Exploratory Data Analysis of Graduate Admission data

18 minute read

Introduction

In this post, I’ll apply different EDA (Exploratory Data Analysis) techniques on the Graduate Admission 2 data.

The goal in this data is to predict the student’s chance of admission to a postgraduate education, given several predictor variables for the student.

The code can be found on GitHub at this repo: Graduate-admission.

Import libraries

import pandas as pd
import plotly.express as px
from scipy import stats

Load data

There are two data files:

Admission_Predict.csv
Admission_Predict_Ver1.1.csv

Will use the second one, since it contains more data points.

df = pd.read_csv("data/Admission_Predict_Ver1.1.csv")

According to the dataset author on Kaggle, the columns in this data represents:

GRE Score: The Graduate Record Examinations is a standardized test that is an admissions requirement for many graduate schools in the United States and Canada.
TOEFL Score: Score in TOEFL exam.
University Rating: Student undergraduate university ranking.
SOP: Statement of Purpose strength.
LOR: Letter of Recommendation strength.
CGPA: Undergraduate GPA.
Research: Whether student has research experience or not.
Chance of Admit: Admission chance.

Getting to know the data

In this section, we’ll take a quick look at the data, to see how many row are there, and whther there are any missing values or not, to decie what kind of preprocessing will be needed.

df.head()

	Serial No.	GRE Score	TOEFL Score	University Rating	SOP	LOR	CGPA	Research	Chance of Admit
0	1	337	118	4	4.5	4.5	9.65	1	0.92
1	2	324	107	4	4.0	4.5	8.87	1	0.76
2	3	316	104	3	3.0	3.5	8.00	1	0.72
3	4	322	110	3	3.5	2.5	8.67	1	0.80
4	5	314	103	2	2.0	3.0	8.21	0	0.65

df.columns

Index(['Serial No.', 'GRE Score', 'TOEFL Score', 'University Rating', 'SOP',
       'LOR ', 'CGPA', 'Research', 'Chance of Admit '],
      dtype='object')

df.shape

(500, 9)

df.isnull().sum()

Serial No.           0
GRE Score            0
TOEFL Score          0
University Rating    0
SOP                  0
LOR                  0
CGPA                 0
Research             0
Chance of Admit      0
dtype: int64

df.dtypes

Serial No.             int64
GRE Score              int64
TOEFL Score            int64
University Rating      int64
SOP                  float64
LOR                  float64
CGPA                 float64
Research               int64
Chance of Admit      float64
dtype: object

The dataset consists of 500 samples and 9 columns: 8 predictors and one target variable.

There are no missing values (which is a very good thing!), but some column names need to be cleaned, and the Serial No. must be removed, as it has nothing to do with the student’s overall admission chance.

Lookin at the dtypes it seems that all columns are in the correct data type, discrete columns are in int64 and continuous in float64.

Data cleaning and Preprocessing

As stated in the previous section, only few cleaning will be performed, mainly:

remove extra whitespace from column names.
drop Serial No. column
convert Research column to bool.

df.columns

Index(['Serial No.', 'GRE Score', 'TOEFL Score', 'University Rating', 'SOP',
       'LOR ', 'CGPA', 'Research', 'Chance of Admit '],
      dtype='object')

Pandas has a great feature which allows us to apply multiple functions on the DataFrame in a sequential order: the pipe method.

Here, I’ll define two separate functions for applying each processing step, and then call them using the pipe function.

def read_data():
    temp_df = pd.read_csv("data/Admission_Predict_Ver1.1.csv")
    return temp_df

def normalize_column_names(temp_df):
    return temp_df.rename(
        columns={"LOR ": "LOR", "Chance of Admit ": "Chance of Admit"}
    )

def drop_noisy_columns(temp_df):
    return temp_df.drop(columns=["Serial No."])

def normalize_dtypes(temp_df):
    return temp_df.astype({"Research": bool, "University Rating": str})

def sort_uni_ranking(temp_df):
    return temp_df.sort_values(by="University Rating")

Now, we plug them together:

df = (
    read_data()
    .pipe(normalize_column_names)
    .pipe(drop_noisy_columns)
    .pipe(normalize_dtypes)
    .pipe(sort_uni_ranking)
)

df.columns

Index(['GRE Score', 'TOEFL Score', 'University Rating', 'SOP', 'LOR', 'CGPA',
       'Research', 'Chance of Admit'],
      dtype='object')

df.shape

(500, 8)

df.dtypes

GRE Score              int64
TOEFL Score            int64
University Rating     object
SOP                  float64
LOR                  float64
CGPA                 float64
Research                bool
Chance of Admit      float64
dtype: object

We cleaned the data with a clean code!

