Predicting Student Success and Dropout
Pritesh Shah
2023-11-27
Introduction
- The dataset central to our project comes from the prestigious UCI
Machine Learning Repository, a well-known source in the data science
community for its diverse and high-quality datasets. This particular
dataset focuses on a critical issue in the educational sector:
predicting student dropout and academic success.
- The dataset offers a rich array of variables encompassing various
aspects of student profiles, academic records, and socio-economic
backgrounds. By analyzing this data, we aim to uncover patterns and
insights that can help in understanding the factors influencing student
performance and retention. Our analysis could provide valuable
information for educational institutions to develop strategies to
enhance student success and reduce dropout rates.
- The goal of this project is to apply comprehensive data analysis
techniques and statistical methods using R to explore and model this
dataset. Through hypothesis testing, generalized linear models, and
other statistical tests, we aim to not only predict student dropout and
academic success but also to gain deeper insights into the dynamics of
student performance within the educational framework. SOURCE - https://archive.ics.uci.edu/dataset/697/predict+students+dropout+and+academic+success
Dataset Overview
Purpose and Creation
- Objective: Developed to understand how to reduce
academic dropout and failure in higher education.
- Approach: Utilizes machine learning to identify
at-risk students early in their academic journey, enabling timely
intervention strategies.
Dataset Composition
- Contents: Includes data on students’ academic
paths, demographics, and socio-economic factors at enrollment.
- Classification Task: Formulated as a three-category
classification – dropout, enrolled, and graduate – by the end of the
course’s normal duration.
Funding and Support
- Funded By: SATDAP program under grant
POCI-05-5762-FSE-000191, Portugal.
Data Characteristics
- Instances: Each instance represents an individual
student.
- Data Split (Usage in Project): 80% for training and
20% for testing.
- Preprocessing: Rigorous data cleaning for
anomalies, outliers, and missing values.
- Missing Values: None.
Data Exploration and
Initial Findings
This section will cover the initial exploration of the dataset,
looking into summary statistics, data structure, and preliminary
visualizations to uncover insights and patterns.
# Load necessary libraries
library(tidyverse)
# Load the dataset
students_data <- read_delim("data.csv", delim = ";")
# TOp 10
head(students_data, 10)
## # A tibble: 10 × 37
## `Marital status` `Application mode` `Application order` Course
## <dbl> <dbl> <dbl> <dbl>
## 1 1 17 5 171
## 2 1 15 1 9254
## 3 1 1 5 9070
## 4 1 17 2 9773
## 5 2 39 1 8014
## 6 2 39 1 9991
## 7 1 1 1 9500
## 8 1 18 4 9254
## 9 1 1 3 9238
## 10 1 1 1 9238
## # ℹ 33 more variables: `Daytime/evening attendance\t` <dbl>,
## # `Previous qualification` <dbl>, `Previous qualification (grade)` <dbl>,
## # Nacionality <dbl>, `Mother's qualification` <dbl>,
## # `Father's qualification` <dbl>, `Mother's occupation` <dbl>,
## # `Father's occupation` <dbl>, `Admission grade` <dbl>, Displaced <dbl>,
## # `Educational special needs` <dbl>, Debtor <dbl>,
## # `Tuition fees up to date` <dbl>, Gender <dbl>, …
Dataset Structure
- Understanding the structure of our dataset is important to get a
sense of the types of variables we are working with and to plan our
analysis accordingly.
# Examine the structure of the dataset
str(students_data)
## spc_tbl_ [4,424 × 37] (S3: spec_tbl_df/tbl_df/tbl/data.frame)
## $ Marital status : num [1:4424] 1 1 1 1 2 2 1 1 1 1 ...
## $ Application mode : num [1:4424] 17 15 1 17 39 39 1 18 1 1 ...
## $ Application order : num [1:4424] 5 1 5 2 1 1 1 4 3 1 ...
## $ Course : num [1:4424] 171 9254 9070 9773 8014 ...
## $ Daytime/evening attendance : num [1:4424] 1 1 1 1 0 0 1 1 1 1 ...
## $ Previous qualification : num [1:4424] 1 1 1 1 1 19 1 1 1 1 ...
## $ Previous qualification (grade) : num [1:4424] 122 160 122 122 100 ...
## $ Nacionality : num [1:4424] 1 1 1 1 1 1 1 1 62 1 ...
## $ Mother's qualification : num [1:4424] 19 1 37 38 37 37 19 37 1 1 ...
## $ Father's qualification : num [1:4424] 12 3 37 37 38 37 38 37 1 19 ...
## $ Mother's occupation : num [1:4424] 5 3 9 5 9 9 7 9 9 4 ...
## $ Father's occupation : num [1:4424] 9 3 9 3 9 7 10 9 9 7 ...
## $ Admission grade : num [1:4424] 127 142 125 120 142 ...
## $ Displaced : num [1:4424] 1 1 1 1 0 0 1 1 0 1 ...
## $ Educational special needs : num [1:4424] 0 0 0 0 0 0 0 0 0 0 ...
## $ Debtor : num [1:4424] 0 0 0 0 0 1 0 0 0 1 ...
## $ Tuition fees up to date : num [1:4424] 1 0 0 1 1 1 1 0 1 0 ...
## $ Gender : num [1:4424] 1 1 1 0 0 1 0 1 0 0 ...
## $ Scholarship holder : num [1:4424] 0 0 0 0 0 0 1 0 1 0 ...
## $ Age at enrollment : num [1:4424] 20 19 19 20 45 50 18 22 21 18 ...
## $ International : num [1:4424] 0 0 0 0 0 0 0 0 1 0 ...
## $ Curricular units 1st sem (credited) : num [1:4424] 0 0 0 0 0 0 0 0 0 0 ...
## $ Curricular units 1st sem (enrolled) : num [1:4424] 0 6 6 6 6 5 7 5 6 6 ...
## $ Curricular units 1st sem (evaluations) : num [1:4424] 0 6 0 8 9 10 9 5 8 9 ...
## $ Curricular units 1st sem (approved) : num [1:4424] 0 6 0 6 5 5 7 0 6 5 ...
## $ Curricular units 1st sem (grade) : num [1:4424] 0 14 0 13.4 12.3 ...
## $ Curricular units 1st sem (without evaluations): num [1:4424] 0 0 0 0 0 0 0 0 0 0 ...
## $ Curricular units 2nd sem (credited) : num [1:4424] 0 0 0 0 0 0 0 0 0 0 ...
## $ Curricular units 2nd sem (enrolled) : num [1:4424] 0 6 6 6 6 5 8 5 6 6 ...
## $ Curricular units 2nd sem (evaluations) : num [1:4424] 0 6 0 10 6 17 8 5 7 14 ...
## $ Curricular units 2nd sem (approved) : num [1:4424] 0 6 0 5 6 5 8 0 6 2 ...
## $ Curricular units 2nd sem (grade) : num [1:4424] 0 13.7 0 12.4 13 ...
## $ Curricular units 2nd sem (without evaluations): num [1:4424] 0 0 0 0 0 5 0 0 0 0 ...
## $ Unemployment rate : num [1:4424] 10.8 13.9 10.8 9.4 13.9 16.2 15.5 15.5 16.2 8.9 ...
## $ Inflation rate : num [1:4424] 1.4 -0.3 1.4 -0.8 -0.3 0.3 2.8 2.8 0.3 1.4 ...
## $ GDP : num [1:4424] 1.74 0.79 1.74 -3.12 0.79 -0.92 -4.06 -4.06 -0.92 3.51 ...
## $ Target : chr [1:4424] "Dropout" "Graduate" "Dropout" "Graduate" ...
## - attr(*, "spec")=
## .. cols(
## .. `Marital status` = col_double(),
## .. `Application mode` = col_double(),
## .. `Application order` = col_double(),
## .. Course = col_double(),
## .. `Daytime/evening attendance ` = col_double(),
## .. `Previous qualification` = col_double(),
## .. `Previous qualification (grade)` = col_double(),
## .. Nacionality = col_double(),
## .. `Mother's qualification` = col_double(),
## .. `Father's qualification` = col_double(),
## .. `Mother's occupation` = col_double(),
## .. `Father's occupation` = col_double(),
## .. `Admission grade` = col_double(),
## .. Displaced = col_double(),
## .. `Educational special needs` = col_double(),
## .. Debtor = col_double(),
## .. `Tuition fees up to date` = col_double(),
## .. Gender = col_double(),
## .. `Scholarship holder` = col_double(),
## .. `Age at enrollment` = col_double(),
## .. International = col_double(),
## .. `Curricular units 1st sem (credited)` = col_double(),
## .. `Curricular units 1st sem (enrolled)` = col_double(),
## .. `Curricular units 1st sem (evaluations)` = col_double(),
## .. `Curricular units 1st sem (approved)` = col_double(),
## .. `Curricular units 1st sem (grade)` = col_double(),
## .. `Curricular units 1st sem (without evaluations)` = col_double(),
## .. `Curricular units 2nd sem (credited)` = col_double(),
## .. `Curricular units 2nd sem (enrolled)` = col_double(),
## .. `Curricular units 2nd sem (evaluations)` = col_double(),
## .. `Curricular units 2nd sem (approved)` = col_double(),
## .. `Curricular units 2nd sem (grade)` = col_double(),
## .. `Curricular units 2nd sem (without evaluations)` = col_double(),
## .. `Unemployment rate` = col_double(),
## .. `Inflation rate` = col_double(),
## .. GDP = col_double(),
## .. Target = col_character()
## .. )
## - attr(*, "problems")=<externalptr>
Summary Statistics
- Summary statistics provide an initial overview of the data, offering
insights into the central tendency, dispersion, and shape of the
dataset’s distribution.
# Display summary statistics for numerical variables
summary(select_if(students_data, is.numeric))
## Marital status Application mode Application order Course
## Min. :1.000 Min. : 1.00 Min. :0.000 Min. : 33
## 1st Qu.:1.000 1st Qu.: 1.00 1st Qu.:1.000 1st Qu.:9085
## Median :1.000 Median :17.00 Median :1.000 Median :9238
## Mean :1.179 Mean :18.67 Mean :1.728 Mean :8857
## 3rd Qu.:1.000 3rd Qu.:39.00 3rd Qu.:2.000 3rd Qu.:9556
## Max. :6.000 Max. :57.00 Max. :9.000 Max. :9991
## Daytime/evening attendance\t Previous qualification
## Min. :0.0000 Min. : 1.000
## 1st Qu.:1.0000 1st Qu.: 1.000
## Median :1.0000 Median : 1.000
## Mean :0.8908 Mean : 4.578
## 3rd Qu.:1.0000 3rd Qu.: 1.000
## Max. :1.0000 Max. :43.000
## Previous qualification (grade) Nacionality Mother's qualification
## Min. : 95.0 Min. : 1.000 Min. : 1.00
## 1st Qu.:125.0 1st Qu.: 1.000 1st Qu.: 2.00
## Median :133.1 Median : 1.000 Median :19.00
## Mean :132.6 Mean : 1.873 Mean :19.56
## 3rd Qu.:140.0 3rd Qu.: 1.000 3rd Qu.:37.00
## Max. :190.0 Max. :109.000 Max. :44.00
## Father's qualification Mother's occupation Father's occupation Admission grade
## Min. : 1.00 Min. : 0.00 Min. : 0.00 Min. : 95.0
## 1st Qu.: 3.00 1st Qu.: 4.00 1st Qu.: 4.00 1st Qu.:117.9
## Median :19.00 Median : 5.00 Median : 7.00 Median :126.1
## Mean :22.28 Mean : 10.96 Mean : 11.03 Mean :127.0
## 3rd Qu.:37.00 3rd Qu.: 9.00 3rd Qu.: 9.00 3rd Qu.:134.8
## Max. :44.00 Max. :194.00 Max. :195.00 Max. :190.0
## Displaced Educational special needs Debtor
## Min. :0.0000 Min. :0.00000 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:0.00000 1st Qu.:0.0000
## Median :1.0000 Median :0.00000 Median :0.0000
## Mean :0.5484 Mean :0.01153 Mean :0.1137
## 3rd Qu.:1.0000 3rd Qu.:0.00000 3rd Qu.:0.0000
## Max. :1.0000 Max. :1.00000 Max. :1.0000
## Tuition fees up to date Gender Scholarship holder Age at enrollment
## Min. :0.0000 Min. :0.0000 Min. :0.0000 Min. :17.00
## 1st Qu.:1.0000 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:19.00
## Median :1.0000 Median :0.0000 Median :0.0000 Median :20.00
## Mean :0.8807 Mean :0.3517 Mean :0.2484 Mean :23.27
## 3rd Qu.:1.0000 3rd Qu.:1.0000 3rd Qu.:0.0000 3rd Qu.:25.00
## Max. :1.0000 Max. :1.0000 Max. :1.0000 Max. :70.00
## International Curricular units 1st sem (credited)
## Min. :0.00000 Min. : 0.00
## 1st Qu.:0.00000 1st Qu.: 0.00
## Median :0.00000 Median : 0.00
## Mean :0.02486 Mean : 0.71
## 3rd Qu.:0.00000 3rd Qu.: 0.00
## Max. :1.00000 Max. :20.00
## Curricular units 1st sem (enrolled) Curricular units 1st sem (evaluations)
## Min. : 0.000 Min. : 0.000
## 1st Qu.: 5.000 1st Qu.: 6.000
## Median : 6.000 Median : 8.000
## Mean : 6.271 Mean : 8.299
## 3rd Qu.: 7.000 3rd Qu.:10.000
## Max. :26.000 Max. :45.000
## Curricular units 1st sem (approved) Curricular units 1st sem (grade)
## Min. : 0.000 Min. : 0.00
## 1st Qu.: 3.000 1st Qu.:11.00
## Median : 5.000 Median :12.29
## Mean : 4.707 Mean :10.64
## 3rd Qu.: 6.000 3rd Qu.:13.40
## Max. :26.000 Max. :18.88
## Curricular units 1st sem (without evaluations)
## Min. : 0.0000
## 1st Qu.: 0.0000
## Median : 0.0000
## Mean : 0.1377
## 3rd Qu.: 0.0000
## Max. :12.0000
## Curricular units 2nd sem (credited) Curricular units 2nd sem (enrolled)
## Min. : 0.0000 Min. : 0.000
## 1st Qu.: 0.0000 1st Qu.: 5.000
## Median : 0.0000 Median : 6.000
## Mean : 0.5418 Mean : 6.232
## 3rd Qu.: 0.0000 3rd Qu.: 7.000
## Max. :19.0000 Max. :23.000
## Curricular units 2nd sem (evaluations) Curricular units 2nd sem (approved)
## Min. : 0.000 Min. : 0.000
## 1st Qu.: 6.000 1st Qu.: 2.000
## Median : 8.000 Median : 5.000
## Mean : 8.063 Mean : 4.436
## 3rd Qu.:10.000 3rd Qu.: 6.000
## Max. :33.000 Max. :20.000
## Curricular units 2nd sem (grade)
## Min. : 0.00
## 1st Qu.:10.75
## Median :12.20
## Mean :10.23
## 3rd Qu.:13.33
## Max. :18.57
## Curricular units 2nd sem (without evaluations) Unemployment rate
## Min. : 0.0000 Min. : 7.60
## 1st Qu.: 0.0000 1st Qu.: 9.40
## Median : 0.0000 Median :11.10
## Mean : 0.1503 Mean :11.57
## 3rd Qu.: 0.0000 3rd Qu.:13.90
## Max. :12.0000 Max. :16.20
## Inflation rate GDP
## Min. :-0.800 Min. :-4.060000
## 1st Qu.: 0.300 1st Qu.:-1.700000
## Median : 1.400 Median : 0.320000
## Mean : 1.228 Mean : 0.001969
## 3rd Qu.: 2.600 3rd Qu.: 1.790000
## Max. : 3.700 Max. : 3.510000
Filtering
library(dplyr)
# We filter the dataframe with Target column = 'Enrolled'
students_data <- students_data %>% filter(Target != "Enrolled")
## [1] "Marital status"
## [2] "Application mode"
## [3] "Application order"
## [4] "Course"
## [5] "Daytime/evening attendance\t"
## [6] "Previous qualification"
## [7] "Previous qualification (grade)"
## [8] "Nacionality"
## [9] "Mother's qualification"
## [10] "Father's qualification"
## [11] "Mother's occupation"
## [12] "Father's occupation"
## [13] "Admission grade"
## [14] "Displaced"
## [15] "Educational special needs"
## [16] "Debtor"
## [17] "Tuition fees up to date"
## [18] "Gender"
## [19] "Scholarship holder"
## [20] "Age at enrollment"
## [21] "International"
## [22] "Curricular units 1st sem (credited)"
## [23] "Curricular units 1st sem (enrolled)"
## [24] "Curricular units 1st sem (evaluations)"
## [25] "Curricular units 1st sem (approved)"
## [26] "Curricular units 1st sem (grade)"
## [27] "Curricular units 1st sem (without evaluations)"
## [28] "Curricular units 2nd sem (credited)"
## [29] "Curricular units 2nd sem (enrolled)"
## [30] "Curricular units 2nd sem (evaluations)"
## [31] "Curricular units 2nd sem (approved)"
## [32] "Curricular units 2nd sem (grade)"
## [33] "Curricular units 2nd sem (without evaluations)"
## [34] "Unemployment rate"
## [35] "Inflation rate"
## [36] "GDP"
## [37] "Target"
Encoding
Encoding refers to the process of converting data from one format
or representation to another. In the context of data analysis and
machine learning, encoding is often used to transform categorical or
text data into numerical form, which can be more easily processed and
utilized by algorithms.
