel('Countries')
X = fulldata[['Peace Score','Happiness Score', 'Cost of Living Index']]
y = fulldata[['Student Count']]
clf = SVR(kernel = 'poly', degree = 3,C=1.0, epsilon=0.2)
clf.fit(X,y)
predictions = clf.predict(X)
axis = list(range(0,103))
predicted = clf.predict(X)
counter = 0
for index, row in fulldata.iterrows():
regression = row[1] - predicted[counter]
fdc.at[index, 'residuals'] = regression
counter = counter +1
fdc
residualplot = sns.scatterplot(x=axis, y="residuals", alpha=.6, s=60,
data = fdc)
print("R^2 Value: "+ str(clf.score(X,y)))
Visually, we can see that the residuals seem to be much less scattered, as well as the predicted values being generally closer to the actual values. However, the R^2 value is still terrible, likely due to the factors explained before. The model is still unable to accurately deal with the countries of higher student count, and the differences between the predicted and actual values are still quite high all around.
Conclusion¶
Looking at the predictions of our machine learning algorithm's, it is clear that the accuracy of our model leaves something to be desired. However, this is most likely due to the severe limitations of our data. This includes the small amount of data that we have stemming from only having sources of a single year, as well as only utilizing three features and potentially missing some more important decisive factors. To improve on this aspect, we will have to focus much more heavily on the data collection. Given the nature of using countries as a data point, we will perhaps have to find more historical data about the number of students from the United States studying abroad, which may prove to be difficult given its somewhat niche nature. We will also have to find historical data for each of our features, as well as figure out what other features would likely impact a student's decision.
From the visualization of our data, at the very least, we can see trends between the features and the number of students studying at the country, as well as between features themselves, leading us to believe that there is some correlation that can be found between them. However, a large problem stems from the fact that the outliers are just too large, contributing to the difficulties of forming an accurate prediction model.
Another factor to take into consideration is the ever-changing political states of this world, which can possibly contribute to sporadic changes in country features, as well as the number of students studying at which country. This means that the concept of accurately predicting the number of students studying at country is a very difficult idea to tackle, especially in the future. This makes using historical data potentially much more difficult. Regardless, should we have all the necessary data, we can still validate the accuracy of our model by comparing predictions of past data, as well as do further analysis on the features that we have confirmed to impact the decision. Should we remain optimistic, a fun future project (assuming we have all the necessary data and features) could be using machine learning to see how each of the individual fluctuating features change over the years, and using these predicted values, run these predicted "future" countries through a more improved model in an attempt to predict the proportion of students studying abroad in the future.