Exploratory Data Analysis (EDA)

In this section, we’ll explore the data visually and summarize it using descriptive statistic methods.

To keep things simpler, we’ll divide this section into three subsections:

Univariate analysis: in this section we’ll focus only at one variable at a time, and study the variable descriptive statistics with some charts like: Bar chart, Line chart, Histogram, Boxplot, etc …, and how the variable is distributed, and if there is any skewness in the distribution.
Bivariate analysis: in this section we’ll study the relation between two variables, and present different statistics such as Correlation, Covariance, and will use some other charts like: scatterplot, and will make use of the hue parameter of the previous charts.
Multivariate analysis: in this section we’ll study the relation between three or more variables, and will use additional type of charts, such as parplot.

Univariate Analysis

Here in this section, will perform analysis on each variable individually, but according to the variable type different methods and visualization will be used, main types of variables:

Numerical: numerical variables are variables which measures things like: counts, grades, etc …, and they don’t have a finite set of values, and they can be divided to:
- Continuous: continuous variables are continous measurements such as weight, height.
- Discrete: discrete variables represent counts such as number of children in a family, number of rooms in a house.
Categorical: a categorical variable is a variable which takes one of a limited values, and it can be further divided to:
- Nominal: nominal variable has a finite set of possible values, which don’t have any ordereing relation among them, like countries, for example we can’t say that France is higher than Germany: France > Germany, therfore, there’s no sense of ordering between the values in a noinal variable.
- Ordinal: in contrast to Nominal variable, ordinal varible defines an ordering relation between the values, such as the student performance in an exam, which can be: Bad, Good, Very Good, and Excellent (there’s an ordering relation among theses values, and we can say that Bad is lower than Good: Bad < Good)
- Binary: binary variables are a special case of nominal variables, but they only have two possible values, like admission status which can either be Accepted or Not Accepted.

resources:

Let’s see what are the types of variables in our dataset:

df.describe()

	GRE Score	TOEFL Score	SOP	LOR	CGPA	Chance of Admit
count	500.000000	500.000000	500.000000	500.00000	500.000000	500.00000
mean	316.472000	107.192000	3.374000	3.48400	8.576440	0.72174
std	11.295148	6.081868	0.991004	0.92545	0.604813	0.14114
min	290.000000	92.000000	1.000000	1.00000	6.800000	0.34000
25%	308.000000	103.000000	2.500000	3.00000	8.127500	0.63000
50%	317.000000	107.000000	3.500000	3.50000	8.560000	0.72000
75%	325.000000	112.000000	4.000000	4.00000	9.040000	0.82000
max	340.000000	120.000000	5.000000	5.00000	9.920000	0.97000

Discrete: GRE Score and TOEFL Score are discrete variables.
Continuous: CGPA and Chance of Admit are continuous variables.
Ordinal: University Rating, SOP and LOR are ordinal variables.
Binary: Research is a binary variable.

`GRE Score`

The GRE Score is a discrete variable.

df["GRE Score"].describe()

count    500.000000
mean     316.472000
std       11.295148
min      290.000000
25%      308.000000
50%      317.000000
75%      325.000000
max      340.000000
Name: GRE Score, dtype: float64

print(df["GRE Score"].mode())

0    312
dtype: int64

print(stats.skew(df["GRE Score"]))

-0.03972223277299966

fig = px.histogram(
    df,
    x="GRE Score",
    nbins=20,
    marginal="box",
    title="Distribution of the <b>GRE Score</b> variable",
)

fig.show()

We can conclude from the previous chart the following:

The GRE scores are very close to a normal distribution, with a small negative skewnewss (left skewed).
The most common scores are between 310 and 325.
The average score is 316 with a standard deviation of 11.2.
There are no outliers.