Label Encoding: In label encoding, each unique category in a
categorical variable is assigned an integer label. For example, if we
have categories like “Red,” “Green,” and “Blue,” they could be encoded
as 0, 1, and 2, respectively. However, caution should be exercised when
using label encoding for ordinal data, as the numerical representation
may introduce an unintended ordinal relationship.
students_data$Target <- as.numeric(as.factor(students_data$Target)) - 1
table(students_data$Target)
##
## 0 1
## 1421 2209
Distribution
Table of Graduate and Non Graduate
library(dplyr)
# Grouping by Target Variables
target_counts <- students_data %>%
group_by(Target) %>%
summarise(Count = n())
library(ggplot2)
ggplot(target_counts, aes(x = Target, y = Count)) +
geom_bar(stat = "identity", fill = "blue") + # Use color of your choice
labs(title = "Distribution of Target Value", x = "Target", y = "Count") +
theme_minimal()
Correlation Matrix :
A correlation matrix is a table that shows the pairwise
correlations between variables in a dataset. Each cell in the table
represents the correlation between two variables, and the strength and
direction of the correlation is indicated by the color and magnitude of
the cell.
Correlation matrices are commonly used in data analysis to
identify relationships between variables and to help understand the
structure of the data. The values in the correlation matrix range from
-1 to 1, with -1 indicating a perfect negative correlation, 1 indicating
a perfect positive correlation, and 0 indicating no
correlation.
corr_matrix <- cor(students_data, use = "complete.obs")
corr_matrix
## Marital status Application mode
## Marital status 1.000000000 0.274984888
## Application mode 0.274984888 1.000000000
## Application order -0.130370462 -0.287245455
## Course 0.042012181 0.063112076
## Daytime/evening attendance\t -0.265822964 -0.310854207
## Previous qualification 0.070984437 0.416665526
## Previous qualification (grade) -0.038868508 -0.071189971
## Nacionality -0.008899064 -0.011710863
## Mother's qualification 0.185116875 0.122697099
## Father's qualification 0.124995407 0.098215810
## Mother's occupation 0.053892219 0.041650084
## Father's occupation 0.050498926 0.025629078
## Admission grade -0.012439707 -0.038311074
## Displaced -0.240543910 -0.308729857
## Educational special needs -0.027433732 -0.024611371
## Debtor 0.039469818 0.121455544
## Tuition fees up to date -0.096920476 -0.154142743
## Gender -0.001123579 0.186338223
## Scholarship holder -0.069684064 -0.174835480
## Age at enrollment 0.522359459 0.531601471
## International -0.026152910 -0.004620347
## Curricular units 1st sem (credited) 0.066665806 0.248882502
## Curricular units 1st sem (enrolled) 0.058093648 0.168856601
## Curricular units 1st sem (evaluations) 0.059191112 0.220351054
## Curricular units 1st sem (approved) -0.037691108 -0.037249973
## Curricular units 1st sem (grade) -0.069442294 -0.133919376
## Curricular units 1st sem (without evaluations) 0.041534688 0.054923049
## Curricular units 2nd sem (credited) 0.067507697 0.244575086
## Curricular units 2nd sem (enrolled) 0.041255869 0.130559160
## Curricular units 2nd sem (evaluations) 0.030786334 0.163626213
## Curricular units 2nd sem (approved) -0.058400138 -0.085269834
## Curricular units 2nd sem (grade) -0.079536308 -0.137288308
## Curricular units 2nd sem (without evaluations) 0.025192764 0.060433763
## Unemployment rate -0.018958618 0.072869635
## Inflation rate 0.011931982 -0.021895253
## GDP -0.028390888 -0.023945331
## Target -0.100479066 -0.244507198
## Application order Course
## Marital status -0.130370462 0.0420121808
## Application mode -0.287245455 0.0631120760
## Application order 1.000000000 0.0562382877
## Course 0.056238288 1.0000000000
## Daytime/evening attendance\t 0.165494312 -0.0338865911
## Previous qualification -0.187880754 -0.0002299108
## Previous qualification (grade) -0.051715210 -0.0817922401
## Nacionality -0.026705804 -0.0364924860
## Mother's qualification -0.058649069 0.0399756186
## Father's qualification -0.055254427 0.0439308584
## Mother's occupation -0.032459252 0.0215177985
## Father's occupation -0.025308012 0.0191560916
## Admission grade -0.092324392 -0.1238654097
## Displaced 0.345790590 -0.0901363776
## Educational special needs 0.025712303 -0.0195910342
## Debtor -0.066227070 -0.0231029751
## Tuition fees up to date 0.061610100 0.0234887249
## Gender -0.106059375 -0.0948875640
## Scholarship holder 0.072899324 0.0181229469
## Age at enrollment -0.281641405 0.0363233730
## International -0.030575528 -0.0248193104
## Curricular units 1st sem (credited) -0.133504417 -0.0811948762
## Curricular units 1st sem (enrolled) -0.015181806 0.3416727807
## Curricular units 1st sem (evaluations) -0.086004486 0.2644446254
## Curricular units 1st sem (approved) 0.038273821 0.1886017324
## Curricular units 1st sem (grade) 0.060776419 0.3815116017
## Curricular units 1st sem (without evaluations) -0.038958325 0.0315388220
## Curricular units 2nd sem (credited) -0.127598900 -0.0780371144
## Curricular units 2nd sem (enrolled) 0.033124779 0.4152615151
## Curricular units 2nd sem (evaluations) -0.042519456 0.2810163954
## Curricular units 2nd sem (approved) 0.072595010 0.1997389234
## Curricular units 2nd sem (grade) 0.059817104 0.3350156384
## Curricular units 2nd sem (without evaluations) -0.026822038 0.0334543925
## Unemployment rate -0.099767308 0.0103754501
## Inflation rate -0.004227682 0.0278550603
## GDP 0.033031479 -0.0144113208
## Target 0.094354627 0.0381354030
## Daytime/evening attendance\t
## Marital status -0.265822964
## Application mode -0.310854207
## Application order 0.165494312
## Course -0.033886591
## Daytime/evening attendance\t 1.000000000
## Previous qualification -0.087616264
## Previous qualification (grade) 0.063810246
## Nacionality 0.030334072
## Mother's qualification -0.188876221
## Father's qualification -0.135725453
## Mother's occupation -0.034175134
## Father's occupation -0.030081802
## Admission grade 0.018610287
## Displaced 0.243652709
## Educational special needs 0.029207309
## Debtor 0.003899878
## Tuition fees up to date 0.052186286
## Gender -0.030506555
## Scholarship holder 0.110239582
## Age at enrollment -0.453741010
## International 0.032493997
## Curricular units 1st sem (credited) -0.124037541
## Curricular units 1st sem (enrolled) -0.041503009
## Curricular units 1st sem (evaluations) -0.048431811
## Curricular units 1st sem (approved) 0.028265156
## Curricular units 1st sem (grade) 0.073269528
## Curricular units 1st sem (without evaluations) 0.039307133
## Curricular units 2nd sem (credited) -0.105493795
## Curricular units 2nd sem (enrolled) 0.006914694
## Curricular units 2nd sem (evaluations) 0.009976676
## Curricular units 2nd sem (approved) 0.054210519
## Curricular units 2nd sem (grade) 0.058370913
## Curricular units 2nd sem (without evaluations) -0.010504098
## Unemployment rate 0.067192423
## Inflation rate -0.017326292
## GDP 0.005007459
## Target 0.084495936
## Previous qualification
## Marital status 0.0709844372
## Application mode 0.4166655255
## Application order -0.1878807536
## Course -0.0002299108
## Daytime/evening attendance\t -0.0876162638
## Previous qualification 1.0000000000
## Previous qualification (grade) 0.0891936786
## Nacionality -0.0252106597
## Mother's qualification -0.0213992200
## Father's qualification 0.0038648221
## Mother's occupation 0.0098097088
## Father's occupation 0.0155767961
## Admission grade 0.1649622207
## Displaced -0.1268110690
## Educational special needs -0.0024457761
## Debtor 0.1007710318
## Tuition fees up to date -0.0670204293
## Gender 0.0946672717
## Scholarship holder -0.0717480241
## Age at enrollment 0.1690457031
## International -0.0239951281
## Curricular units 1st sem (credited) 0.1686440346
## Curricular units 1st sem (enrolled) 0.0788294946
## Curricular units 1st sem (evaluations) 0.1235732721
## Curricular units 1st sem (approved) 0.0181253947
## Curricular units 1st sem (grade) -0.0109377380
## Curricular units 1st sem (without evaluations) 0.0201549400
## Curricular units 2nd sem (credited) 0.1473886480
## Curricular units 2nd sem (enrolled) 0.0543749402
## Curricular units 2nd sem (evaluations) 0.0941753837
## Curricular units 2nd sem (approved) -0.0108541713
## Curricular units 2nd sem (grade) -0.0089326576
## Curricular units 2nd sem (without evaluations) 0.0222574734
## Unemployment rate 0.1024512489
## Inflation rate -0.0707456702
## GDP 0.0721206630
## Target -0.0623229026
## Previous qualification (grade)
## Marital status -0.038868508
## Application mode -0.071189971
## Application order -0.051715210
## Course -0.081792240
## Daytime/evening attendance\t 0.063810246
## Previous qualification 0.089193679
## Previous qualification (grade) 1.000000000
## Nacionality 0.053888429
## Mother's qualification -0.073035406
## Father's qualification -0.047146817
## Mother's occupation -0.017383335
## Father's occupation -0.022168912
## Admission grade 0.577240558
## Displaced -0.010237683
## Educational special needs 0.009245684
## Debtor -0.062200747
## Tuition fees up to date 0.079245884
## Gender -0.057654392
## Scholarship holder 0.069053847
## Age at enrollment -0.133534725
## International 0.055494489
## Curricular units 1st sem (credited) -0.017717487
## Curricular units 1st sem (enrolled) -0.033502571
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## Curricular units 2nd sem (approved) 0.055231897
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## Unemployment rate 0.043345286
## Inflation rate 0.019246805
## GDP -0.054348729
## Target 0.109463653
## Nacionality
## Marital status -0.0088990643
## Application mode -0.0117108635
## Application order -0.0267058036
## Course -0.0364924860
## Daytime/evening attendance\t 0.0303340721
## Previous qualification -0.0252106597
## Previous qualification (grade) 0.0538884286
## Nacionality 1.0000000000
## Mother's qualification -0.0381678159
## Father's qualification -0.0730332542
## Mother's occupation 0.0103311447
## Father's occupation 0.0082969342
## Admission grade 0.0134995612
## Displaced -0.0035212282
## Educational special needs -0.0032157354
## Debtor 0.0464569829
## Tuition fees up to date -0.0359847775
## Gender -0.0243806428
## Scholarship holder -0.0020016526
## Age at enrollment -0.0049586990
## International 0.7973873768
## Curricular units 1st sem (credited) 0.0001779127
## Curricular units 1st sem (enrolled) -0.0206323235
## Curricular units 1st sem (evaluations) -0.0186714216
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## Curricular units 2nd sem (without evaluations) -0.0143881566
## Unemployment rate 0.0031099603
## Inflation rate -0.0054395975
## GDP 0.0170799129
## Target -0.0155163084
## Mother's qualification
## Marital status 0.18511688
## Application mode 0.12269710
## Application order -0.05864907
## Course 0.03997562
## Daytime/evening attendance\t -0.18887622
## Previous qualification -0.02139922
## Previous qualification (grade) -0.07303541
## Nacionality -0.03816782
## Mother's qualification 1.00000000
## Father's qualification 0.54389028
## Mother's occupation 0.09365422
## Father's occupation 0.06747057
## Admission grade -0.06885529
## Displaced -0.07711462
## Educational special needs -0.01193007
## Debtor 0.01122862
## Tuition fees up to date -0.03118454
## Gender -0.04237701
## Scholarship holder 0.02686919
## Age at enrollment 0.29184418
## International -0.02066896
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## Curricular units 1st sem (enrolled) 0.05175281
## Curricular units 1st sem (evaluations) 0.05070191
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## Curricular units 1st sem (without evaluations) 0.01511193
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## Curricular units 2nd sem (evaluations) 0.03350960
## Curricular units 2nd sem (approved) -0.02640645
## Curricular units 2nd sem (grade) -0.03443447
## Curricular units 2nd sem (without evaluations) 0.02979860
## Unemployment rate -0.12217076
## Inflation rate 0.05798709
## GDP -0.07634191
## Target -0.05398879
## Father's qualification
## Marital status 0.124995407
## Application mode 0.098215810
## Application order -0.055254427
## Course 0.043930858
## Daytime/evening attendance\t -0.135725453
## Previous qualification 0.003864822
## Previous qualification (grade) -0.047146817
## Nacionality -0.073033254
## Mother's qualification 0.543890285
## Father's qualification 1.000000000
## Mother's occupation 0.070683714
## Father's occupation 0.069975860
## Admission grade -0.057358216
## Displaced -0.066560932
## Educational special needs 0.004515551
## Debtor -0.006252859
## Tuition fees up to date -0.024533843
## Gender -0.059074937
## Scholarship holder 0.093946759
## Age at enrollment 0.194839691
## International -0.069160356
## Curricular units 1st sem (credited) 0.045511043
## Curricular units 1st sem (enrolled) 0.044325077
## Curricular units 1st sem (evaluations) 0.043275743
## Curricular units 1st sem (approved) 0.008895938
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## Curricular units 2nd sem (approved) 0.001244693
## Curricular units 2nd sem (grade) -0.008767686
## Curricular units 2nd sem (without evaluations) 0.004102638
## Unemployment rate -0.075372419
## Inflation rate 0.062772016
## GDP -0.059914004
## Target -0.005865480
## Mother's occupation
## Marital status 0.0538922189
## Application mode 0.0416500842
## Application order -0.0324592520
## Course 0.0215177985
## Daytime/evening attendance\t -0.0341751340
## Previous qualification 0.0098097088
## Previous qualification (grade) -0.0173833353
## Nacionality 0.0103311447
## Mother's qualification 0.0936542154
## Father's qualification 0.0706837145
## Mother's occupation 1.0000000000
## Father's occupation 0.8865682817
## Admission grade -0.0455051544
## Displaced -0.0730063450
## Educational special needs 0.0094471004
## Debtor 0.0867010216
## Tuition fees up to date -0.0227177492
## Gender -0.0135582432
## Scholarship holder -0.0032395693
## Age at enrollment 0.0608744514
## International 0.0041245103
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## Curricular units 1st sem (enrolled) -0.0083474875
## Curricular units 1st sem (evaluations) -0.0129520444
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## Curricular units 2nd sem (approved) -0.0312088907
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## Curricular units 2nd sem (without evaluations) 0.0285714656
## Unemployment rate -0.1100526543
## Inflation rate 0.0513658779
## GDP 0.0931998553
## Target 0.0007724444
## Father's occupation
## Marital status 0.0504989264
## Application mode 0.0256290775
## Application order -0.0253080119
## Course 0.0191560916
## Daytime/evening attendance\t -0.0300818025
## Previous qualification 0.0155767961
## Previous qualification (grade) -0.0221689116
## Nacionality 0.0082969342
## Mother's qualification 0.0674705683
## Father's qualification 0.0699758601
## Mother's occupation 0.8865682817
## Father's occupation 1.0000000000
## Admission grade -0.0380957109
## Displaced -0.0738732501
## Educational special needs 0.0236425024
## Debtor 0.0868409440
## Tuition fees up to date -0.0085053597
## Gender -0.0251208803
## Scholarship holder 0.0005518803
## Age at enrollment 0.0359223738
## International -0.0010780292
## Curricular units 1st sem (credited) -0.0016615371
## Curricular units 1st sem (enrolled) -0.0200216881
## Curricular units 1st sem (evaluations) -0.0225967935
## Curricular units 1st sem (approved) -0.0261813056
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## Curricular units 2nd sem (approved) -0.0309937036
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## Curricular units 2nd sem (without evaluations) -0.0003946159
## Unemployment rate -0.1208883774
## Inflation rate 0.0585727745
## GDP 0.1020322430
## Target 0.0050655254
## Admission grade Displaced
## Marital status -0.012439707 -0.2405439104
## Application mode -0.038311074 -0.3087298567
## Application order -0.092324392 0.3457905900
## Course -0.123865410 -0.0901363776
## Daytime/evening attendance\t 0.018610287 0.2436527085
## Previous qualification 0.164962221 -0.1268110690
## Previous qualification (grade) 0.577240558 -0.0102376826
## Nacionality 0.013499561 -0.0035212282
## Mother's qualification -0.068855291 -0.0771146208
## Father's qualification -0.057358216 -0.0665609324
## Mother's occupation -0.045505154 -0.0730063450
## Father's occupation -0.038095711 -0.0738732501
## Admission grade 1.000000000 -0.0068789239
## Displaced -0.006878924 1.0000000000
## Educational special needs -0.013359080 -0.0050988263
## Debtor -0.024911472 -0.0937175693
## Tuition fees up to date 0.071801910 0.1054034111
## Gender 0.009604421 -0.1278955255
## Scholarship holder 0.022258760 0.0863365234
## Age at enrollment -0.035725515 -0.3700182967
## International 0.024341215 -0.0007902275
## Curricular units 1st sem (credited) 0.038948283 -0.1033222120
## Curricular units 1st sem (enrolled) -0.030325466 -0.0716307817
## Curricular units 1st sem (evaluations) -0.071484458 -0.0753909147
## Curricular units 1st sem (approved) 0.085109543 0.0573949567
## Curricular units 1st sem (grade) 0.097692780 0.0778085324
## Curricular units 1st sem (without evaluations) 0.009637376 -0.0317566717
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## Curricular units 2nd sem (enrolled) -0.040766432 -0.0464305564
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## Curricular units 2nd sem (approved) 0.089429456 0.0764655838
## Curricular units 2nd sem (grade) 0.095342474 0.0844626264
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## Unemployment rate 0.037428878 -0.1203673215
## Inflation rate -0.023618530 -0.0090256041
## GDP -0.014623531 0.0649234624
## Target 0.128057716 0.1261130353
## Educational special needs
## Marital status -0.0274337319
## Application mode -0.0246113708
## Application order 0.0257123027
## Course -0.0195910342
## Daytime/evening attendance\t 0.0292073095
## Previous qualification -0.0024457761
## Previous qualification (grade) 0.0092456835
## Nacionality -0.0032157354
## Mother's qualification -0.0119300733
## Father's qualification 0.0045155515
## Mother's occupation 0.0094471004
## Father's occupation 0.0236425024
## Admission grade -0.0133590802
## Displaced -0.0050988263
## Educational special needs 1.0000000000
## Debtor 0.0037317267
## Tuition fees up to date 0.0105033655
## Gender -0.0097935882
## Scholarship holder 0.0317501350
## Age at enrollment -0.0348776323
## International 0.0009081975
## Curricular units 1st sem (credited) -0.0236205192
## Curricular units 1st sem (enrolled) -0.0374710048
## Curricular units 1st sem (evaluations) -0.0349979954
## Curricular units 1st sem (approved) -0.0233603045
## Curricular units 1st sem (grade) -0.0123130816
## Curricular units 1st sem (without evaluations) -0.0200420125
## Curricular units 2nd sem (credited) -0.0199283072
## Curricular units 2nd sem (enrolled) -0.0324881230
## Curricular units 2nd sem (evaluations) -0.0223192359
## Curricular units 2nd sem (approved) -0.0181423894
## Curricular units 2nd sem (grade) -0.0148084934
## Curricular units 2nd sem (without evaluations) -0.0130113358
## Unemployment rate 0.0439133207
## Inflation rate 0.0044519463
## GDP 0.0109778222
## Target -0.0072536541
## Debtor
## Marital status 0.039469818
## Application mode 0.121455544
## Application order -0.066227070
## Course -0.023102975
## Daytime/evening attendance\t 0.003899878
## Previous qualification 0.100771032
## Previous qualification (grade) -0.062200747
## Nacionality 0.046456983
## Mother's qualification 0.011228618
## Father's qualification -0.006252859
## Mother's occupation 0.086701022
## Father's occupation 0.086840944
## Admission grade -0.024911472
## Displaced -0.093717569
## Educational special needs 0.003731727
## Debtor 1.000000000
## Tuition fees up to date -0.434905505
## Gender 0.052769750
## Scholarship holder -0.065204206
## Age at enrollment 0.104141791
## International 0.069681684
## Curricular units 1st sem (credited) 0.011378570
## Curricular units 1st sem (enrolled) -0.030502509
## Curricular units 1st sem (evaluations) 0.029885845
## Curricular units 1st sem (approved) -0.130204489
## Curricular units 1st sem (grade) -0.110521704
## Curricular units 1st sem (without evaluations) 0.013739707
## Curricular units 2nd sem (credited) 0.007596731
## Curricular units 2nd sem (enrolled) -0.050772378
## Curricular units 2nd sem (evaluations) 0.014412368
## Curricular units 2nd sem (approved) -0.166305417
## Curricular units 2nd sem (grade) -0.146603084
## Curricular units 2nd sem (without evaluations) 0.069970149
## Unemployment rate 0.042791833
## Inflation rate -0.019516137
## GDP 0.040475119
## Target -0.267207199
## Tuition fees up to date
## Marital status -0.096920476
## Application mode -0.154142743
## Application order 0.061610100
## Course 0.023488725
## Daytime/evening attendance\t 0.052186286
## Previous qualification -0.067020429
## Previous qualification (grade) 0.079245884
## Nacionality -0.035984777
## Mother's qualification -0.031184539
## Father's qualification -0.024533843
## Mother's occupation -0.022717749
## Father's occupation -0.008505360
## Admission grade 0.071801910
## Displaced 0.105403411
## Educational special needs 0.010503366
## Debtor -0.434905505
## Tuition fees up to date 1.000000000
## Gender -0.122230829
## Scholarship holder 0.169590432
## Age at enrollment -0.196370195
## International -0.055777486
## Curricular units 1st sem (credited) 0.012925552
## Curricular units 1st sem (enrolled) 0.074593360
## Curricular units 1st sem (evaluations) 0.017089721
## Curricular units 1st sem (approved) 0.277787215
## Curricular units 1st sem (grade) 0.275555173
## Curricular units 1st sem (without evaluations) -0.069509209
## Curricular units 2nd sem (credited) 0.020305999
## Curricular units 2nd sem (enrolled) 0.103347329
## Curricular units 2nd sem (evaluations) 0.055691377
## Curricular units 2nd sem (approved) 0.329016595
## Curricular units 2nd sem (grade) 0.318721332
## Curricular units 2nd sem (without evaluations) -0.095138580
## Unemployment rate 0.009479328
## Inflation rate -0.011067208
## GDP 0.027771339
## Target 0.442137576
## Gender Scholarship holder
## Marital status -0.001123579 -0.0696840641
## Application mode 0.186338223 -0.1748354799
## Application order -0.106059375 0.0728993242
## Course -0.094887564 0.0181229469
## Daytime/evening attendance\t -0.030506555 0.1102395821
## Previous qualification 0.094667272 -0.0717480241
## Previous qualification (grade) -0.057654392 0.0690538471
## Nacionality -0.024380643 -0.0020016526
## Mother's qualification -0.042377014 0.0268691851
## Father's qualification -0.059074937 0.0939467593
## Mother's occupation -0.013558243 -0.0032395693
## Father's occupation -0.025120880 0.0005518803
## Admission grade 0.009604421 0.0222587602
## Displaced -0.127895526 0.0863365234
## Educational special needs -0.009793588 0.0317501350
## Debtor 0.052769750 -0.0652042058
## Tuition fees up to date -0.122230829 0.1695904323
## Gender 1.000000000 -0.1879936026
## Scholarship holder -0.187993603 1.0000000000
## Age at enrollment 0.179886992 -0.2125880721
## International -0.032754790 -0.0202977224
## Curricular units 1st sem (credited) 0.021284750 -0.0922431297
## Curricular units 1st sem (enrolled) -0.095088297 -0.0087229645
## Curricular units 1st sem (evaluations) -0.017692822 -0.0486560556
## Curricular units 1st sem (approved) -0.201067641 0.1685236319
## Curricular units 1st sem (grade) -0.207081647 0.1961803331
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## Curricular units 2nd sem (enrolled) -0.126659262 0.0249821954
## Curricular units 2nd sem (evaluations) -0.048000438 0.0059029352
## Curricular units 2nd sem (approved) -0.234662506 0.2149965076
## Curricular units 2nd sem (grade) -0.219696016 0.2123418406
## Curricular units 2nd sem (without evaluations) 0.057754996 -0.0605970409
## Unemployment rate 0.030019885 0.0663505308
## Inflation rate -0.004466468 -0.0446216070
## GDP -0.021930626 0.0378416090
## Target -0.251954812 0.3130176626
## Age at enrollment International
## Marital status 0.522359459 -0.0261529096
## Application mode 0.531601471 -0.0046203475
## Application order -0.281641405 -0.0305755278
## Course 0.036323373 -0.0248193104
## Daytime/evening attendance\t -0.453741010 0.0324939967
## Previous qualification 0.169045703 -0.0239951281
## Previous qualification (grade) -0.133534725 0.0554944894
## Nacionality -0.004958699 0.7973873768
## Mother's qualification 0.291844176 -0.0206689605
## Father's qualification 0.194839691 -0.0691603561
## Mother's occupation 0.060874451 0.0041245103
## Father's occupation 0.035922374 -0.0010780292
## Admission grade -0.035725515 0.0243412152
## Displaced -0.370018297 -0.0007902275
## Educational special needs -0.034877632 0.0009081975
## Debtor 0.104141791 0.0696816842
## Tuition fees up to date -0.196370195 -0.0557774864
## Gender 0.179886992 -0.0327547902
## Scholarship holder -0.212588072 -0.0202977224
## Age at enrollment 1.000000000 -0.0073268510
## International -0.007326851 1.0000000000
## Curricular units 1st sem (credited) 0.219844849 0.0110664422
## Curricular units 1st sem (enrolled) 0.131782619 -0.0035389958
## Curricular units 1st sem (evaluations) 0.144850763 0.0067143797
## Curricular units 1st sem (approved) -0.082984362 0.0055584135
## Curricular units 1st sem (grade) -0.180722842 0.0020563021
## Curricular units 1st sem (without evaluations) 0.078435416 0.0104367704
## Curricular units 2nd sem (credited) 0.196484855 0.0062369324
## Curricular units 2nd sem (enrolled) 0.071177163 -0.0196064863
## Curricular units 2nd sem (evaluations) 0.059554292 -0.0135386575
## Curricular units 2nd sem (approved) -0.147667741 -0.0106479784
## Curricular units 2nd sem (grade) -0.194144614 -0.0030661788
## Curricular units 2nd sem (without evaluations) 0.080135112 -0.0126596779
## Unemployment rate 0.027128841 -0.0080886395
## Inflation rate 0.030084827 -0.0059092366
## GDP -0.069184294 0.0239967415
## Target -0.267229383 0.0061812622
## Curricular units 1st sem (credited)
## Marital status 0.0666658056
## Application mode 0.2488825016
## Application order -0.1335044173
## Course -0.0811948762
## Daytime/evening attendance\t -0.1240375415
## Previous qualification 0.1686440346
## Previous qualification (grade) -0.0177174867
## Nacionality 0.0001779127
## Mother's qualification 0.0481236633
## Father's qualification 0.0455110435
## Mother's occupation 0.0124307756
## Father's occupation -0.0016615371
## Admission grade 0.0389482827
## Displaced -0.1033222120
## Educational special needs -0.0236205192
## Debtor 0.0113785705
## Tuition fees up to date 0.0129255522
## Gender 0.0212847505
## Scholarship holder -0.0922431297
## Age at enrollment 0.2198448490
## International 0.0110664422
## Curricular units 1st sem (credited) 1.0000000000
## Curricular units 1st sem (enrolled) 0.7828630989
## Curricular units 1st sem (evaluations) 0.5691778726
## Curricular units 1st sem (approved) 0.6360712142
## Curricular units 1st sem (grade) 0.1288935113
## Curricular units 1st sem (without evaluations) 0.1438114138
## Curricular units 2nd sem (credited) 0.9470934916
## Curricular units 2nd sem (enrolled) 0.6507074484
## Curricular units 2nd sem (evaluations) 0.4481363420
## Curricular units 2nd sem (approved) 0.4957623482
## Curricular units 2nd sem (grade) 0.1423434937
## Curricular units 2nd sem (without evaluations) 0.0690010912
## Unemployment rate 0.0133131348
## Inflation rate 0.0300380029
## GDP -0.0441689610
## Target 0.0469000165
## Curricular units 1st sem (enrolled)
## Marital status 0.058093648
## Application mode 0.168856601
## Application order -0.015181806
## Course 0.341672781
## Daytime/evening attendance\t -0.041503009
## Previous qualification 0.078829495
## Previous qualification (grade) -0.033502571
## Nacionality -0.020632324
## Mother's qualification 0.051752809
## Father's qualification 0.044325077
## Mother's occupation -0.008347488
## Father's occupation -0.020021688
## Admission grade -0.030325466
## Displaced -0.071630782
## Educational special needs -0.037471005
## Debtor -0.030502509
## Tuition fees up to date 0.074593360
## Gender -0.095088297
## Scholarship holder -0.008722965
## Age at enrollment 0.131782619
## International -0.003538996
## Curricular units 1st sem (credited) 0.782863099
## Curricular units 1st sem (enrolled) 1.000000000
## Curricular units 1st sem (evaluations) 0.697722805
## Curricular units 1st sem (approved) 0.773579121
## Curricular units 1st sem (grade) 0.376441833
## Curricular units 1st sem (without evaluations) 0.146640999
## Curricular units 2nd sem (credited) 0.763276122
## Curricular units 2nd sem (enrolled) 0.941286497
## Curricular units 2nd sem (evaluations) 0.618506171
## Curricular units 2nd sem (approved) 0.674879775
## Curricular units 2nd sem (grade) 0.366015170
## Curricular units 2nd sem (without evaluations) 0.075677055
## Unemployment rate 0.039787624
## Inflation rate 0.051166973
## GDP -0.047367353
## Target 0.161073516
## Curricular units 1st sem (evaluations)
## Marital status 0.059191112
## Application mode 0.220351054
## Application order -0.086004486
## Course 0.264444625
## Daytime/evening attendance\t -0.048431811
## Previous qualification 0.123573272
## Previous qualification (grade) -0.072595009
## Nacionality -0.018671422
## Mother's qualification 0.050701915
## Father's qualification 0.043275743
## Mother's occupation -0.012952044
## Father's occupation -0.022596793
## Admission grade -0.071484458
## Displaced -0.075390915
## Educational special needs -0.034997995
## Debtor 0.029885845
## Tuition fees up to date 0.017089721
## Gender -0.017692822
## Scholarship holder -0.048656056
## Age at enrollment 0.144850763
## International 0.006714380
## Curricular units 1st sem (credited) 0.569177873
## Curricular units 1st sem (enrolled) 0.697722805
## Curricular units 1st sem (evaluations) 1.000000000
## Curricular units 1st sem (approved) 0.559968743
## Curricular units 1st sem (grade) 0.425038957
## Curricular units 1st sem (without evaluations) 0.267383338
## Curricular units 2nd sem (credited) 0.546979877
## Curricular units 2nd sem (enrolled) 0.625967030
## Curricular units 2nd sem (evaluations) 0.790615831
## Curricular units 2nd sem (approved) 0.466743792
## Curricular units 2nd sem (grade) 0.353549744
## Curricular units 2nd sem (without evaluations) 0.158399196
## Unemployment rate 0.067011285
## Inflation rate 0.008853894
## GDP -0.111697754
## Target 0.059786259
## Curricular units 1st sem (approved)
## Marital status -0.0376911081
## Application mode -0.0372499732
## Application order 0.0382738206
## Course 0.1886017324
## Daytime/evening attendance\t 0.0282651562
## Previous qualification 0.0181253947
## Previous qualification (grade) 0.0541199020
## Nacionality -0.0056305657
## Mother's qualification -0.0180278568
## Father's qualification 0.0088959377
## Mother's occupation -0.0260075698
## Father's occupation -0.0261813056
## Admission grade 0.0851095425
## Displaced 0.0573949567
## Educational special needs -0.0233603045
## Debtor -0.1302044893
## Tuition fees up to date 0.2777872151
## Gender -0.2010676407
## Scholarship holder 0.1685236319
## Age at enrollment -0.0829843625
## International 0.0055584135
## Curricular units 1st sem (credited) 0.6360712142
## Curricular units 1st sem (enrolled) 0.7735791213
## Curricular units 1st sem (evaluations) 0.5599687430
## Curricular units 1st sem (approved) 1.0000000000
## Curricular units 1st sem (grade) 0.7101565019
## Curricular units 1st sem (without evaluations) 0.0134838955
## Curricular units 2nd sem (credited) 0.6158337742
## Curricular units 2nd sem (enrolled) 0.7373747998
## Curricular units 2nd sem (evaluations) 0.5790888556
## Curricular units 2nd sem (approved) 0.9163339785
## Curricular units 2nd sem (grade) 0.7093678200
## Curricular units 2nd sem (without evaluations) -0.0389737422
## Unemployment rate 0.0422513672
## Inflation rate -0.0038579765
## GDP -0.0001203888
## Target 0.5548808565
## Curricular units 1st sem (grade)
## Marital status -0.069442294
## Application mode -0.133919376
## Application order 0.060776419
## Course 0.381511602
## Daytime/evening attendance\t 0.073269528
## Previous qualification -0.010937738
## Previous qualification (grade) 0.077190851
## Nacionality -0.003854159
## Mother's qualification -0.044137419
## Father's qualification -0.006825700
## Mother's occupation -0.030964874
## Father's occupation -0.020282980
## Admission grade 0.097692780
## Displaced 0.077808532
## Educational special needs -0.012313082
## Debtor -0.110521704
## Tuition fees up to date 0.275555173
## Gender -0.207081647
## Scholarship holder 0.196180333
## Age at enrollment -0.180722842
## International 0.002056302
## Curricular units 1st sem (credited) 0.128893511
## Curricular units 