This variable doesn’t need any further processing.

`TOEFL Score`

The TOEFL Score is a discrete variable.

df["TOEFL Score"].describe()

count    500.000000
mean     107.192000
std        6.081868
min       92.000000
25%      103.000000
50%      107.000000
75%      112.000000
max      120.000000
Name: TOEFL Score, dtype: float64

print(df["TOEFL Score"].mode())

0    110
dtype: int64

print(stats.skew(df["TOEFL Score"]))

0.09531393010261811

fig = px.histogram(
    df,
    x="TOEFL Score",
    marginal="box",
    nbins=15,
    title="Distribution of <b>TOEFL Score</b> variable",
)

fig.show()

df["TOEFL Score"].value_counts()[:4]

  44
  37
  29
  28
Name: TOEFL Score, dtype: int64

From the previous chart, we can conclude:

TOEFL scores are also normally distributed, with a small positive (right skewness).
The average TOEFL score is 107 with a standard deviation 6.
The most common scores are: 110, 105, 104 and 112.
There are no outliers.

The variable doesn’t need any further processing.

`University Rating`

The University Rating is an ordinal variable, it represents the student’s undergraduate university ranking on a scale 1-5.

df["University Rating"].value_counts()

  162
  126
  105
   73
   34
Name: University Rating, dtype: int64

temp_df = df.groupby(by="University Rating", as_index=False).agg(
    counts=pd.NamedAgg(column="University Rating", aggfunc="count")
)

temp_df["University Rating"] = temp_df["University Rating"].astype(str)

fig = px.bar(
    data_frame=temp_df,
    x="University Rating",
    y="counts",
    color="University Rating",
    color_discrete_sequence=px.colors.qualitative.D3,
    title="Distribution of <b>University rating</b> variable",
)

fig.show()

We can see that the most common rating is in the middle: 3. The chart shows that the ratings are distributed in a similar fashion to the normal distrbution.

`SOP`

SOP stands for the strength of Statement of Purpose which is a necessary document for graduate applications. The values were (mostly) entered by the students, and it’s on scale 1-5, so this is an ordinal variable.

df["SOP"].value_counts()

0    89
5    88
0    80
5    64
5    63
0    43
0    42
5    25
0     6
Name: SOP, dtype: int64

temp_df = df.groupby(by="SOP", as_index=False).agg(
    counts=pd.NamedAgg(column="SOP", aggfunc="count")
)

temp_df["SOP"] = temp_df["SOP"].astype(str)

fig = px.bar(
    data_frame=temp_df,
    x="SOP",
    y="counts",
    color="SOP",
    color_discrete_sequence=px.colors.qualitative.Prism,
    title="Distribution of <b>SOP</b> variable",
)

fig.show()

Most students estimated the strength of their Statement of Purpose between 3 and 4.

`LOR`

LOR stands for the strength of Letter of Recommendation. The values were (mostly) entered by the students, and it’s on scale 1-5, so this is an ordinal variable.

df["LOR"].value_counts()

0    99
0    94
5    86
5    63
5    50
0    50
0    46
5    11
0     1
Name: LOR, dtype: int64

temp_df = df.groupby(by="LOR", as_index=False).agg(
    counts=pd.NamedAgg(column="LOR", aggfunc="count")
)

temp_df["LOR"] = temp_df["LOR"].astype(str)

fig = px.bar(
    data_frame=temp_df,
    x="LOR",
    y="counts",
    color="LOR",
    color_discrete_sequence=px.colors.qualitative.Prism,
    title="Distribution of <b>LOR</b> variable",
)

fig.show()

Most of the students rated the strength of ther Letter of Recommendation between 3 and 4.

`CGPA`

The CGPA stands for the student’s cumulative grade point average, which represents the average of grade points obtained in all the subjects by the student.

It’s a continuous variable, on a scale 0-10.

df["CGPA"].describe()

count    500.000000
mean       8.576440
std        0.604813
min        6.800000
25%        8.127500
50%        8.560000
75%        9.040000
max        9.920000
Name: CGPA, dtype: float64

print(stats.skew(df["CGPA"]))

-0.026532613141817388

fig = fig = px.histogram(
    data_frame=df,
    x="CGPA",
    marginal="box",
    nbins=12,
    title="Distribution of <b>CGPA</b> variable",
)

fig.show()

As we can see, this variable is very close to a normal distribution, with a small negative (left) skewness, and there are no outliers.

`Research`

The Research variable indicates whether the student has any research experience or not, so it’s a Binary variable.

Although, it would be better to have a variable like Research duration which expresses for how long was the student involved in a research activity.

df["Research"].value_counts()

True     280
False    220
Name: Research, dtype: int64

temp_df = df.groupby(by="Research", as_index=False).agg(
    counts=pd.NamedAgg(column="Research", aggfunc="count")
)

fig = px.bar(
    data_frame=temp_df,
    x="Research",
    y="counts",
    color="Research",
    color_continuous_scale=px.colors.qualitative.D3,
    title="Distribution of <b>Research</b> variable",
)

fig.show()

From this plot, we can see that the number of students who have a research experience is almost equal to the number of students who don’t.

Later, we’ll study the relation of this variable with other variables.

`Chance of Admit`

Quoting the dataste author from this thread:

chance of admit is a parameter that was asked to individuals (some values manually entered) before the results of the application

So thie column is not an actual probability of admission estimated by the universities or something, rather, it’s an estimation by the student themselves of how likely they’ll be admitted to the university.

df["Chance of Admit"].describe()

count    500.00000
mean       0.72174
std        0.14114
min        0.34000
25%        0.63000
50%        0.72000
75%        0.82000
max        0.97000
Name: Chance of Admit, dtype: float64

print(stats.skew(df["Chance of Admit"]))

-0.2890955854789938

fig = px.histogram(
    data_frame=df,
    x="Chance of Admit",
    marginal="box",
    title="Distribution of <b>Chance of Admit</b> variable",
)

fig.show()

df[df["Chance of Admit"] < 0.36]

	GRE Score	TOEFL Score	University Rating	SOP	LOR	CGPA	Research	Chance of Admit
376	297	96	2	2.5	2.0	7.43	False	0.34
92	298	98	2	4.0	3.0	8.03	False	0.34

The plot shows that most student estimated their chance of admission between 0.7 and 0.75.

The distribution is moderately skewed to the left with a negative skew value -0.29.

There are also two outlier values 0.34.

Bivariate Analysis

In this section, we’ll focus on studying the relationship between two different variables, to answer different question, like

What is the relation between variable x and variable y? is it linear or non-linear?
In case of a linear relation, is positive linear relation or negative linear relation? and how strong is the relation?
How the distribution for two variables changes?

Correlation matrix

We’ll start off by computing the correlation matrix using .corr method of pandas, which computes the pairwise correlation of columns.

The method used for calculating the correlation between two variables x and y is the Pearson correlation coefficient.

The pearson coefficient is a measure of the linear correlation between two variables x and y, and it takes values between -1 and +1.

A negative value indicates a negative correlation (i.e. when one variable increases the other decreases), and a positive value is the opposite (the two variables increases/decreases at the same time)

Here, we’ll compute the correlations only for GRE Score, TOEFL Score and CGPA variables, because they are numeric variables, and they weren’t estimated by the students themselves.

numeric_cols = ["GRE Score", "TOEFL Score", "CGPA"]

corr = df[numeric_cols].corr()

fig = px.imshow(
    corr,
    color_continuous_scale="PuBu",
    color_continuous_midpoint=0.6,
    title="Correlation matrix",
)

fig.show()

We can see from the correlation matrix that the three variables have a strong positive correlation. We’ll look closer at the relations between variables using scatter plots.

Scatter plot

Scatter plots are a good way to show the spread of points for two variables x and y, and view the relation between the two variables (e.g. linear, non-linear, …) and the trend of the linear relation (positive, negative)

An easy way to show multiple scatter plots on the same figure is either using scatter_matrix or pairplot.

fig = px.scatter_matrix(
    df,
    dimensions=numeric_cols,
    title="Scatter matrix of student's <b>TOEFL Score</b>, <b>GRE Score</b>, and <b>CGPA</b>",
)

fig.update_traces(diagonal_visible=False)

fig.show()

It’s evident from these plots that the relation between the variables is positive linear relation, with some outlier points, and they all have an upward trend.