1st sem (enrolled) 0.376441833
## Curricular units 1st sem (evaluations) 0.425038957
## Curricular units 1st sem (approved) 0.710156502
## Curricular units 1st sem (grade) 1.000000000
## Curricular units 1st sem (without evaluations) -0.064171407
## Curricular units 2nd sem (credited) 0.120199212
## Curricular units 2nd sem (enrolled) 0.407084299
## Curricular units 2nd sem (evaluations) 0.503364953
## Curricular units 2nd sem (approved) 0.691906958
## Curricular units 2nd sem (grade) 0.845863703
## Curricular units 2nd sem (without evaluations) -0.055861084
## Unemployment rate 0.010272286
## Inflation rate -0.029067740
## GDP 0.054168423
## Target 0.519927094
## Curricular units 1st sem (without evaluations)
## Marital status 0.041534688
## Application mode 0.054923049
## Application order -0.038958325
## Course 0.031538822
## Daytime/evening attendance\t 0.039307133
## Previous qualification 0.020154940
## Previous qualification (grade) -0.011856961
## Nacionality -0.002041738
## Mother's qualification 0.015111933
## Father's qualification -0.006681164
## Mother's occupation 0.024175385
## Father's occupation 0.003252840
## Admission grade 0.009637376
## Displaced -0.031756672
## Educational special needs -0.020042013
## Debtor 0.013739707
## Tuition fees up to date -0.069509209
## Gender 0.006808012
## Scholarship holder -0.069637354
## Age at enrollment 0.078435416
## International 0.010436770
## Curricular units 1st sem (credited) 0.143811414
## Curricular units 1st sem (enrolled) 0.146640999
## Curricular units 1st sem (evaluations) 0.267383338
## Curricular units 1st sem (approved) 0.013483896
## Curricular units 1st sem (grade) -0.064171407
## Curricular units 1st sem (without evaluations) 1.000000000
## Curricular units 2nd sem (credited) 0.144377902
## Curricular units 2nd sem (enrolled) 0.123588280
## Curricular units 2nd sem (evaluations) 0.170003632
## Curricular units 2nd sem (approved) 0.001457851
## Curricular units 2nd sem (grade) -0.068724636
## Curricular units 2nd sem (without evaluations) 0.601572509
## Unemployment rate -0.035046139
## Inflation rate -0.037235258
## GDP -0.130765710
## Target -0.074642260
## Curricular units 2nd sem (credited)
## Marital status 0.067507697
## Application mode 0.244575086
## Application order -0.127598900
## Course -0.078037114
## Daytime/evening attendance\t -0.105493795
## Previous qualification 0.147388648
## Previous qualification (grade) -0.026106966
## Nacionality -0.004657413
## Mother's qualification 0.041687446
## Father's qualification 0.047033556
## Mother's occupation 0.005301619
## Father's occupation -0.009842470
## Admission grade 0.038345287
## Displaced -0.096240305
## Educational special needs -0.019928307
## Debtor 0.007596731
## Tuition fees up to date 0.020305999
## Gender 0.023026866
## Scholarship holder -0.079377788
## Age at enrollment 0.196484855
## International 0.006236932
## Curricular units 1st sem (credited) 0.947093492
## Curricular units 1st sem (enrolled) 0.763276122
## Curricular units 1st sem (evaluations) 0.546979877
## Curricular units 1st sem (approved) 0.615833774
## Curricular units 1st sem (grade) 0.120199212
## Curricular units 1st sem (without evaluations) 0.144377902
## Curricular units 2nd sem (credited) 1.000000000
## Curricular units 2nd sem (enrolled) 0.683086145
## Curricular units 2nd sem (evaluations) 0.453716294
## Curricular units 2nd sem (approved) 0.522684405
## Curricular units 2nd sem (grade) 0.140180575
## Curricular units 2nd sem (without evaluations) 0.084506039
## Unemployment rate 0.013465989
## Inflation rate 0.019395150
## GDP -0.038570078
## Target 0.052401971
## Curricular units 2nd sem (enrolled)
## Marital status 0.041255869
## Application mode 0.130559160
## Application order 0.033124779
## Course 0.415261515
## Daytime/evening attendance\t 0.006914694
## Previous qualification 0.054374940
## Previous qualification (grade) -0.036162317
## Nacionality -0.029475897
## Mother's qualification 0.033218883
## Father's qualification 0.029756408
## Mother's occupation -0.020566614
## Father's occupation -0.032043455
## Admission grade -0.040766432
## Displaced -0.046430556
## Educational special needs -0.032488123
## Debtor -0.050772378
## Tuition fees up to date 0.103347329
## Gender -0.126659262
## Scholarship holder 0.024982195
## Age at enrollment 0.071177163
## International -0.019606486
## Curricular units 1st sem (credited) 0.650707448
## Curricular units 1st sem (enrolled) 0.941286497
## Curricular units 1st sem (evaluations) 0.625967030
## Curricular units 1st sem (approved) 0.737374800
## Curricular units 1st sem (grade) 0.407084299
## Curricular units 1st sem (without evaluations) 0.123588280
## Curricular units 2nd sem (credited) 0.683086145
## Curricular units 2nd sem (enrolled) 1.000000000
## Curricular units 2nd sem (evaluations) 0.625080234
## Curricular units 2nd sem (approved) 0.704444531
## Curricular units 2nd sem (grade) 0.400772723
## Curricular units 2nd sem (without evaluations) 0.070363321
## Unemployment rate 0.066219125
## Inflation rate 0.028390417
## GDP -0.026076338
## Target 0.182896541
## Curricular units 2nd sem (evaluations)
## Marital status 0.030786334
## Application mode 0.163626213
## Application order -0.042519456
## Course 0.281016395
## Daytime/evening attendance\t 0.009976676
## Previous qualification 0.094175384
## Previous qualification (grade) -0.061730068
## Nacionality -0.032890285
## Mother's qualification 0.033509600
## Father's qualification 0.014678362
## Mother's occupation -0.026873395
## Father's occupation -0.033925637
## Admission grade -0.060954204
## Displaced -0.035873577
## Educational special needs -0.022319236
## Debtor 0.014412368
## Tuition fees up to date 0.055691377
## Gender -0.048000438
## Scholarship holder 0.005902935
## Age at enrollment 0.059554292
## International -0.013538658
## Curricular units 1st sem (credited) 0.448136342
## Curricular units 1st sem (enrolled) 0.618506171
## Curricular units 1st sem (evaluations) 0.790615831
## Curricular units 1st sem (approved) 0.579088856
## Curricular units 1st sem (grade) 0.503364953
## Curricular units 1st sem (without evaluations) 0.170003632
## Curricular units 2nd sem (credited) 0.453716294
## Curricular units 2nd sem (enrolled) 0.625080234
## Curricular units 2nd sem (evaluations) 1.000000000
## Curricular units 2nd sem (approved) 0.508967845
## Curricular units 2nd sem (grade) 0.463193961
## Curricular units 2nd sem (without evaluations) 0.166442584
## Unemployment rate 0.055229026
## Inflation rate -0.001421750
## GDP -0.021845762
## Target 0.119238767
## Curricular units 2nd sem (approved)
## Marital status -0.058400138
## Application mode -0.085269834
## Application order 0.072595010
## Course 0.199738923
## Daytime/evening attendance\t 0.054210519
## Previous qualification -0.010854171
## Previous qualification (grade) 0.055231897
## Nacionality -0.024522999
## Mother's qualification -0.026406448
## Father's qualification 0.001244693
## Mother's occupation -0.031208891
## Father's occupation -0.030993704
## Admission grade 0.089429456
## Displaced 0.076465584
## Educational special needs -0.018142389
## Debtor -0.166305417
## Tuition fees up to date 0.329016595
## Gender -0.234662506
## Scholarship holder 0.214996508
## Age at enrollment -0.147667741
## International -0.010647978
## Curricular units 1st sem (credited) 0.495762348
## Curricular units 1st sem (enrolled) 0.674879775
## Curricular units 1st sem (evaluations) 0.466743792
## Curricular units 1st sem (approved) 0.916333978
## Curricular units 1st sem (grade) 0.691906958
## Curricular units 1st sem (without evaluations) 0.001457851
## Curricular units 2nd sem (credited) 0.522684405
## Curricular units 2nd sem (enrolled) 0.704444531
## Curricular units 2nd sem (evaluations) 0.508967845
## Curricular units 2nd sem (approved) 1.000000000
## Curricular units 2nd sem (grade) 0.786837628
## Curricular units 2nd sem (without evaluations) -0.052389244
## Unemployment rate 0.040061375
## Inflation rate -0.026750824
## GDP 0.014514087
## Target 0.653995246
## Curricular units 2nd sem (grade)
## Marital status -0.079536308
## Application mode -0.137288308
## Application order 0.059817104
## Course 0.335015638
## Daytime/evening attendance\t 0.058370913
## Previous qualification -0.008932658
## Previous qualification (grade) 0.068239628
## Nacionality -0.014859444
## Mother's qualification -0.034434474
## Father's qualification -0.008767686
## Mother's occupation -0.030782454
## Father's occupation -0.025478739
## Admission grade 0.095342474
## Displaced 0.084462626
## Educational special needs -0.014808493
## Debtor -0.146603084
## Tuition fees up to date 0.318721332
## Gender -0.219696016
## Scholarship holder 0.212341841
## Age at enrollment -0.194144614
## International -0.003066179
## Curricular units 1st sem (credited) 0.142343494
## Curricular units 1st sem (enrolled) 0.366015170
## Curricular units 1st sem (evaluations) 0.353549744
## Curricular units 1st sem (approved) 0.709367820
## Curricular units 1st sem (grade) 0.845863703
## Curricular units 1st sem (without evaluations) -0.068724636
## Curricular units 2nd sem (credited) 0.140180575
## Curricular units 2nd sem (enrolled) 0.400772723
## Curricular units 2nd sem (evaluations) 0.463193961
## Curricular units 2nd sem (approved) 0.786837628
## Curricular units 2nd sem (grade) 1.000000000
## Curricular units 2nd sem (without evaluations) -0.079508070
## Unemployment rate 0.000261185
## Inflation rate -0.042638776
## GDP 0.066077451
## Target 0.605350126
## Curricular units 2nd sem (without evaluations)
## Marital status 0.0251927638
## Application mode 0.0604337629
## Application order -0.0268220378
## Course 0.0334543925
## Daytime/evening attendance\t -0.0105040981
## Previous qualification 0.0222574734
## Previous qualification (grade) -0.0236537200
## Nacionality -0.0143881566
## Mother's qualification 0.0297985991
## Father's qualification 0.0041026381
## Mother's occupation 0.0285714656
## Father's occupation -0.0003946159
## Admission grade -0.0128231980
## Displaced -0.0416964564
## Educational special needs -0.0130113358
## Debtor 0.0699701491
## Tuition fees up to date -0.0951385799
## Gender 0.0577549960
## Scholarship holder -0.0605970409
## Age at enrollment 0.0801351117
## International -0.0126596779
## Curricular units 1st sem (credited) 0.0690010912
## Curricular units 1st sem (enrolled) 0.0756770547
## Curricular units 1st sem (evaluations) 0.1583991960
## Curricular units 1st sem (approved) -0.0389737422
## Curricular units 1st sem (grade) -0.0558610836
## Curricular units 1st sem (without evaluations) 0.6015725092
## Curricular units 2nd sem (credited) 0.0845060387
## Curricular units 2nd sem (enrolled) 0.0703633212
## Curricular units 2nd sem (evaluations) 0.1664425843
## Curricular units 2nd sem (approved) -0.0523892438
## Curricular units 2nd sem (grade) -0.0795080705
## Curricular units 2nd sem (without evaluations) 1.0000000000
## Unemployment rate 0.0040666870
## Inflation rate -0.0305520017
## GDP -0.0798569714
## Target -0.1026868286
## Unemployment rate Inflation rate
## Marital status -0.018958618 0.011931982
## Application mode 0.072869635 -0.021895253
## Application order -0.099767308 -0.004227682
## Course 0.010375450 0.027855060
## Daytime/evening attendance\t 0.067192423 -0.017326292
## Previous qualification 0.102451249 -0.070745670
## Previous qualification (grade) 0.043345286 0.019246805
## Nacionality 0.003109960 -0.005439597
## Mother's qualification -0.122170762 0.057987092
## Father's qualification -0.075372419 0.062772016
## Mother's occupation -0.110052654 0.051365878
## Father's occupation -0.120888377 0.058572774
## Admission grade 0.037428878 -0.023618530
## Displaced -0.120367321 -0.009025604
## Educational special needs 0.043913321 0.004451946
## Debtor 0.042791833 -0.019516137
## Tuition fees up to date 0.009479328 -0.011067208
## Gender 0.030019885 -0.004466468
## Scholarship holder 0.066350531 -0.044621607
## Age at enrollment 0.027128841 0.030084827
## International -0.008088640 -0.005909237
## Curricular units 1st sem (credited) 0.013313135 0.030038003
## Curricular units 1st sem (enrolled) 0.039787624 0.051166973
## Curricular units 1st sem (evaluations) 0.067011285 0.008853894
## Curricular units 1st sem (approved) 0.042251367 -0.003857977
## Curricular units 1st sem (grade) 0.010272286 -0.029067740
## Curricular units 1st sem (without evaluations) -0.035046139 -0.037235258
## Curricular units 2nd sem (credited) 0.013465989 0.019395150
## Curricular units 2nd sem (enrolled) 0.066219125 0.028390417
## Curricular units 2nd sem (evaluations) 0.055229026 -0.001421750
## Curricular units 2nd sem (approved) 0.040061375 -0.026750824
## Curricular units 2nd sem (grade) 0.000261185 -0.042638776
## Curricular units 2nd sem (without evaluations) 0.004066687 -0.030552002
## Unemployment rate 1.000000000 -0.029666307
## Inflation rate -0.029666307 1.000000000
## GDP -0.341742297 -0.125788640
## Target 0.004198105 -0.030325866
## GDP Target
## Marital status -0.0283908884 -0.1004790663
## Application mode -0.0239453313 -0.2445071981
## Application order 0.0330314793 0.0943546272
## Course -0.0144113208 0.0381354030
## Daytime/evening attendance\t 0.0050074595 0.0844959357
## Previous qualification 0.0721206630 -0.0623229026
## Previous qualification (grade) -0.0543487286 0.1094636531
## Nacionality 0.0170799129 -0.0155163084
## Mother's qualification -0.0763419141 -0.0539887950
## Father's qualification -0.0599140035 -0.0058654799
## Mother's occupation 0.0931998553 0.0007724444
## Father's occupation 0.1020322430 0.0050655254
## Admission grade -0.0146235307 0.1280577162
## Displaced 0.0649234624 0.1261130353
## Educational special needs 0.0109778222 -0.0072536541
## Debtor 0.0404751192 -0.2672071989
## Tuition fees up to date 0.0277713391 0.4421375758
## Gender -0.0219306264 -0.2519548120
## Scholarship holder 0.0378416090 0.3130176626
## Age at enrollment -0.0691842941 -0.2672293832
## International 0.0239967415 0.0061812622
## Curricular units 1st sem (credited) -0.0441689610 0.0469000165
## Curricular units 1st sem (enrolled) -0.0473673531 0.1610735164
## Curricular units 1st sem (evaluations) -0.1116977536 0.0597862595
## Curricular units 1st sem (approved) -0.0001203888 0.5548808565
## Curricular units 1st sem (grade) 0.0541684231 0.5199270935
## Curricular units 1st sem (without evaluations) -0.1307657097 -0.0746422602
## Curricular units 2nd sem (credited) -0.0385700780 0.0524019712
## Curricular units 2nd sem (enrolled) -0.0260763377 0.1828965409
## Curricular units 2nd sem (evaluations) -0.0218457622 0.1192387668
## Curricular units 2nd sem (approved) 0.0145140870 0.6539952461
## Curricular units 2nd sem (grade) 0.0660774509 0.6053501259
## Curricular units 2nd sem (without evaluations) -0.0798569714 -0.1026868286
## Unemployment rate -0.3417422966 0.0041981052
## Inflation rate -0.1257886399 -0.0303258660
## GDP 1.0000000000 0.0502601468
## Target 0.0502601468 1.0000000000
Heatmap -1 For Correlation
matrix
## Warning: package 'reshape2' was built under R version 4.3.2
##
## Attaching package: 'reshape2'
## The following object is masked from 'package:tidyr':
##
## smiths
## Loading required package: viridisLite
Feature Selection :
- Feature selection is an essential process in data analysis and
machine learning, focused on choosing the most relevant and informative
subset of features from the original dataset. The primary goal is to
improve the model’s performance, reduce complexity, and enhance
interpretability.
- By eliminating irrelevant, redundant, or noisy features, feature
selection helps prevent overfitting and enables the model to generalize
better to new data. This, in turn, reduces computation time and memory
requirements during model training and evaluation. Various techniques
can be employed for feature selection, including filter methods that
rank features based on statistical measures, wrapper methods that
utilize the model’s predictive performance, and embedded methods that
incorporate feature selection within the model training process.
- Additionally, dimensionality reduction techniques like PCA offer an
alternative approach by projecting the data onto a lower-dimensional
space. Ultimately, selecting the right features is critical to producing
more efficient and accurate models, facilitating data-driven insights
and decision-making with enhanced clarity and efficiency.