Let’s show the scatter for each two variables at a time:

`TOEFL Score` vs. `GRE Score`

corr_value = df["TOEFL Score"].corr(df["GRE Score"])

fig = px.scatter(
    data_frame=df,
    x="TOEFL Score",
    y="GRE Score",
    marginal_x="histogram",
    marginal_y="histogram",
    trendline="ols",
    trendline_color_override="red",
    title=f"Correlation between <b>TOEFL Score</b> and <b>GRE Score</b> is: {corr_value:.2f}",
)

fig.show()

`TOEFL Score` vs. `CGPA`

corr_value = df["TOEFL Score"].corr(df["CGPA"])

fig = px.scatter(
    data_frame=df,
    x="TOEFL Score",
    y="CGPA",
    marginal_x="histogram",
    marginal_y="histogram",
    trendline="ols",
    trendline_color_override="red",
    title=f"Correlation between <b>TOEFL Score</b> and <b>CGPA</b> is: {corr_value:.2f}",
)

fig.show()

`GRE Score` vs. `CGPA`

corr_value = df["GRE Score"].corr(df["CGPA"])

fig = px.scatter(
    data_frame=df,
    x="GRE Score",
    y="CGPA",
    marginal_x="histogram",
    marginal_y="histogram",
    trendline="ols",
    trendline_color_override="red",
    title=f"Correlation between <b>GRE Score</b> and <b>CGPA</b> is: {corr_value:.2f}",
)

fig.show()

From the previous three charts we can say that: students who perform well in their TOEFL exams tend to also perform well in GRE exams, and they mostly have high GPA (higher than 9).

Bivariate distributions

Another way to study the relation between two variables is with 2D Histograms (distribution).

Just like the distributions we used in the Univariate Analysis section, we can show the distribution for two variables x and y, which would give us better insights on how much the values from the two variables overlap, and show cluster regions in the 2D space.

Compared to scatter plots, 2D histograms are better at handling large amounts of data, as they use rectangular bins, and count the number of points withing each bin.

`TOEFL Score` vs. `GRE Score`

fig = px.density_heatmap(
    data_frame=df,
    x="TOEFL Score",
    y="GRE Score",
    color_continuous_scale="PuBu",
    title="Joint distribution of <b>TOEFL Score</b> and <b>GRE Score</b> variables",
)

fig.show()

We can see from this chart some clusters (regions).

For example there are two clusters of students who scored between 110 and 115 in the TOEFL exam and between 320 and 330 in the GRE exam. These two clusters account for about 100 students (which is 20% of the total dataset).

`TOEFL Score` vs. `CGPA`

fig = px.density_heatmap(
    data_frame=df,
    x="TOEFL Score",
    y="CGPA",
    color_continuous_scale="PuBu",
    title="Joint distribution of <b>TOEFL Score</b> and <b>CGPA</b> variables",
)

fig.show()

This chart shows that about 170 students has TOEFL score in range [105-115] and their CGPA is in range [8-9]

`GRE Score` vs. `CGPA`

fig = px.density_heatmap(
    data_frame=df,
    x="GRE Score",
    y="CGPA",
    color_continuous_scale="PuBu",
    title="Bivariate distribution of <b>GRE Score</b> and <b>CGPA</b> variables",
)

fig.show()

This chart shows that almost 120 students has GRE scores in the range [310-320] and their CGPA is in thae range [8-9].

`Research`

One interesting question would be: How does research experience affects other variables? Do students who have research experience have beeter CGPA? Do they have better scores in TOEFL or GRE (or both)?

We can display the same distributions we used in the Univariate analysis section, with conditioning on Research variable:

fig = px.histogram(
    data_frame=df,
    x="TOEFL Score",
    color="Research",
    barmode="group",
    title="Conditional distribution of <b>TOEFL Score</b> variable on the <b>Research</b> variable",
)

fig.show()

fig = px.histogram(
    data_frame=df,
    x="GRE Score",
    color="Research",
    barmode="group",
    title="Conditional distribution of <b>GRE Score</b> variable on the <b>Research</b> variable",
)

fig.show()

fig = px.histogram(
    data_frame=df,
    x="CGPA",
    color="Research",
    barmode="group",
    title="Conditional distribution of <b>CGPA</b> variable on the <b>Research</b> variable",
)

fig.show()

We can see that students who engage in research activities and have research experience, tend to perform better in both TOEFL and GRE exams, and they have higher GPA, in comparison to students who have no research experience.

`University Rating`

The University Rating variable represents the ranking of the university from which the student graduated.

We might ask: How does the relation between student different scores changes for different university ranking?

Let’s see how the university ranking affects student’s scores and GPA:

fig = px.histogram(
    data_frame=df,
    x="TOEFL Score",
    color="University Rating",
    barmode="group",
    color_discrete_sequence=px.colors.sequential.Blugrn,
    title="Conditional distribution of <b>TOEFL Score</b> variable on the <b>University Rating</b> variable",
)

fig.show()

fig = px.histogram(
    data_frame=df,
    x="GRE Score",
    color="University Rating",
    color_discrete_sequence=px.colors.sequential.Blugrn,
    barmode="group",
    title="Conditional distribution of <b>GRE Score</b> variable on the <b>University Rating</b> variable",
)

fig.show()

fig = px.histogram(
    data_frame=df,
    x="CGPA",
    color="University Rating",
    color_discrete_sequence=px.colors.sequential.Blugrn,
    barmode="group",
    title="Conditional distribution of <b>CGPA</b> variable on the <b>University Rating</b> variable",
)

fig.show()

The university ranking plays an important role in student’s scores and GPA, we can observe that students who go to higher ranking universities, have higher scores in the TOEFL and GRE exams, and they have higher GPA.

Multivariate Analysis

So far, all the plots we used before were used either to explore one variable, or to show the relation between a pair of variables.

However, we are often interested in answering the question: How does the relation between two variables changes as a function of a third variable?

In this section, we’ll focus on answering these kinds of questions, where we’ll use similar plots to the ones we used before, with conditioning on other variable.

Scatter matrix with `Research`

We start by plotting the scatter matrix for variables TOEFL Score, GRE Score and CGPA (just as we did in bivariate analysis section), with showing the relation to Research variable with color coding.

This will draw an overall picture of how these variables are related to each other, and how this relation changes when whether student has a research experience or not.

fig = px.scatter_matrix(
    data_frame=df,
    dimensions=numeric_cols,
    color="Research",
    title="Scatter matrix for <b>TOEFL Score</b>, <b>GRE Score</b>, and <b>CGPA</b> conditioning on <b>Research</b> variable",
)

fig.update_traces(diagonal_visible=False)

fig.show()

We can how students who have research experience tend to have higher scores and better GPA.

Bivariate distribution with `University Rating`

As we saw earlier, the ranking of student’s university plays an important role in other variables, and higher university ranking is linked with better performance in TOEFL and GRE exams, and higher GPA.

Here, we’ll show the bivariate distribution of each pair of variables, for different university ranking values.

This way, we will be able to study the relation between two variables x and y as a function of the university ranking value.

`TOEFL Score` vs. `GRE Score`

fig = px.density_heatmap(
    data_frame=df,
    x="TOEFL Score",
    y="GRE Score",
    color_continuous_scale="PuBu",
    facet_col="University Rating",
    title="<b>TOEFL Score</b> vs. <b>GRE Score</b> for different values of <b>University Rating</b>",
)

fig.show()

`TOEFL Score` vs. `CGPA`

fig = px.density_heatmap(
    data_frame=df,
    x="TOEFL Score",
    y="CGPA",
    facet_col="University Rating",
    color_continuous_scale="PuBu",
    title="<b>TOEFL Score</b> vs. <b>CGPA</b> for different values of <b>University Rating</b>",
)

fig.show()

`GRE Score` vs. `CGPA`

fig = px.density_heatmap(
    data_frame=df,
    x="GRE Score",
    y="CGPA",
    facet_col="University Rating",
    color_continuous_scale="PuBu",
    title="<b>GRE Score</b> vs. <b>CGPA</b> for different values of <b>University Rating</b>",
)

fig.show()

All these charts support our previous hypothesis: University ranking influences positively student’s performance.