library(dplyr)
students_data <- students_data %>%
select(-c(International, Nacionality, `Father's qualification`,
`Curricular units 1st sem (credited)`, `Curricular units 1st sem (enrolled)`,
`Curricular units 1st sem (approved)`, Course, `Educational special needs`,
`Unemployment rate`, `Inflation rate`))
## Marital status Application mode
## Marital status 1.000000000 0.27498489
## Application mode 0.274984888 1.00000000
## Application order -0.130370462 -0.28724546
## Daytime/evening attendance\t -0.265822964 -0.31085421
## Previous qualification 0.070984437 0.41666553
## Previous qualification (grade) -0.038868508 -0.07118997
## Mother's qualification 0.185116875 0.12269710
## Mother's occupation 0.053892219 0.04165008
## Father's occupation 0.050498926 0.02562908
## Admission grade -0.012439707 -0.03831107
## Displaced -0.240543910 -0.30872986
## Debtor 0.039469818 0.12145554
## Tuition fees up to date -0.096920476 -0.15414274
## Gender -0.001123579 0.18633822
## Scholarship holder -0.069684064 -0.17483548
## Age at enrollment 0.522359459 0.53160147
## Curricular units 1st sem (evaluations) 0.059191112 0.22035105
## Curricular units 1st sem (grade) -0.069442294 -0.13391938
## Curricular units 1st sem (without evaluations) 0.041534688 0.05492305
## Curricular units 2nd sem (credited) 0.067507697 0.24457509
## Curricular units 2nd sem (enrolled) 0.041255869 0.13055916
## Curricular units 2nd sem (evaluations) 0.030786334 0.16362621
## Curricular units 2nd sem (approved) -0.058400138 -0.08526983
## Curricular units 2nd sem (grade) -0.079536308 -0.13728831
## Curricular units 2nd sem (without evaluations) 0.025192764 0.06043376
## GDP -0.028390888 -0.02394533
## Target -0.100479066 -0.24450720
## Application order
## Marital status -0.13037046
## Application mode -0.28724546
## Application order 1.00000000
## Daytime/evening attendance\t 0.16549431
## Previous qualification -0.18788075
## Previous qualification (grade) -0.05171521
## Mother's qualification -0.05864907
## Mother's occupation -0.03245925
## Father's occupation -0.02530801
## Admission grade -0.09232439
## Displaced 0.34579059
## Debtor -0.06622707
## Tuition fees up to date 0.06161010
## Gender -0.10605938
## Scholarship holder 0.07289932
## Age at enrollment -0.28164140
## Curricular units 1st sem (evaluations) -0.08600449
## Curricular units 1st sem (grade) 0.06077642
## Curricular units 1st sem (without evaluations) -0.03895833
## Curricular units 2nd sem (credited) -0.12759890
## Curricular units 2nd sem (enrolled) 0.03312478
## Curricular units 2nd sem (evaluations) -0.04251946
## Curricular units 2nd sem (approved) 0.07259501
## Curricular units 2nd sem (grade) 0.05981710
## Curricular units 2nd sem (without evaluations) -0.02682204
## GDP 0.03303148
## Target 0.09435463
## Daytime/evening attendance\t
## Marital status -0.265822964
## Application mode -0.310854207
## Application order 0.165494312
## Daytime/evening attendance\t 1.000000000
## Previous qualification -0.087616264
## Previous qualification (grade) 0.063810246
## Mother's qualification -0.188876221
## Mother's occupation -0.034175134
## Father's occupation -0.030081802
## Admission grade 0.018610287
## Displaced 0.243652709
## Debtor 0.003899878
## Tuition fees up to date 0.052186286
## Gender -0.030506555
## Scholarship holder 0.110239582
## Age at enrollment -0.453741010
## Curricular units 1st sem (evaluations) -0.048431811
## Curricular units 1st sem (grade) 0.073269528
## Curricular units 1st sem (without evaluations) 0.039307133
## Curricular units 2nd sem (credited) -0.105493795
## Curricular units 2nd sem (enrolled) 0.006914694
## Curricular units 2nd sem (evaluations) 0.009976676
## Curricular units 2nd sem (approved) 0.054210519
## Curricular units 2nd sem (grade) 0.058370913
## Curricular units 2nd sem (without evaluations) -0.010504098
## GDP 0.005007459
## Target 0.084495936
## Previous qualification
## Marital status 0.070984437
## Application mode 0.416665526
## Application order -0.187880754
## Daytime/evening attendance\t -0.087616264
## Previous qualification 1.000000000
## Previous qualification (grade) 0.089193679
## Mother's qualification -0.021399220
## Mother's occupation 0.009809709
## Father's occupation 0.015576796
## Admission grade 0.164962221
## Displaced -0.126811069
## Debtor 0.100771032
## Tuition fees up to date -0.067020429
## Gender 0.094667272
## Scholarship holder -0.071748024
## Age at enrollment 0.169045703
## Curricular units 1st sem (evaluations) 0.123573272
## Curricular units 1st sem (grade) -0.010937738
## Curricular units 1st sem (without evaluations) 0.020154940
## Curricular units 2nd sem (credited) 0.147388648
## Curricular units 2nd sem (enrolled) 0.054374940
## Curricular units 2nd sem (evaluations) 0.094175384
## Curricular units 2nd sem (approved) -0.010854171
## Curricular units 2nd sem (grade) -0.008932658
## Curricular units 2nd sem (without evaluations) 0.022257473
## GDP 0.072120663
## Target -0.062322903
## Previous qualification (grade)
## Marital status -0.03886851
## Application mode -0.07118997
## Application order -0.05171521
## Daytime/evening attendance\t 0.06381025
## Previous qualification 0.08919368
## Previous qualification (grade) 1.00000000
## Mother's qualification -0.07303541
## Mother's occupation -0.01738334
## Father's occupation -0.02216891
## Admission grade 0.57724056
## Displaced -0.01023768
## Debtor -0.06220075
## Tuition fees up to date 0.07924588
## Gender -0.05765439
## Scholarship holder 0.06905385
## Age at enrollment -0.13353473
## Curricular units 1st sem (evaluations) -0.07259501
## Curricular units 1st sem (grade) 0.07719085
## Curricular units 1st sem (without evaluations) -0.01185696
## Curricular units 2nd sem (credited) -0.02610697
## Curricular units 2nd sem (enrolled) -0.03616232
## Curricular units 2nd sem (evaluations) -0.06173007
## Curricular units 2nd sem (approved) 0.05523190
## Curricular units 2nd sem (grade) 0.06823963
## Curricular units 2nd sem (without evaluations) -0.02365372
## GDP -0.05434873
## Target 0.10946365
## Mother's qualification
## Marital status 0.18511688
## Application mode 0.12269710
## Application order -0.05864907
## Daytime/evening attendance\t -0.18887622
## Previous qualification -0.02139922
## Previous qualification (grade) -0.07303541
## Mother's qualification 1.00000000
## Mother's occupation 0.09365422
## Father's occupation 0.06747057
## Admission grade -0.06885529
## Displaced -0.07711462
## Debtor 0.01122862
## Tuition fees up to date -0.03118454
## Gender -0.04237701
## Scholarship holder 0.02686919
## Age at enrollment 0.29184418
## Curricular units 1st sem (evaluations) 0.05070191
## Curricular units 1st sem (grade) -0.04413742
## Curricular units 1st sem (without evaluations) 0.01511193
## Curricular units 2nd sem (credited) 0.04168745
## Curricular units 2nd sem (enrolled) 0.03321888
## Curricular units 2nd sem (evaluations) 0.03350960
## Curricular units 2nd sem (approved) -0.02640645
## Curricular units 2nd sem (grade) -0.03443447
## Curricular units 2nd sem (without evaluations) 0.02979860
## GDP -0.07634191
## Target -0.05398879
## Mother's occupation
## Marital status 0.0538922189
## Application mode 0.0416500842
## Application order -0.0324592520
## Daytime/evening attendance\t -0.0341751340
## Previous qualification 0.0098097088
## Previous qualification (grade) -0.0173833353
## Mother's qualification 0.0936542154
## Mother's occupation 1.0000000000
## Father's occupation 0.8865682817
## Admission grade -0.0455051544
## Displaced -0.0730063450
## Debtor 0.0867010216
## Tuition fees up to date -0.0227177492
## Gender -0.0135582432
## Scholarship holder -0.0032395693
## Age at enrollment 0.0608744514
## Curricular units 1st sem (evaluations) -0.0129520444
## Curricular units 1st sem (grade) -0.0309648742
## Curricular units 1st sem (without evaluations) 0.0241753849
## Curricular units 2nd sem (credited) 0.0053016188
## Curricular units 2nd sem (enrolled) -0.0205666136
## Curricular units 2nd sem (evaluations) -0.0268733946
## Curricular units 2nd sem (approved) -0.0312088907
## Curricular units 2nd sem (grade) -0.0307824542
## Curricular units 2nd sem (without evaluations) 0.0285714656
## GDP 0.0931998553
## Target 0.0007724444
## Father's occupation
## Marital status 0.0504989264
## Application mode 0.0256290775
## Application order -0.0253080119
## Daytime/evening attendance\t -0.0300818025
## Previous qualification 0.0155767961
## Previous qualification (grade) -0.0221689116
## Mother's qualification 0.0674705683
## Mother's occupation 0.8865682817
## Father's occupation 1.0000000000
## Admission grade -0.0380957109
## Displaced -0.0738732501
## Debtor 0.0868409440
## Tuition fees up to date -0.0085053597
## Gender -0.0251208803
## Scholarship holder 0.0005518803
## Age at enrollment 0.0359223738
## Curricular units 1st sem (evaluations) -0.0225967935
## Curricular units 1st sem (grade) -0.0202829796
## Curricular units 1st sem (without evaluations) 0.0032528400
## Curricular units 2nd sem (credited) -0.0098424697
## Curricular units 2nd sem (enrolled) -0.0320434549
## Curricular units 2nd sem (evaluations) -0.0339256371
## Curricular units 2nd sem (approved) -0.0309937036
## Curricular units 2nd sem (grade) -0.0254787395
## Curricular units 2nd sem (without evaluations) -0.0003946159
## GDP 0.1020322430
## Target 0.0050655254
## Admission grade Displaced
## Marital status -0.012439707 -0.240543910
## Application mode -0.038311074 -0.308729857
## Application order -0.092324392 0.345790590
## Daytime/evening attendance\t 0.018610287 0.243652709
## Previous qualification 0.164962221 -0.126811069
## Previous qualification (grade) 0.577240558 -0.010237683
## Mother's qualification -0.068855291 -0.077114621
## Mother's occupation -0.045505154 -0.073006345
## Father's occupation -0.038095711 -0.073873250
## Admission grade 1.000000000 -0.006878924
## Displaced -0.006878924 1.000000000
## Debtor -0.024911472 -0.093717569
## Tuition fees up to date 0.071801910 0.105403411
## Gender 0.009604421 -0.127895526
## Scholarship holder 0.022258760 0.086336523
## Age at enrollment -0.035725515 -0.370018297
## Curricular units 1st sem (evaluations) -0.071484458 -0.075390915
## Curricular units 1st sem (grade) 0.097692780 0.077808532
## Curricular units 1st sem (without evaluations) 0.009637376 -0.031756672
## Curricular units 2nd sem (credited) 0.038345287 -0.096240305
## Curricular units 2nd sem (enrolled) -0.040766432 -0.046430556
## Curricular units 2nd sem (evaluations) -0.060954204 -0.035873577
## Curricular units 2nd sem (approved) 0.089429456 0.076465584
## Curricular units 2nd sem (grade) 0.095342474 0.084462626
## Curricular units 2nd sem (without evaluations) -0.012823198 -0.041696456
## GDP -0.014623531 0.064923462
## Target 0.128057716 0.126113035
## Debtor
## Marital status 0.039469818
## Application mode 0.121455544
## Application order -0.066227070
## Daytime/evening attendance\t 0.003899878
## Previous qualification 0.100771032
## Previous qualification (grade) -0.062200747
## Mother's qualification 0.011228618
## Mother's occupation 0.086701022
## Father's occupation 0.086840944
## Admission grade -0.024911472
## Displaced -0.093717569
## Debtor 1.000000000
## Tuition fees up to date -0.434905505
## Gender 0.052769750
## Scholarship holder -0.065204206
## Age at enrollment 0.104141791
## Curricular units 1st sem (evaluations) 0.029885845
## Curricular units 1st sem (grade) -0.110521704
## Curricular units 1st sem (without evaluations) 0.013739707
## Curricular units 2nd sem (credited) 0.007596731
## Curricular units 2nd sem (enrolled) -0.050772378
## Curricular units 2nd sem (evaluations) 0.014412368
## Curricular units 2nd sem (approved) -0.166305417
## Curricular units 2nd sem (grade) -0.146603084
## Curricular units 2nd sem (without evaluations) 0.069970149
## GDP 0.040475119
## Target -0.267207199
## Tuition fees up to date
## Marital status -0.09692048
## Application mode -0.15414274
## Application order 0.06161010
## Daytime/evening attendance\t 0.05218629
## Previous qualification -0.06702043
## Previous qualification (grade) 0.07924588
## Mother's qualification -0.03118454
## Mother's occupation -0.02271775
## Father's occupation -0.00850536
## Admission grade 0.07180191
## Displaced 0.10540341
## Debtor -0.43490550
## Tuition fees up to date 1.00000000
## Gender -0.12223083
## Scholarship holder 0.16959043
## Age at enrollment -0.19637020
## Curricular units 1st sem (evaluations) 0.01708972
## Curricular units 1st sem (grade) 0.27555517
## Curricular units 1st sem (without evaluations) -0.06950921
## Curricular units 2nd sem (credited) 0.02030600
## Curricular units 2nd sem (enrolled) 0.10334733
## Curricular units 2nd sem (evaluations) 0.05569138
## Curricular units 2nd sem (approved) 0.32901659
## Curricular units 2nd sem (grade) 0.31872133
## Curricular units 2nd sem (without evaluations) -0.09513858
## GDP 0.02777134
## Target 0.44213758
## Gender Scholarship holder
## Marital status -0.001123579 -0.0696840641
## Application mode 0.186338223 -0.1748354799
## Application order -0.106059375 0.0728993242
## Daytime/evening attendance\t -0.030506555 0.1102395821
## Previous qualification 0.094667272 -0.0717480241
## Previous qualification (grade) -0.057654392 0.0690538471
## Mother's qualification -0.042377014 0.0268691851
## Mother's occupation -0.013558243 -0.0032395693
## Father's occupation -0.025120880 0.0005518803
## Admission grade 0.009604421 0.0222587602
## Displaced -0.127895526 0.0863365234
## Debtor 0.052769750 -0.0652042058
## Tuition fees up to date -0.122230829 0.1695904323
## Gender 1.000000000 -0.1879936026
## Scholarship holder -0.187993603 1.0000000000
## Age at enrollment 0.179886992 -0.2125880721
## Curricular units 1st sem (evaluations) -0.017692822 -0.0486560556
## Curricular units 1st sem (grade) -0.207081647 0.1961803331
## Curricular units 1st sem (without evaluations) 0.006808012 -0.0696373536
## Curricular units 2nd sem (credited) 0.023026866 -0.0793777875
## Curricular units 2nd sem (enrolled) -0.126659262 0.0249821954
## Curricular units 2nd sem (evaluations) -0.048000438 0.0059029352
## Curricular units 2nd sem (approved) -0.234662506 0.2149965076
## Curricular units 2nd sem (grade) -0.219696016 0.2123418406
## Curricular units 2nd sem (without evaluations) 0.057754996 -0.0605970409
## GDP -0.021930626 0.0378416090
## Target -0.251954812 0.3130176626
## Age at enrollment
## Marital status 0.52235946
## Application mode 0.53160147
## Application order -0.28164140
## Daytime/evening attendance\t -0.45374101
## Previous qualification 0.16904570
## Previous qualification (grade) -0.13353473
## Mother's qualification 0.29184418
## Mother's occupation 0.06087445
## Father's occupation 0.03592237
## Admission grade -0.03572551
## Displaced -0.37001830
## Debtor 0.10414179
## Tuition fees up to date -0.19637020
## Gender 0.17988699
## Scholarship holder -0.21258807
## Age at enrollment 1.00000000
## Curricular units 1st sem (evaluations) 0.14485076
## Curricular units 1st sem (grade) -0.18072284
## Curricular units 1st sem (without evaluations) 0.07843542
## Curricular units 2nd sem (credited) 0.19648486
## Curricular units 2nd sem (enrolled) 0.07117716
## Curricular units 2nd sem (evaluations) 0.05955429
## Curricular units 2nd sem (approved) -0.14766774
## Curricular units 2nd sem (grade) -0.19414461
## Curricular units 2nd sem (without evaluations) 0.08013511
## GDP -0.06918429
## Target -0.26722938
## Curricular units 1st sem (evaluations)
## Marital status 0.05919111
## Application mode 0.22035105
## Application order -0.08600449
## Daytime/evening attendance\t -0.04843181
## Previous qualification 0.12357327
## Previous qualification (grade) -0.07259501
## Mother's qualification 0.05070191
## Mother's occupation -0.01295204
## Father's occupation -0.02259679
## Admission grade -0.07148446
## Displaced -0.07539091
## Debtor 0.02988585
## Tuition fees up to date 0.01708972
## Gender -0.01769282
## Scholarship holder -0.04865606
## Age at enrollment 0.14485076
## Curricular units 1st sem (evaluations) 1.00000000
## Curricular units 1st sem (grade) 0.42503896
## Curricular units 1st sem (without evaluations) 0.26738334
## Curricular units 2nd sem (credited) 0.54697988
## Curricular units 2nd sem (enrolled) 0.62596703
## Curricular units 2nd sem (evaluations) 0.79061583
## Curricular units 2nd sem (approved) 0.46674379
## Curricular units 2nd sem (grade) 0.35354974
## Curricular units 2nd sem (without evaluations) 0.15839920
## GDP -0.11169775
## Target 0.05978626
## Curricular units 1st sem (grade)
## Marital status -0.06944229
## Application mode -0.13391938
## Application order 0.06077642
## Daytime/evening attendance\t 0.07326953
## Previous qualification -0.01093774
## Previous qualification (grade) 0.07719085
## Mother's qualification -0.04413742
## Mother's occupation -0.03096487
## Father's occupation -0.02028298
## Admission grade 0.09769278
## Displaced 0.07780853
## Debtor -0.11052170
## Tuition fees up to date 0.27555517
## Gender -0.20708165
## Scholarship holder 0.19618033
## Age at enrollment -0.18072284
## Curricular units 1st sem (evaluations) 0.42503896
## Curricular units 1st sem (grade) 1.00000000
## Curricular units 1st sem (without evaluations) -0.06417141
## Curricular units 2nd sem (credited) 0.12019921
## Curricular units 2nd sem (enrolled) 0.40708430
## Curricular units 2nd sem (evaluations) 0.50336495
## Curricular units 2nd sem (approved) 0.69190696
## Curricular units 2nd sem (grade) 0.84586370
## Curricular units 2nd sem (without evaluations) -0.05586108
## GDP 0.05416842
## Target 0.51992709
## Curricular units 1st sem (without evaluations)
## Marital status 0.041534688
## Application mode 0.054923049
## Application order -0.038958325
## Daytime/evening attendance\t 0.039307133
## Previous qualification 0.020154940
## Previous qualification (grade) -0.011856961
## Mother's qualification 0.015111933
## Mother's occupation 0.024175385
## Father's occupation 0.003252840
## Admission grade 0.009637376
## Displaced -0.031756672
## Debtor 0.013739707
## Tuition fees up to date -0.069509209
## Gender 0.006808012
## Scholarship holder -0.069637354
## Age at enrollment 0.078435416
## Curricular units 1st sem (evaluations) 0.267383338
## Curricular units 1st sem (grade) -0.064171407
## Curricular units 1st sem (without evaluations) 1.000000000
## Curricular units 2nd sem (credited) 0.144377902
## Curricular units 2nd sem (enrolled) 0.123588280
## Curricular units 2nd sem (evaluations) 0.170003632
## Curricular units 2nd sem (approved) 0.001457851
## Curricular units 2nd sem (grade) -0.068724636
## Curricular units 2nd sem (without evaluations) 0.601572509
## GDP -0.130765710
## Target -0.074642260
## Curricular units 2nd sem (credited)
## Marital status 0.067507697
## Application mode 0.244575086
## Application order -0.127598900
## Daytime/evening attendance\t -0.105493795
## Previous qualification 0.147388648
## Previous qualification (grade) -0.026106966
## Mother's qualification 0.041687446
## Mother's occupation 0.005301619
## Father's occupation -0.009842470
## Admission grade 0.038345287
## Displaced -0.096240305
## Debtor 0.007596731
## Tuition fees up to date 0.020305999
## Gender 0.023026866
## Scholarship holder -0.079377788
## Age at enrollment 0.196484855
## Curricular units 1st sem (evaluations) 0.546979877
## Curricular units 1st sem (grade) 0.120199212
## Curricular units 1st sem (without evaluations) 0.144377902
## Curricular units 2nd sem (credited) 1.000000000
## Curricular units 2nd sem (enrolled) 0.683086145
## Curricular units 2nd sem (evaluations) 0.453716294
## Curricular units 2nd sem (approved) 0.522684405
## Curricular units 2nd sem (grade) 0.140180575
## Curricular units 2nd sem (without evaluations) 0.084506039
## GDP -0.038570078
## Target 0.052401971
## Curricular units 2nd sem (enrolled)
## Marital status 0.041255869
## Application mode 0.130559160
## Application order 0.033124779
## Daytime/evening attendance\t 0.006914694
## Previous qualification 0.054374940
## Previous qualification (grade) -0.036162317
## Mother's qualification 0.033218883
## Mother's occupation -0.020566614
## Father's occupation -0.032043455
## Admission grade -0.040766432
## Displaced -0.046430556
## Debtor -0.050772378
## Tuition fees up to date 0.103347329
## Gender -0.126659262
## Scholarship holder 0.024982195
## Age at enrollment 0.071177163
## Curricular units 1st sem (evaluations) 0.625967030
## Curricular units 1st sem (grade) 0.407084299
## Curricular units 1st sem (without evaluations) 0.123588280
## Curricular units 2nd sem (credited) 0.683086145
## Curricular units 2nd sem (enrolled) 1.000000000
## Curricular units 2nd sem (evaluations) 0.625080234
## Curricular units 2nd sem (approved) 0.704444531
## Curricular units 2nd sem (grade) 0.400772723
## Curricular units 2nd sem (without evaluations) 0.070363321
## GDP -0.026076338
## Target 0.182896541
## Curricular units 2nd sem (evaluations)
## Marital status 0.030786334
## Application mode 0.163626213
## Application order -0.042519456
## Daytime/evening attendance\t 0.009976676
## Previous qualification 0.094175384
## Previous qualification (grade) -0.061730068
## Mother's qualification 0.033509600
## Mother's occupation -0.026873395
## Father's occupation -0.033925637
## Admission grade -0.060954204
## Displaced -0.035873577
## Debtor 0.014412368
## Tuition fees up to date 0.055691377
## Gender -0.048000438
## Scholarship holder 0.005902935
## Age at enrollment 0.059554292
## Curricular units 1st sem (evaluations) 0.790615831
## Curricular units 1st sem (grade) 0.503364953
## Curricular units 1st sem (without evaluations) 0.170003632
## Curricular units 2nd sem (credited) 0.453716294
## Curricular units 2nd sem (enrolled) 0.625080234
## Curricular units 2nd sem (evaluations) 1.000000000
## Curricular units 2nd sem (approved) 0.508967845
## Curricular units 2nd sem (grade) 0.463193961
## Curricular units 2nd sem (without evaluations) 0.166442584
## GDP -0.021845762
## Target 0.119238767
## Curricular units 2nd sem (approved)
## Marital status -0.058400138
## Application mode -0.085269834
## Application order 0.072595010
## Daytime/evening attendance\t 0.054210519
## Previous qualification -0.010854171
## Previous qualification (grade) 0.055231897
## Mother's qualification -0.026406448
## Mother's occupation -0.031208891
## Father's occupation -0.030993704
## Admission grade 0.089429456
## Displaced 0.076465584
## Debtor -0.166305417
## Tuition fees up to date 0.329016595
## Gender -0.234662506
## Scholarship holder 0.214996508
## Age at enrollment -0.147667741
## Curricular units 1st sem (evaluations) 0.466743792
## Curricular units 1st sem (grade) 0.691906958
## Curricular units 1st sem (without evaluations) 0.001457851
## Curricular units 2nd sem (credited) 0.522684405
## Curricular units 2nd sem (enrolled) 0.704444531
## Curricular units 2nd sem (evaluations) 0.508967845
## Curricular units 2nd sem (approved) 1.000000000
## Curricular units 2nd sem (grade) 0.786837628
## Curricular units 2nd sem (without evaluations) -0.052389244
## GDP 0.014514087
## Target 0.653995246
## Curricular units 2nd sem (grade)
## Marital status -0.079536308
## Application mode -0.137288308
## Application order 0.059817104
## Daytime/evening attendance\t 0.058370913
## Previous qualification -0.008932658
## Previous qualification (grade) 0.068239628
## Mother's qualification -0.034434474
## Mother's occupation -0.030782454
## Father's occupation -0.025478739
## Admission grade 0.095342474
## Displaced 0.084462626
## Debtor -0.146603084
## Tuition fees up to date 0.318721332
## Gender -0.219696016
## Scholarship holder 0.212341841
## Age at enrollment -0.194144614
## Curricular units 1st sem (evaluations) 0.353549744
## Curricular units 1st sem (grade) 0.845863703
## Curricular units 1st sem (without evaluations) -0.068724636
## Curricular units 2nd sem (credited) 0.140180575
## Curricular units 2nd sem (enrolled) 0.400772723
## Curricular units 2nd sem (evaluations) 0.463193961
## Curricular units 2nd sem (approved) 0.786837628
## Curricular units 2nd sem (grade) 1.000000000
## Curricular units 2nd sem (without evaluations) -0.079508070
## GDP 0.066077451
## Target 0.605350126
## Curricular units 2nd sem (without evaluations)
## Marital status 0.0251927638
## Application mode 0.0604337629
## Application order -0.0268220378
## Daytime/evening attendance\t -0.0105040981
## Previous qualification 0.0222574734
## Previous qualification (grade) -0.0236537200
## Mother's qualification 0.0297985991
## Mother's occupation 0.0285714656
## Father's occupation -0.0003946159
## Admission grade -0.0128231980
## Displaced -0.0416964564
## Debtor 0.0699701491
## Tuition fees up to date -0.0951385799
## Gender 0.0577549960
## Scholarship holder -0.0605970409
## Age at enrollment 0.0801351117
## Curricular units 1st sem (evaluations) 0.1583991960
## Curricular units 1st sem (grade) -0.0558610836
## Curricular units 1st sem (without evaluations) 0.6015725092
## Curricular units 2nd sem (credited) 0.0845060387
## Curricular units 2nd sem (enrolled) 0.0703633212
## Curricular units 2nd sem (evaluations) 0.1664425843
## Curricular units 2nd sem (approved) -0.0523892438
## Curricular units 2nd sem (grade) -0.0795080705
## Curricular units 2nd sem (without evaluations) 1.0000000000
## GDP -0.0798569714
## Target -0.1026868286
## GDP Target
## Marital status -0.028390888 -0.1004790663
## Application mode -0.023945331 -0.2445071981
## Application order 0.033031479 0.0943546272
## Daytime/evening attendance\t 0.005007459 0.0844959357
## Previous qualification 0.072120663 -0.0623229026
## Previous qualification (grade) -0.054348729 0.1094636531
## Mother's qualification -0.076341914 -0.0539887950
## Mother's occupation 0.093199855 0.0007724444
## Father's occupation 0.102032243 0.0050655254
## Admission grade -0.014623531 0.1280577162
## Displaced 0.064923462 0.1261130353
## Debtor 0.040475119 -0.2672071989
## Tuition fees up to date 0.027771339 0.4421375758
## Gender -0.021930626 -0.2519548120
## Scholarship holder 0.037841609 0.3130176626
## Age at enrollment -0.069184294 -0.2672293832
## Curricular units 1st sem (evaluations) -0.111697754 0.0597862595
## Curricular units 1st sem (grade) 0.054168423 0.5199270935
## Curricular units 1st sem (without evaluations) -0.130765710 -0.0746422602
## Curricular units 2nd sem (credited) -0.038570078 0.0524019712
## Curricular units 2nd sem (enrolled) -0.026076338 0.1828965409
## Curricular units 2nd sem (evaluations) -0.021845762 0.1192387668
## Curricular units 2nd sem (approved) 0.014514087 0.6539952461
## Curricular units 2nd sem (grade) 0.066077451 0.6053501259
## Curricular units 2nd sem (without evaluations) -0.079856971 -0.1026868286
## GDP 1.000000000 0.0502601468
## Target 0.050260147 1.0000000000
## # A tibble: 6 × 27
## `Marital status` `Application mode` `Application order` Daytime/evening atte…¹
## <dbl> <dbl> <dbl> <dbl>
## 1 1 17 5 1
## 2 1 15 1 1
## 3 1 1 5 1
## 4 1 17 2 1
## 5 2 39 1 0
## 6 2 39 1 0
## # ℹ abbreviated name: ¹`Daytime/evening attendance\t`
## # ℹ 23 more variables: `Previous qualification` <dbl>,
## # `Previous qualification (grade)` <dbl>, `Mother's qualification` <dbl>,
## # `Mother's occupation` <dbl>, `Father's occupation` <dbl>,
## # `Admission grade` <dbl>, Displaced <dbl>, Debtor <dbl>,
## # `Tuition fees up to date` <dbl>, Gender <dbl>, `Scholarship holder` <dbl>,
## # `Age at enrollment` <dbl>, …
HeatMap -2 For Correlation Matrix
## # A tibble: 6 × 26
## `Marital status` `Application mode` `Application order` Daytime/evening atte…¹
## <dbl> <dbl> <dbl> <dbl>
## 1 1 17 5 1
## 2 1 15 1 1
## 3 1 1 5 1
## 4 1 17 2 1
## 5 2 39 1 0
## 6 2 39 1 0
## # ℹ abbreviated name: ¹`Daytime/evening attendance\t`
## # ℹ 22 more variables: `Previous qualification` <dbl>,
## # `Previous qualification (grade)` <dbl>, `Mother's qualification` <dbl>,
## # `Mother's occupation` <dbl>, `Father's occupation` <dbl>,
## # `Admission grade` <dbl>, Displaced <dbl>, Debtor <dbl>,
## # `Tuition fees up to date` <dbl>, Gender <dbl>, `Scholarship holder` <dbl>,
## # `Age at enrollment` <dbl>, …
## Marital status Application mode
## Marital status 1.000000000 0.27498489
## Application mode 0.274984888 1.00000000
## Application order -0.130370462 -0.28724546
## Daytime/evening attendance\t -0.265822964 -0.31085421
## Previous qualification 0.070984437 0.41666553
## Previous qualification (grade) -0.038868508 -0.07118997
## Mother's qualification 0.185116875 0.12269710
## Mother's occupation 0.053892219 0.04165008
## Father's occupation 0.050498926 0.02562908
## Admission grade -0.012439707 -0.03831107
## Displaced -0.240543910 -0.30872986
## Debtor 0.039469818 0.12145554
## Tuition fees up to date -0.096920476 -0.15414274
## Gender -0.001123579 0.18633822
## Scholarship holder -0.069684064 -0.17483548
## Age at enrollment 0.522359459 0.53160147
## Curricular units 1st sem (evaluations) 0.059191112 0.22035105
## Curricular units 1st sem (grade) -0.069442294 -0.13391938
## Curricular units 1st sem (without evaluations) 0.041534688 0.05492305
## Curricular units 2nd sem (credited) 0.067507697 0.24457509
## Curricular units 2nd sem (enrolled) 0.041255869 0.13055916
## Curricular units 2nd sem (evaluations) 0.030786334 0.16362621
## Curricular units 2nd sem (approved) -0.058400138 -0.08526983
## Curricular units 2nd sem (grade) -0.079536308 -0.13728831
## Curricular units 2nd sem (without evaluations) 0.025192764 0.06043376
## GDP -0.028390888 -0.02394533
## Target -0.100479066 -0.24450720
## Application order
## Marital status -0.13037046
## Application mode -0.28724546
## Application order 1.00000000
## Daytime/evening attendance\t 0.16549431
## Previous qualification -0.18788075
## Previous qualification (grade) -0.05171521
## Mother's qualification -0.05864907
## Mother's occupation -0.03245925
## Father's occupation -0.02530801
## Admission grade -0.09232439
## Displaced 0.34579059
## Debtor -0.06622707
## Tuition fees up to date 0.06161010
## Gender -0.10605938
## Scholarship holder 0.07289932
## Age at enrollment -0.28164140
## Curricular units 1st sem (evaluations) -0.08600449
## Curricular units 1st sem (grade) 0.06077642
## Curricular units 1st sem (without evaluations) -0.03895833
## Curricular units 2nd sem (credited) -0.12759890
## Curricular units 2nd sem (enrolled) 0.03312478
## Curricular units 2nd sem (evaluations) -0.04251946
## Curricular units 2nd sem (approved) 0.07259501
## Curricular units 2nd sem (grade) 0.05981710
## Curricular units 2nd sem (without evaluations) -0.02682204
## GDP 0.03303148
## Target 0.09435463
## Daytime/evening attendance\t
## Marital status -0.265822964
## Application mode -0.310854207
## Application order 0.165494312
## Daytime/evening attendance\t 1.000000000
## Previous qualification -0.087616264
## Previous qualification (grade) 0.063810246
## Mother's qualification -0.188876221
## Mother's occupation -0.034175134
## Father's occupation -0.030081802
## Admission grade 0.018610287
## Displaced 0.243652709
## Debtor 0.003899878
## Tuition fees up to date 0.052186286
## Gender -0.030506555
## Scholarship holder 0.110239582
## Age at enrollment -0.453741010
## Curricular units 1st sem (evaluations) -0.048431811
## Curricular units 1st sem (grade) 0.073269528
## Curricular units 1st sem (without evaluations) 0.039307133
## Curricular units 2nd sem (credited) -0.105493795
## Curricular units 2nd sem (enrolled) 0.006914694
## Curricular units 2nd sem (evaluations) 0.009976676
## Curricular units 2nd sem (approved) 0.054210519
## Curricular units 2nd sem (grade) 0.058370913
## Curricular units 2nd sem (without evaluations) -0.010504098
## GDP 0.005007459
## Target 0.084495936
## Previous qualification
## Marital status 0.070984437
## Application mode 0.416665526
## Application order -0.187880754
## Daytime/evening attendance\t -0.087616264
## Previous qualification 1.000000000
## Previous qualification (grade) 0.089193679
## Mother's qualification -0.021399220
## Mother's occupation 0.009809709
## Father's occupation 0.015576796
## Admission grade 0.164962221
## Displaced -0.126811069
## Debtor 0.100771032
## Tuition fees up to date -0.067020429
## Gender 0.094667272
## Scholarship holder -0.071748024
## Age at enrollment 0.169045703
## Curricular units 1st sem (evaluations) 0.123573272
## Curricular units 1st sem (grade) -0.010937738
## Curricular units 1st sem (without evaluations) 0.020154940
## Curricular units 2nd sem (credited) 0.147388648
## Curricular units 2nd sem (enrolled) 0.054374940
## Curricular units 2nd sem (evaluations) 0.094175384
## Curricular units 2nd sem (approved) -0.010854171
## Curricular units 2nd sem (grade) -0.008932658
## Curricular units 2nd sem (without evaluations) 0.022257473
## GDP 0.072120663
## Target -0.062322903
## Previous qualification (grade)
## Marital status -0.03886851
## Application mode -0.07118997
## Application order -0.05171521
## Daytime/evening attendance\t 0.06381025
## Previous qualification 0.08919368
## Previous qualification (grade) 1.00000000
## Mother's qualification -0.07303541
## Mother's occupation -0.01738334
## Father's occupation -0.02216891
## Admission grade 0.57724056
## Displaced -0.01023768
## Debtor -0.06220075
## Tuition fees up to date 0.07924588
## Gender -0.05765439
## Scholarship holder 0.06905385
## Age at enrollment -0.13353473
## Curricular units 1st sem (evaluations) -0.07259501
## Curricular units 1st sem (grade) 0.07719085
## Curricular units 1st sem (without evaluations) -0.01185696
## Curricular units 2nd sem (credited) -0.02610697
## Curricular units 2nd sem (enrolled) -0.03616232
## Curricular units 2nd sem (evaluations) -0.06173007
## Curricular units 2nd sem (approved) 0.05523190
## Curricular units 2nd sem (grade) 0.06823963
## Curricular units 2nd sem (without evaluations) -0.02365372
## GDP -0.05434873
## Target 0.10946365
## Mother's qualification
## Marital status 0.18511688
## Application mode 0.12269710
## Application order -0.05864907
## Daytime/evening attendance\t -0.18887622
## Previous qualification -0.02139922
## Previous qualification (grade) -0.07303541
## Mother's qualification 1.00000000
## Mother's occupation 0.09365422
## Father's occupation 0.06747057
## Admission grade -0.06885529
## Displaced -0.07711462
## Debtor 0.01122862
## Tuition fees up to date -0.03118454
## Gender -0.04237701
## Scholarship holder 0.02686919
## Age at enrollment 0.29184418
## Curricular units 1st sem (evaluations) 0.05070191
## Curricular units 1st sem (grade) -0.04413742
## Curricular units 1st sem (without evaluations) 0.01511193
## Curricular units 2nd sem (credited) 0.04168745
## Curricular units 2nd sem (enrolled) 0.03321888
## Curricular units 2nd sem (evaluations) 0.03350960
## Curricular units 2nd sem (approved) -0.02640645
## Curricular units 2nd sem (grade) -0.03443447
## Curricular units 2nd sem (without evaluations) 0.02979860
## GDP -0.07634191
## Target -0.05398879
## Mother's occupation
## Marital status 0.0538922189
## Application mode 0.0416500842
## Application order -0.0324592520
## Daytime/evening attendance\t -0.0341751340
## Previous qualification 0.0098097088
## Previous qualification (grade) -0.0173833353
## Mother's qualification 0.0936542154
## Mother's occupation 1.0000000000
## Father's occupation 0.8865682817
## Admission grade -0.0455051544
## Displaced -0.0730063450
## Debtor 0.0867010216
## Tuition fees up to date -0.0227177492
## Gender -0.0135582432
## Scholarship holder -0.0032395693
## Age at enrollment 0.0608744514
## Curricular units 1st sem (evaluations) -0.0129520444
## Curricular units 1st sem (grade) -0.0309648742
## Curricular units 1st sem (without evaluations) 0.0241753849
## Curricular units 2nd sem (credited) 0.0053016188
## Curricular units 2nd sem (enrolled) -0.0205666136
## Curricular units 2nd sem (evaluations) -0.0268733946
## Curricular units 2nd sem (approved) -0.0312088907
## Curricular units 2nd sem (grade) -0.0307824542
## Curricular units 2nd sem (without evaluations) 0.0285714656
## GDP 0.0931998553
## Target 0.0007724444
## Father's occupation
## Marital status 0.0504989264
## Application mode 0.0256290775
## Application order -0.0253080119
## Daytime/evening attendance\t -0.0300818025
## Previous qualification 0.0155767961
## Previous qualification (grade) -0.0221689116
## Mother's qualification 0.0674705683
## Mother's occupation 0.8865682817
## Father's occupation 1.0000000000
## Admission grade -0.0380957109
## Displaced -0.0738732501
## Debtor 0.0868409440
## Tuition fees up to date -0.0085053597
## Gender -0.0251208803
## Scholarship holder 0.0005518803
## Age at enrollment 0.0359223738
## Curricular units 1st sem (evaluations) -0.0225967935
## Curricular units 1st sem (grade) -0.0202829796
## Curricular units 1st sem (without evaluations) 0.0032528400
## Curricular units 2nd sem (credited) -0.0098424697
## Curricular units 2nd sem (enrolled) -0.0320434549
## Curricular units 2nd sem (evaluations) -0.0339256371
## Curricular units 2nd sem (approved) -0.0309937036
## Curricular units 2nd sem (grade) -0.0254787395
## Curricular units 2nd sem (without evaluations) -0.0003946159
## GDP 0.1020322430
## Target 0.0050655254
## Admission grade Displaced
## Marital status -0.012439707 -0.240543910
## Application mode -0.038311074 -0.308729857
## Application order -0.092324392 0.345790590
## Daytime/evening attendance\t 0.018610287 0.243652709
## Previous qualification 0.164962221 -0.126811069
## Previous qualification (grade) 0.577240558 -0.010237683
## Mother's qualification -0.068855291 -0.077114621
## Mother's occupation -0.045505154 -0.073006345
## Father's occupation -0.038095711 -0.073873250
## Admission grade 1.000000000 -0.006878924
## Displaced -0.006878924 1.000000000
## Debtor -0.024911472 -0.093717569
## Tuition fees up to date 0.071801910 0.105403411
## Gender 0.009604421 -0.127895526
## Scholarship holder 0.022258760 0.086336523
## Age at enrollment -0.035725515 -0.370018297
## Curricular units 1st sem (evaluations) -0.071484458 -0.075390915
## Curricular units 1st sem (grade) 0.097692780 0.077808532
## Curricular units 1st sem (without evaluations) 0.009637376 -0.031756672
## Curricular units 2nd sem (credited) 0.038345287 -0.096240305
## Curricular units 2nd sem (enrolled) -0.040766432 -0.046430556
## Curricular units 2nd sem (evaluations) -0.060954204 -0.035873577
## Curricular units 2nd sem (approved) 0.089429456 0.076465584
## Curricular