`Research` and `University Rating`

In all previous plots we used either the Research variable or University Rating variable, however, it would very helpful to see how these two variables interact with each other, and how other vriables interact with them.

Here, we’ll use scatterplot to show relation between two variables x and y, and show how this relation changes for different values of Research and University Rating.

This would be useful for answering questions:

Do students who go to higher-ranking universitries, are more involved in research activiteis?
How research experience and university ranking influence student’s performance in exams and GPA?
Are there any outlier points?

`TOEFL Score` vs. `GRE Score`

fig = px.scatter(
    data_frame=df,
    x="TOEFL Score",
    y="GRE Score",
    color="Research",
    facet_col="University Rating",
    trendline="ols",
    symbol="Research",
    title="Scatter matrix for <b>TOEFL Score</b> vs. <b>GRE Score</b> conditioning on <b>University Rating</b> and <b>Research</b> variables",
)

fig.show()

`TOEFL Score` vs. `CGPA`

fig = px.scatter(
    data_frame=df,
    x="TOEFL Score",
    y="CGPA",
    color="Research",
    facet_col="University Rating",
    trendline="ols",
    symbol="Research",
    title="Scatter matrix for <b>TOEFL Score</b> vs. <b>CGPA</b> conditioning on <b>University Rating</b> and <b>Research</b> variables",
)

fig.show()

`GRE Score` vs. `CGPA`

fig = px.scatter(
    data_frame=df,
    x="GRE Score",
    y="CGPA",
    color="Research",
    facet_col="University Rating",
    trendline="ols",
    symbol="Research",
    title="Scatter matrix for <b>GRE Score</b> vs. <b>CGPA</b> conditioning on <b>University Rating</b> and <b>Research</b> variables",
)

fig.show()

As we can see, higher university ranking is linked with having research experience, and they both affect student’s scores and GPA.

We can also see that there are some outlier points, where student goes to a low-ranking university and has no research experience, but have good scores.

This way of studying how the relation between two variables changes as a function of other variables is very useful when we have a very large amount of data, and we want to study the relation between two quanitative variables, and how this relation changes with respect to other categorical variables, as we will have fewer points to investigate, rather than a single scatter plot with too many points.

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Introduction

Import libraries

Load data

Getting to know the data

Data cleaning and Preprocessing

Exploratory Data Analysis (EDA)

Univariate Analysis

GRE Score

TOEFL Score

University Rating

SOP

LOR

CGPA

Research

Chance of Admit

Bivariate Analysis

Correlation matrix

Scatter plot

TOEFL Score vs. GRE Score

TOEFL Score vs. CGPA

GRE Score vs. CGPA

Bivariate distributions

TOEFL Score vs. GRE Score

TOEFL Score vs. CGPA

GRE Score vs. CGPA

Research

University Rating

Multivariate Analysis

Scatter matrix with Research

Bivariate distribution with University Rating

TOEFL Score vs. GRE Score

TOEFL Score vs. CGPA

GRE Score vs. CGPA

Research and University Rating

TOEFL Score vs. GRE Score

TOEFL Score vs. CGPA

GRE Score vs. CGPA

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`GRE Score`

`TOEFL Score`

`University Rating`

`SOP`

`LOR`

`CGPA`

`Research`

`Chance of Admit`

`TOEFL Score` vs. `GRE Score`

`TOEFL Score` vs. `CGPA`

`GRE Score` vs. `CGPA`

`TOEFL Score` vs. `GRE Score`

`TOEFL Score` vs. `CGPA`

`GRE Score` vs. `CGPA`

`Research`

`University Rating`

Scatter matrix with `Research`

Bivariate distribution with `University Rating`

`TOEFL Score` vs. `GRE Score`

`TOEFL Score` vs. `CGPA`

`GRE Score` vs. `CGPA`

`Research` and `University Rating`

`TOEFL Score` vs. `GRE Score`

`TOEFL Score` vs. `CGPA`

`GRE Score` vs. `CGPA`