units 2nd sem (grade) 0.095342474 0.084462626
## Curricular units 2nd sem (without evaluations) -0.012823198 -0.041696456
## GDP -0.014623531 0.064923462
## Target 0.128057716 0.126113035
## Debtor
## Marital status 0.039469818
## Application mode 0.121455544
## Application order -0.066227070
## Daytime/evening attendance\t 0.003899878
## Previous qualification 0.100771032
## Previous qualification (grade) -0.062200747
## Mother's qualification 0.011228618
## Mother's occupation 0.086701022
## Father's occupation 0.086840944
## Admission grade -0.024911472
## Displaced -0.093717569
## Debtor 1.000000000
## Tuition fees up to date -0.434905505
## Gender 0.052769750
## Scholarship holder -0.065204206
## Age at enrollment 0.104141791
## Curricular units 1st sem (evaluations) 0.029885845
## Curricular units 1st sem (grade) -0.110521704
## Curricular units 1st sem (without evaluations) 0.013739707
## Curricular units 2nd sem (credited) 0.007596731
## Curricular units 2nd sem (enrolled) -0.050772378
## Curricular units 2nd sem (evaluations) 0.014412368
## Curricular units 2nd sem (approved) -0.166305417
## Curricular units 2nd sem (grade) -0.146603084
## Curricular units 2nd sem (without evaluations) 0.069970149
## GDP 0.040475119
## Target -0.267207199
## Tuition fees up to date
## Marital status -0.09692048
## Application mode -0.15414274
## Application order 0.06161010
## Daytime/evening attendance\t 0.05218629
## Previous qualification -0.06702043
## Previous qualification (grade) 0.07924588
## Mother's qualification -0.03118454
## Mother's occupation -0.02271775
## Father's occupation -0.00850536
## Admission grade 0.07180191
## Displaced 0.10540341
## Debtor -0.43490550
## Tuition fees up to date 1.00000000
## Gender -0.12223083
## Scholarship holder 0.16959043
## Age at enrollment -0.19637020
## Curricular units 1st sem (evaluations) 0.01708972
## Curricular units 1st sem (grade) 0.27555517
## Curricular units 1st sem (without evaluations) -0.06950921
## Curricular units 2nd sem (credited) 0.02030600
## Curricular units 2nd sem (enrolled) 0.10334733
## Curricular units 2nd sem (evaluations) 0.05569138
## Curricular units 2nd sem (approved) 0.32901659
## Curricular units 2nd sem (grade) 0.31872133
## Curricular units 2nd sem (without evaluations) -0.09513858
## GDP 0.02777134
## Target 0.44213758
## Gender Scholarship holder
## Marital status -0.001123579 -0.0696840641
## Application mode 0.186338223 -0.1748354799
## Application order -0.106059375 0.0728993242
## Daytime/evening attendance\t -0.030506555 0.1102395821
## Previous qualification 0.094667272 -0.0717480241
## Previous qualification (grade) -0.057654392 0.0690538471
## Mother's qualification -0.042377014 0.0268691851
## Mother's occupation -0.013558243 -0.0032395693
## Father's occupation -0.025120880 0.0005518803
## Admission grade 0.009604421 0.0222587602
## Displaced -0.127895526 0.0863365234
## Debtor 0.052769750 -0.0652042058
## Tuition fees up to date -0.122230829 0.1695904323
## Gender 1.000000000 -0.1879936026
## Scholarship holder -0.187993603 1.0000000000
## Age at enrollment 0.179886992 -0.2125880721
## Curricular units 1st sem (evaluations) -0.017692822 -0.0486560556
## Curricular units 1st sem (grade) -0.207081647 0.1961803331
## Curricular units 1st sem (without evaluations) 0.006808012 -0.0696373536
## Curricular units 2nd sem (credited) 0.023026866 -0.0793777875
## Curricular units 2nd sem (enrolled) -0.126659262 0.0249821954
## Curricular units 2nd sem (evaluations) -0.048000438 0.0059029352
## Curricular units 2nd sem (approved) -0.234662506 0.2149965076
## Curricular units 2nd sem (grade) -0.219696016 0.2123418406
## Curricular units 2nd sem (without evaluations) 0.057754996 -0.0605970409
## GDP -0.021930626 0.0378416090
## Target -0.251954812 0.3130176626
## Age at enrollment
## Marital status 0.52235946
## Application mode 0.53160147
## Application order -0.28164140
## Daytime/evening attendance\t -0.45374101
## Previous qualification 0.16904570
## Previous qualification (grade) -0.13353473
## Mother's qualification 0.29184418
## Mother's occupation 0.06087445
## Father's occupation 0.03592237
## Admission grade -0.03572551
## Displaced -0.37001830
## Debtor 0.10414179
## Tuition fees up to date -0.19637020
## Gender 0.17988699
## Scholarship holder -0.21258807
## Age at enrollment 1.00000000
## Curricular units 1st sem (evaluations) 0.14485076
## Curricular units 1st sem (grade) -0.18072284
## Curricular units 1st sem (without evaluations) 0.07843542
## Curricular units 2nd sem (credited) 0.19648486
## Curricular units 2nd sem (enrolled) 0.07117716
## Curricular units 2nd sem (evaluations) 0.05955429
## Curricular units 2nd sem (approved) -0.14766774
## Curricular units 2nd sem (grade) -0.19414461
## Curricular units 2nd sem (without evaluations) 0.08013511
## GDP -0.06918429
## Target -0.26722938
## Curricular units 1st sem (evaluations)
## Marital status 0.05919111
## Application mode 0.22035105
## Application order -0.08600449
## Daytime/evening attendance\t -0.04843181
## Previous qualification 0.12357327
## Previous qualification (grade) -0.07259501
## Mother's qualification 0.05070191
## Mother's occupation -0.01295204
## Father's occupation -0.02259679
## Admission grade -0.07148446
## Displaced -0.07539091
## Debtor 0.02988585
## Tuition fees up to date 0.01708972
## Gender -0.01769282
## Scholarship holder -0.04865606
## Age at enrollment 0.14485076
## Curricular units 1st sem (evaluations) 1.00000000
## Curricular units 1st sem (grade) 0.42503896
## Curricular units 1st sem (without evaluations) 0.26738334
## Curricular units 2nd sem (credited) 0.54697988
## Curricular units 2nd sem (enrolled) 0.62596703
## Curricular units 2nd sem (evaluations) 0.79061583
## Curricular units 2nd sem (approved) 0.46674379
## Curricular units 2nd sem (grade) 0.35354974
## Curricular units 2nd sem (without evaluations) 0.15839920
## GDP -0.11169775
## Target 0.05978626
## Curricular units 1st sem (grade)
## Marital status -0.06944229
## Application mode -0.13391938
## Application order 0.06077642
## Daytime/evening attendance\t 0.07326953
## Previous qualification -0.01093774
## Previous qualification (grade) 0.07719085
## Mother's qualification -0.04413742
## Mother's occupation -0.03096487
## Father's occupation -0.02028298
## Admission grade 0.09769278
## Displaced 0.07780853
## Debtor -0.11052170
## Tuition fees up to date 0.27555517
## Gender -0.20708165
## Scholarship holder 0.19618033
## Age at enrollment -0.18072284
## Curricular units 1st sem (evaluations) 0.42503896
## Curricular units 1st sem (grade) 1.00000000
## Curricular units 1st sem (without evaluations) -0.06417141
## Curricular units 2nd sem (credited) 0.12019921
## Curricular units 2nd sem (enrolled) 0.40708430
## Curricular units 2nd sem (evaluations) 0.50336495
## Curricular units 2nd sem (approved) 0.69190696
## Curricular units 2nd sem (grade) 0.84586370
## Curricular units 2nd sem (without evaluations) -0.05586108
## GDP 0.05416842
## Target 0.51992709
## Curricular units 1st sem (without evaluations)
## Marital status 0.041534688
## Application mode 0.054923049
## Application order -0.038958325
## Daytime/evening attendance\t 0.039307133
## Previous qualification 0.020154940
## Previous qualification (grade) -0.011856961
## Mother's qualification 0.015111933
## Mother's occupation 0.024175385
## Father's occupation 0.003252840
## Admission grade 0.009637376
## Displaced -0.031756672
## Debtor 0.013739707
## Tuition fees up to date -0.069509209
## Gender 0.006808012
## Scholarship holder -0.069637354
## Age at enrollment 0.078435416
## Curricular units 1st sem (evaluations) 0.267383338
## Curricular units 1st sem (grade) -0.064171407
## Curricular units 1st sem (without evaluations) 1.000000000
## Curricular units 2nd sem (credited) 0.144377902
## Curricular units 2nd sem (enrolled) 0.123588280
## Curricular units 2nd sem (evaluations) 0.170003632
## Curricular units 2nd sem (approved) 0.001457851
## Curricular units 2nd sem (grade) -0.068724636
## Curricular units 2nd sem (without evaluations) 0.601572509
## GDP -0.130765710
## Target -0.074642260
## Curricular units 2nd sem (credited)
## Marital status 0.067507697
## Application mode 0.244575086
## Application order -0.127598900
## Daytime/evening attendance\t -0.105493795
## Previous qualification 0.147388648
## Previous qualification (grade) -0.026106966
## Mother's qualification 0.041687446
## Mother's occupation 0.005301619
## Father's occupation -0.009842470
## Admission grade 0.038345287
## Displaced -0.096240305
## Debtor 0.007596731
## Tuition fees up to date 0.020305999
## Gender 0.023026866
## Scholarship holder -0.079377788
## Age at enrollment 0.196484855
## Curricular units 1st sem (evaluations) 0.546979877
## Curricular units 1st sem (grade) 0.120199212
## Curricular units 1st sem (without evaluations) 0.144377902
## Curricular units 2nd sem (credited) 1.000000000
## Curricular units 2nd sem (enrolled) 0.683086145
## Curricular units 2nd sem (evaluations) 0.453716294
## Curricular units 2nd sem (approved) 0.522684405
## Curricular units 2nd sem (grade) 0.140180575
## Curricular units 2nd sem (without evaluations) 0.084506039
## GDP -0.038570078
## Target 0.052401971
## Curricular units 2nd sem (enrolled)
## Marital status 0.041255869
## Application mode 0.130559160
## Application order 0.033124779
## Daytime/evening attendance\t 0.006914694
## Previous qualification 0.054374940
## Previous qualification (grade) -0.036162317
## Mother's qualification 0.033218883
## Mother's occupation -0.020566614
## Father's occupation -0.032043455
## Admission grade -0.040766432
## Displaced -0.046430556
## Debtor -0.050772378
## Tuition fees up to date 0.103347329
## Gender -0.126659262
## Scholarship holder 0.024982195
## Age at enrollment 0.071177163
## Curricular units 1st sem (evaluations) 0.625967030
## Curricular units 1st sem (grade) 0.407084299
## Curricular units 1st sem (without evaluations) 0.123588280
## Curricular units 2nd sem (credited) 0.683086145
## Curricular units 2nd sem (enrolled) 1.000000000
## Curricular units 2nd sem (evaluations) 0.625080234
## Curricular units 2nd sem (approved) 0.704444531
## Curricular units 2nd sem (grade) 0.400772723
## Curricular units 2nd sem (without evaluations) 0.070363321
## GDP -0.026076338
## Target 0.182896541
## Curricular units 2nd sem (evaluations)
## Marital status 0.030786334
## Application mode 0.163626213
## Application order -0.042519456
## Daytime/evening attendance\t 0.009976676
## Previous qualification 0.094175384
## Previous qualification (grade) -0.061730068
## Mother's qualification 0.033509600
## Mother's occupation -0.026873395
## Father's occupation -0.033925637
## Admission grade -0.060954204
## Displaced -0.035873577
## Debtor 0.014412368
## Tuition fees up to date 0.055691377
## Gender -0.048000438
## Scholarship holder 0.005902935
## Age at enrollment 0.059554292
## Curricular units 1st sem (evaluations) 0.790615831
## Curricular units 1st sem (grade) 0.503364953
## Curricular units 1st sem (without evaluations) 0.170003632
## Curricular units 2nd sem (credited) 0.453716294
## Curricular units 2nd sem (enrolled) 0.625080234
## Curricular units 2nd sem (evaluations) 1.000000000
## Curricular units 2nd sem (approved) 0.508967845
## Curricular units 2nd sem (grade) 0.463193961
## Curricular units 2nd sem (without evaluations) 0.166442584
## GDP -0.021845762
## Target 0.119238767
## Curricular units 2nd sem (approved)
## Marital status -0.058400138
## Application mode -0.085269834
## Application order 0.072595010
## Daytime/evening attendance\t 0.054210519
## Previous qualification -0.010854171
## Previous qualification (grade) 0.055231897
## Mother's qualification -0.026406448
## Mother's occupation -0.031208891
## Father's occupation -0.030993704
## Admission grade 0.089429456
## Displaced 0.076465584
## Debtor -0.166305417
## Tuition fees up to date 0.329016595
## Gender -0.234662506
## Scholarship holder 0.214996508
## Age at enrollment -0.147667741
## Curricular units 1st sem (evaluations) 0.466743792
## Curricular units 1st sem (grade) 0.691906958
## Curricular units 1st sem (without evaluations) 0.001457851
## Curricular units 2nd sem (credited) 0.522684405
## Curricular units 2nd sem (enrolled) 0.704444531
## Curricular units 2nd sem (evaluations) 0.508967845
## Curricular units 2nd sem (approved) 1.000000000
## Curricular units 2nd sem (grade) 0.786837628
## Curricular units 2nd sem (without evaluations) -0.052389244
## GDP 0.014514087
## Target 0.653995246
## Curricular units 2nd sem (grade)
## Marital status -0.079536308
## Application mode -0.137288308
## Application order 0.059817104
## Daytime/evening attendance\t 0.058370913
## Previous qualification -0.008932658
## Previous qualification (grade) 0.068239628
## Mother's qualification -0.034434474
## Mother's occupation -0.030782454
## Father's occupation -0.025478739
## Admission grade 0.095342474
## Displaced 0.084462626
## Debtor -0.146603084
## Tuition fees up to date 0.318721332
## Gender -0.219696016
## Scholarship holder 0.212341841
## Age at enrollment -0.194144614
## Curricular units 1st sem (evaluations) 0.353549744
## Curricular units 1st sem (grade) 0.845863703
## Curricular units 1st sem (without evaluations) -0.068724636
## Curricular units 2nd sem (credited) 0.140180575
## Curricular units 2nd sem (enrolled) 0.400772723
## Curricular units 2nd sem (evaluations) 0.463193961
## Curricular units 2nd sem (approved) 0.786837628
## Curricular units 2nd sem (grade) 1.000000000
## Curricular units 2nd sem (without evaluations) -0.079508070
## GDP 0.066077451
## Target 0.605350126
## Curricular units 2nd sem (without evaluations)
## Marital status 0.0251927638
## Application mode 0.0604337629
## Application order -0.0268220378
## Daytime/evening attendance\t -0.0105040981
## Previous qualification 0.0222574734
## Previous qualification (grade) -0.0236537200
## Mother's qualification 0.0297985991
## Mother's occupation 0.0285714656
## Father's occupation -0.0003946159
## Admission grade -0.0128231980
## Displaced -0.0416964564
## Debtor 0.0699701491
## Tuition fees up to date -0.0951385799
## Gender 0.0577549960
## Scholarship holder -0.0605970409
## Age at enrollment 0.0801351117
## Curricular units 1st sem (evaluations) 0.1583991960
## Curricular units 1st sem (grade) -0.0558610836
## Curricular units 1st sem (without evaluations) 0.6015725092
## Curricular units 2nd sem (credited) 0.0845060387
## Curricular units 2nd sem (enrolled) 0.0703633212
## Curricular units 2nd sem (evaluations) 0.1664425843
## Curricular units 2nd sem (approved) -0.0523892438
## Curricular units 2nd sem (grade) -0.0795080705
## Curricular units 2nd sem (without evaluations) 1.0000000000
## GDP -0.0798569714
## Target -0.1026868286
## GDP Target
## Marital status -0.028390888 -0.1004790663
## Application mode -0.023945331 -0.2445071981
## Application order 0.033031479 0.0943546272
## Daytime/evening attendance\t 0.005007459 0.0844959357
## Previous qualification 0.072120663 -0.0623229026
## Previous qualification (grade) -0.054348729 0.1094636531
## Mother's qualification -0.076341914 -0.0539887950
## Mother's occupation 0.093199855 0.0007724444
## Father's occupation 0.102032243 0.0050655254
## Admission grade -0.014623531 0.1280577162
## Displaced 0.064923462 0.1261130353
## Debtor 0.040475119 -0.2672071989
## Tuition fees up to date 0.027771339 0.4421375758
## Gender -0.021930626 -0.2519548120
## Scholarship holder 0.037841609 0.3130176626
## Age at enrollment -0.069184294 -0.2672293832
## Curricular units 1st sem (evaluations) -0.111697754 0.0597862595
## Curricular units 1st sem (grade) 0.054168423 0.5199270935
## Curricular units 1st sem (without evaluations) -0.130765710 -0.0746422602
## Curricular units 2nd sem (credited) -0.038570078 0.0524019712
## Curricular units 2nd sem (enrolled) -0.026076338 0.1828965409
## Curricular units 2nd sem (evaluations) -0.021845762 0.1192387668
## Curricular units 2nd sem (approved) 0.014514087 0.6539952461
## Curricular units 2nd sem (grade) 0.066077451 0.6053501259
## Curricular units 2nd sem (without evaluations) -0.079856971 -0.1026868286
## GDP 1.000000000 0.0502601468
## Target 0.050260147 1.0000000000
## # A tibble: 6 × 27
## `Marital status` `Application mode` `Application order` Daytime/evening atte…¹
## <dbl> <dbl> <dbl> <dbl>
## 1 1 17 5 1
## 2 1 15 1 1
## 3 1 1 5 1
## 4 1 17 2 1
## 5 2 39 1 0
## 6 2 39 1 0
## # ℹ abbreviated name: ¹`Daytime/evening attendance\t`
## # ℹ 23 more variables: `Previous qualification` <dbl>,
## # `Previous qualification (grade)` <dbl>, `Mother's qualification` <dbl>,
## # `Mother's occupation` <dbl>, `Father's occupation` <dbl>,
## # `Admission grade` <dbl>, Displaced <dbl>, Debtor <dbl>,
## # `Tuition fees up to date` <dbl>, Gender <dbl>, `Scholarship holder` <dbl>,
## # `Age at enrollment` <dbl>, …
Correlation Of Graduation Rate :
library(dplyr)
dataset <- students_data %>%
select(-Target)
head(dataset)
## # A tibble: 6 × 26
## `Marital status` `Application mode` `Application order` Daytime/evening atte…¹
## <dbl> <dbl> <dbl> <dbl>
## 1 1 17 5 1
## 2 1 15 1 1
## 3 1 1 5 1
## 4 1 17 2 1
## 5 2 39 1 0
## 6 2 39 1 0
## # ℹ abbreviated name: ¹`Daytime/evening attendance\t`
## # ℹ 22 more variables: `Previous qualification` <dbl>,
## # `Previous qualification (grade)` <dbl>, `Mother's qualification` <dbl>,
## # `Mother's occupation` <dbl>, `Father's occupation` <dbl>,
## # `Admission grade` <dbl>, Displaced <dbl>, Debtor <dbl>,
## # `Tuition fees up to date` <dbl>, Gender <dbl>, `Scholarship holder` <dbl>,
## # `Age at enrollment` <dbl>, …
Plot to check Correlation with Dropout
# Correlation Analysis with Dropout Rates
correlations <- sapply(dataset, function(x) cor(x, students_data$Target, use = "complete.obs"))
corr_df <- data.frame(Variable = names(correlations), Correlation = correlations)
# Bar Plot
ggplot(corr_df, aes(x = Variable, y = Correlation, fill = Correlation)) +
geom_bar(stat = "identity") +
scale_fill_viridis_c(option = "plasma", direction = -1) + # Using the 'plasma' color palette from viridis for visual appeal
labs(title = "Correlation With Dropout") +
theme_minimal() +
theme(axis.text.x = element_text(angle = 90, hjust = 1)) # Rotate x-axis labels for readability
- Variables such as ‘Curricular units 2nd sem (without evaluations)’ and
‘Curricular units 2nd sem (approved)’ show a strong positive correlation
with dropout, suggesting that students’ performance or engagement in the
second semester is indicative of their likelihood to drop out. -
Conversely, factors like ‘Age at enrollment’ and ‘Application mode’ have
a negative correlation, implying that as these increase, the likelihood
of dropout decreases. This might reflect more mature or differently
prepared students being less likely to drop out. - Some variables, such
as ‘Gender’ and ‘Father’s occupation’, appear to have little to no
correlation with dropout rates, which indicates that these factors may
not be significant predictors in this context. - This plot serves as a
guide for identifying factors that could be influential in student
retention strategies. Variables with strong correlations might be
targets for intervention or more detailed analysis.
Splitting Dataset :
Splitting a dataset refers to the process of dividing a given dataset
into two or more subsets for training and evaluation purposes. The most
common type of split is between the training set and the testing (or
validation) set. This division allows us to assess the performance of a
machine learning model on unseen data and evaluate its generalization
capabilities.
Train-Test Split: This is the most basic type of split, where the
dataset is divided into a training set and a testing set. The training
set is used to train the machine learning model, while the testing set
is used to evaluate its performance. The split is typically done using a
fixed ratio, such as 80% for training and 20% for testing.
library(caret)
# Extract features (x) and target variable (y) from the dataset
x <- students_data[, names(students_data) != "Target"]
y <- students_data$Target
# Set a random seed for reproducibility
set.seed(42)
# Create indices for a stratified split, ensuring the target variable's distribution is similar in both sets
trainIndex <- caret::createDataPartition(y, p = 0.7, list = FALSE, times = 1)
# Split the data into training and testing sets using the indices
x_train <- x[trainIndex, ]
y_train <- y[trainIndex]
x_test <- x[-trainIndex, ]
y_test <- y[-trainIndex]
# Output the first few rows of the training feature set to verify the split
head(x_train)
## # A tibble: 6 × 26
## `Marital status` `Application mode` `Application order` Daytime/evening atte…¹
## <dbl> <dbl> <dbl> <dbl>
## 1 1 17 5 1
## 2 1 15 1 1
## 3 1 1 5 1
## 4 1 17 2 1
## 5 1 1 1 1
## 6 1 18 4 1
## # ℹ abbreviated name: ¹`Daytime/evening attendance\t`
## # ℹ 22 more variables: `Previous qualification` <dbl>,
## # `Previous qualification (grade)` <dbl>, `Mother's qualification` <dbl>,
## # `Mother's occupation` <dbl>, `Father's occupation` <dbl>,
## # `Admission grade` <dbl>, Displaced <dbl>, Debtor <dbl>,
## # `Tuition fees up to date` <dbl>, Gender <dbl>, `Scholarship holder` <dbl>,
## # `Age at enrollment` <dbl>, …
# Output the first few elements of the training target variable to verify the split
head(y_train)
## [1] 0 1 0 1 1 0
# Display dimensions of the training and testing sets for confirmation
dim(x_train)
## [1] 2541 26
## [1] 1089 26
## [1] 2541
## [1] 1089
We have test and train split of data and the shape of the data is
(2541, 1085)
Model Selection And Training :
Model Selection:
- Model selection involves choosing the best algorithm or model
architecture for the given problem and dataset. This step requires
careful consideration of various factors, such as the nature of the data
(e.g., numerical or categorical), the problem type (e.g., regression,
classification, clustering), the amount of available data, and the
desired model performance. It is essential to select a model that can
effectively capture the underlying patterns in the data and make
accurate predictions.
Model Training:
- Once the appropriate model has been selected, the next step is to
train it on the dataset. Model training involves adjusting the model’s
parameters using the training data to make accurate predictions on
unseen data. The goal is to minimize the difference between the model’s
predictions and the actual target values during training.
library(randomForest)
y_train <- as.factor(y_train)
y_test <- as.factor(y_test)
# Train the model
clf <- randomForest(x_train, y_train)
y_pred <- predict(clf, x_test)
accuracy <- mean(y_pred == y_test)
print(accuracy)
## [1] 0.9035813
- Implementation Using RandomForest:
- Training Steps:
- Employing the RandomForest algorithm for its robustness and
efficacy.
- Training the model with a subset (70%) of the data to predict
‘Target’.
- Performance:
- Achieved an impressive 90% accuracy in predictions.
- Reflects the model’s strong capability in classifying data
accurately.
Hyper-parameter Tuning :
Hyperparameter tuning is a critical process in machine learning
that involves finding the optimal set of hyperparameters for a given
model. Hyperparameters are configuration settings that are not learned
from the data during model training but are set before the training
process begins. They significantly impact the model’s performance and
generalization ability.
The goal of hyperparameter tuning is to systematically search
through different combinations of hyperparameters to identify the
configuration that yields the best model performance. The process
ensures that the model is well-optimized and capable of making accurate
predictions on new, unseen data.
Grid Search:
- Grid search involves specifying a list of values for each
hyperparameter. The algorithm then exhaustively tries all possible
combinations of hyperparameters to find the best one. This method is
simple and can be effective for a small number of hyperparameters, but
it becomes computationally expensive as the number of hyperparameters
increases.
library(caret)
# Define a sequence of values for mtry
mtry_values <- 2:5 # Testing mtry from 2 to 5
# Create the hyperparameter grid
hyper_grid <- expand.grid(
mtry = mtry_values
)
train_control <- trainControl(method = "cv", number = 3)
random_forest_model <- train(
x_train, y_train,
method = "rf",
trControl = train_control,
tuneGrid = hyper_grid
)
best_mtry <- random_forest_model$bestTune$mtry
print(best_mtry)
## [1] 5
print(random_forest_model$results)
## mtry Accuracy Kappa AccuracySD KappaSD
## 1 2 0.8933471 0.7714765 0.004221983 0.007610192
## 2 3 0.8972835 0.7800736 0.004293759 0.007824840
## 3 4 0.8980729 0.7820145 0.006680476 0.013230672
## 4 5 0.9000407 0.7864352 0.008009054 0.015958694
Best Hyperparameter Value:
- The optimal value for mtry is identified as 5. This is determined
based on the performance metrics obtained from the grid search.
- The output table lists the results for mtry values ranging from 2 to
5.
- For each mtry value, the model’s accuracy and kappa scores, along
with their standard deviations, are provided.
Accuracy and Kappa Scores:
- The accuracy and kappa scores generally increase as the mtry value
increases.
- The highest accuracy (0.9000407) and kappa (0.7864352) scores are
achieved with mtry = 5.
- The standard deviations for accuracy and kappa also increase with
higher mtry values, indicating greater variability in model
performance.
Implications:
- The results suggest that increasing the mtry parameter improves the
model’s performance in terms of accuracy and kappa scores. However, the
increase in standard deviation also points to a potential increase in
model variability.
- Choosing mtry = 5 appears to be the best configuration for this
specific random forest model based on the current dataset and the
metrics considered.
library(randomForest)
final_model <- randomForest(x_train, y_train, mtry = best_mtry)
prediction
y_pred <- predict(final_model, x_test)
accuracy <- mean(y_pred == y_test)
print(accuracy)
## [1] 0.9044995
Interpreting Model Performance Good Accuracy: An accuracy of around
90.3% is generally considered high in many contexts, though the
acceptability of this performance level depends on the specifics of your
task and domain.
Contextual Evaluation: Consider the complexity of your task and
compare this result with a baseline model or existing benchmarks in your
field. For example, if a simple model or a heuristic approach results in
significantly lower accuracy, then your RandomForest model is providing
substantial value.
Overfitting Check: Overfitting happens when a model learns patterns
specific to the training data but doesn’t generalize well to unseen
data. The close performance of the model on training and test sets
usually indicates good generalization, but it’s always good to be
vigilant.
y_pred_factor <- factor(y_pred, levels = levels(y_test))
y_test_factor <- factor(y_test)
conf_matrix <- confusionMatrix(y_pred_factor, y_test_factor)
print(conf_matrix)
## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1
## 0 347 24
## 1 80 638
##
## Accuracy : 0.9045
## 95% CI : (0.8855, 0.9213)
## No Information Rate : 0.6079
## P-Value [Acc > NIR] : < 2.2e-16
##
## Kappa : 0.7949
##
## Mcnemar's Test P-Value : 6.922e-08
##
## Sensitivity : 0.8126
## Specificity : 0.9637
## Pos Pred Value : 0.9353
## Neg Pred Value : 0.8886
## Prevalence : 0.3921
## Detection Rate : 0.3186
## Detection Prevalence : 0.3407
## Balanced Accuracy : 0.8882
##
## 'Positive' Class : 0
##
Confusion Matrix: Matrix Overview:
The confusion matrix compares the predicted values (Prediction)
against the actual values (Reference). There are two classes: 0 and 1.
Results:
Class 0 (Negative Class): 350 true negatives (correctly predicted as
0) and 77 false negatives (incorrectly predicted as 1). Class 1
(Positive Class): 637 true positives (correctly predicted as 1) and 25
false positives (incorrectly predicted as 0). Statistical Measures:
Accuracy: Approximately 90.63% (0.9063). This indicates a high overall
rate of correct predictions by the model.
95% Confidence Interval for Accuracy: Ranges from 88.75% to 92.3%,
suggesting the model’s accuracy is consistently high.
No Information Rate: 60.79%. This is a baseline metric for
comparison, indicating the accuracy that would be achieved by always
predicting the most frequent class.
P-Value [Accuracy > No Information Rate]: Less than 2.2e-16,
indicating the model’s accuracy is significantly better than the no
information rate.
Kappa: Approximately 0.7992. The Kappa statistic measures agreement
between predicted and actual classifications; a value close to 1
indicates strong agreement.
Mcnemar’s Test P-Value: 4.424e-07, suggesting a significant
difference between the model’s performance on different classes.
Sensitivity (True Positive Rate): 81.97%, indicating the proportion
of actual positives correctly identified.
Specificity (True Negative Rate): 96.22%, showing the proportion of
actual negatives correctly identified.
Positive Predictive Value (Precision): 93.33%, reflecting the
proportion of positive identifications that were actually correct.
Negative Predictive Value: 89.22%, indicating the proportion of
negative identifications that were actually correct.
Prevalence of the Positive Class: 39.21%.
Detection Rate: 32.14%, indicating the rate at which the positive
class is correctly identified.
Detection Prevalence: 34.44%, showing how often the model predicts
the positive class.
Balanced Accuracy: 89.10%, a metric that considers both sensitivity
and specificity.
Implications: The model demonstrates high accuracy, sensitivity, and
specificity, indicating it performs well in both identifying the
positive class and avoiding false positives. The high positive and
negative predictive values suggest the model is reliable in its
predictions. The significant kappa value and the results of Mcnemar’s
Test underline the model’s effectiveness beyond chance or bias.
Conclusion: Overall, the model shows excellent performance in
classifying and predicting the two classes, as evidenced by the high
accuracy, sensitivity, specificity, and other statistical measures.
Precision
precision <- 0.9280 # Pos Pred Value from the output
recall <- 0.8150 # Sensitivity from the output
f1_score <- 2 * (precision * recall) / (precision + recall)
## [1] 0.8678371
Balanced Metric: The F1 score is particularly valuable because it
provides a single metric that balances the trade-off between precision
and recall. An F1 score close to 1 indicates high precision and high
recall.
Model Performance: An F1 score of 0.868 suggests that your model has
a good balance between precision and recall. This means it is fairly
accurate in classifying the positive class (class ‘0’ in your case) and
maintains a low rate of false positives and false negatives.
Contextual Evaluation: The relevance of the F1 score depends on the
specific context and requirements of your task. For example, in certain
applications (like medical diagnosis), recall might be more important
than precision, or vice versa.
Overview of the Model:
This model has been developed to predict student success and dropout
rates. Using a sophisticated machine learning approach, it aims to
provide actionable insights that can assist in enhancing educational
strategies and student support mechanisms.
Key Performance Metrics: High Accuracy (90.63%): The model correctly
predicts student outcomes with an accuracy of approximately 90.63%. This
high accuracy rate is indicative of its reliability in identifying
students at risk of dropping out or succeeding.
Sensitivity and Specificity: The model demonstrates a sensitivity of
81.97% and a specificity of 96.22%. This means it is adept at correctly
identifying students who are likely to drop out (sensitivity) while also
accurately recognizing those who are likely to succeed
(specificity).
Predictive Values: With a positive predictive value of 93.33% and a
negative predictive value of 89.22%, the model is highly effective in
its predictions. It ensures that a significant majority of its
predictions are reliable.
Balanced Accuracy (89.10%): The balanced accuracy, considering both
sensitivity and specificity, stands at 89.10%, underscoring the model’s
overall balanced performance across different categories.
Statistical Significance: The model’s performance is statistically
significant, as evidenced by a very low p-value in comparison to the No
Information Rate. This suggests that the model’s predictions are not due
to chance.
Implications for Stakeholders: Decision-Making Tool: The model can
serve as a valuable tool for educational administrators and
policymakers, providing data-driven insights to inform decisions about
student support and intervention strategies. Early Intervention: The
ability to accurately predict student outcomes can facilitate early
intervention for at-risk students, potentially improving retention rates
and academic success. Resource Allocation: By identifying trends and
patterns in student performance, the model can assist in the efficient
allocation of educational resources and support services. Continual
Improvement: The model can be an integral part of a continual
improvement process in educational settings, aiding in the assessment of
current strategies and the development of new approaches based on
data-driven evidence. Conclusion: The model is a robust, accurate, and
reliable tool that can play a critical role in enhancing educational
outcomes. Its ability to predict student success and dropout with high
precision makes it an invaluable asset for stakeholders in the
educational sector.