=Paper=
{{Paper
|id=Vol-3171/paper98
|storemode=property
|title=Statistical Analysis of the Popularity of Programming Language Libraries Based on StackOverflow Queries
|pdfUrl=https://ceur-ws.org/Vol-3171/paper98.pdf
|volume=Vol-3171
|authors=Ihor Rishnyak,Yurii Matseliukh,Taras Batiuk,Lyubomyr Chyrun,Oleksandra Strembitska,Oksana Mlynko,Viktoriia Liashenko,Andrii Lema
|dblpUrl=https://dblp.org/rec/conf/colins/RishnyakMBCSMLL22
}}
==Statistical Analysis of the Popularity of Programming Language Libraries Based on StackOverflow Queries==
https://ceur-ws.org/Vol-3171/paper98.pdf
Statistical Analysis of the Popularity of Programming Language
Libraries Based on StackOverflow Queries
Ihor Rishnyak1, Yurii Matseliukh1, Taras Batiuk1, Lyubomyr Chyrun2, Oleksandra
Strembitska1, Oksana Mlynko1, Viktoriia Liashenko1 and Andrii Lema1
1
Lviv Polytechnic National University, S. Bandera Street, 12, Lviv, 79013, Ukraine
2
Ivan Franko National University of Lviv, University Street, 1, Lviv, 79000, Ukraine
Abstract
This paper presents a statistical analysis of existing trends in the spread of programming
language libraries based on data set studies. The various problems that arise when using
specific libraries of different programming languages for certain periods, the most common is
the month, are studied and analyzed. The results of the study of existing trends in the spread of
programming language libraries, collected in the studied dataset, are presented graphically, set
key descriptive characteristics, taking into account the correlation of data. Trends in the
behavior of the studied indicators using the methods of smoothing time series are determined.
A cluster analysis of programming language libraries was performed, making it possible to
group data by clusters and form appropriate data groups for ranking programming language
libraries.
Keywords 1
Statistical analysis, information technologies, business analysis, programming language
libraries, StackOverflow queries, data processing
1. Introduction
The rapid growth in popularity of programming language libraries based on Stack Overflow queries
has not yet solved the problem of solving complex technical questions that cannot be answered through
queries on the Internet. A typical problem is when developers, looking for answers by submitting
queries in search engines, get all kinds of results, often spam or incorrect, outdated, and sometimes off-
topic. You often have to look for a blog post and then sit with the source for a long time (more than ten
minutes) to identify a way to solve a technical problem in a particular post. Stack Overflow is a place
where developers ask and get a reliable answer. Stack Overflow allows developers to improve their
level as a programmer, using the experience of others. It increases the code experience even for those
already experienced, helping others who have not been able to figure it out themselves. Stack Overflow
is the formation of future technologies as the world's future. The above proves the relevance of the study
of the popularity of libraries of programming languages, where it is crucial to analyze the composition,
structure, and issues of various queries in specific libraries each month. This study is especially relevant
for beginners who are now trying to choose a language. The problem's urgency is no less for experienced
developers to expand their knowledge in studying each subsequent programming language.
From the point of view of business analysts, this analysis can be considered the creation of a library
rating system, i.e., identifying the most significant number of queries and determining the most popular
languages. Based on the analyzed data, the business analyst will be able to assess the decline, growth,
COLINS-2022: 6th International Conference on Computational Linguistics and Intelligent Systems, May 12–13, 2022, Gliwice, Poland
EMAIL: ihor.v.rishnyak@lpnu.ua (I. Rishnyak); indeed.post@gmail.com (Y. Matseliukh); taras.batiuk.mnsa.2020@lpnu.ua (T. Batiuk);
Lyubomyr.Chyrun@lnu.edu.ua (L. Chyrun); oleksandra.strembitska.sa.2019@lpnu.ua (O. Strembitska); oxanamlunko@gmail.com (O.
Mlynko); viktoriia.liashenko.sa.2019@lpnu.ua (V. Liashenko); andrii.lema.sa.2019@lpnu.ua (A. Lema)
ORCID: 0000-0001-5727-3438 (I. Rishnyak); 0000-0002-1721-7703 (Y. Matseliukh); 0000-0001-5797-594X (T. Batiuk); 0000-0002-9448-
1751 (L. Chyrun); 0000-0003-2754-7076 (O. Strembitska); 0000-0001-9878-6846 (O. Mlynko);0000-0003-0966-7912 (V. Liashenko); 0000-
0001-6490-6221 (A. Lema)
©️ 2022 Copyright for this paper by its authors.
Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR Workshop Proceedings (CEUR-WS.org)
and invariability of the popularity of languages in 2009-2019 and offer his vision of the possible
development of specific languages.
The work aims to use the main methods of visualization, graphical display, and primary statistical
processing of numerical data presented by a sample or time series to identify trends in the studied
indicators of programming language libraries, present the nature of their trends, apply time series
smoothing methods and tabulation MS Excel. Determination by methods of correlation analysis of
experimental data presented by time sequences.
2. Related Works
Research on the popularity of programming languages, according to scientists [1-3], is one of the
components of the problem of human capital development. Having hard skills employees and acquiring
soft skills is an important task, as it allows you to solve important social [4-5], economic [6-8] and
technical [9-23] issues. Since its inception, the system we consider in this paper has provided an
opportunity to ask questions about programming and get answers to them for 12 years [24-36].
Confectioners discuss recipes in culinary forums; students discuss their questions in help groups in
telegrams; parents of these children have joint chats on Viber, where they solve problems. Older people
gather under the porches to discuss neighbors or world news, i.e., every branch of people or
professionals should have a place where he can ask his question, hear an expert's opinion, discuss a
topic or give advice. Therefore, the importance of using the StackOverflow system is beyond doubt.
Its relevance has been described in many articles [24-36] and videos on YouTube and other social
networks. Also, if you practice programming, you are interested in specific questions and decided to
enter them in the Google search. One of the first results will be the site Stack Overflow. One example
of relevance is the Wikipedia site. He reports that a 2016 study by Android developers using Stack
Overflow generated ten times more functional code (but less secure, which is a disadvantage) than
developers using official documentation [30, 37].
In researching the chosen topic, we considered the HABR website [31], which was created to publish
news and opinions related to IT and business. These libraries of programming languages will be our
attributes.
• Month is here are the day-month data on the library in the StackOverflow program;
• NLTK is the number of queries about the NLTK library (a set of libraries and programs for
symbolic and statistical processing of natural languages for English, written in the Python
programming language);
• spaCy is the number of requests for the spacy library (open-source library for advanced
natural language processing (NLP) in Python);
• Stanford-NLP is number of queries about Stanford - NLP library;
• Python is the number of queries about the Python library;
• R is number of requests for r library;
• NumPy is the number of queries about the NumPy library (python language extension);
• SciPy - the number of queries about the spicy library;
• MATLAB is the number of queries about the MATLAB library;
• Machine-Learning - the number of requests for machine learning.
In these works [31], the user described his story. For seven years, he used the system we are
discussing, and during this time, he "answered 3516 questions, asked 58, entered the hall of fame in
several languages, met many wise people, and actively used all the site's features.
The issues of the most popular programming languages under discussion and their libraries are
already discussed on the website StackOverflow [30, 37].
Is it possible to trust the answers to your questions on the site and actively use them? - After all,
users are interested in each question and will quickly correct it in case of error. The HABR website [31]
also explains that the average programmer cannot write code without a break of several hours.
Therefore, to avoid unnecessary distractions and overloads, you can have a great time with like-minded
people on StackOverflow [30, 37]. The user is set a rating by answering the question, and his
"reputation" can rise exponentially, depending on the site activity. After a reputation mark of 25,000,
the user gets access to all SO statistics and permission to store queries in the user database.
Thus, the SO system is one of the most popular among professional software developers, system
administrators, and programmers. All questions are marked with a specific topic tag (or multiple tags,
depending on the topics involved) to which the question relates. By clicking on the label, you can view
their list to select the topic that interests you. In our case, these are the themes of libraries of different
programming languages.
3. Methods
To solve the problems in this work, we will use standard methods [38-45].
The correlation field is a graph that establishes a relationship between variables, where X of each
corresponds to the value of the factor feature (abscissa), and Y - the value of the resultant feature
(ordinate) of a particular unit of observation. The number of points on the Graph corresponds to the
number of observation units. The location of the points indicates the presence and direction of
communication [38-45].
Building a correlation field is carried out mainly in the following steps: choose two variables that
change over time. Then measure the value of the dependent variable and enter the result in the table.
Then construct a coordinate plane on the X-axis to indicate the value of the independent variable and
on the Y-axis - the dependent. Then you need to mark the points of the correlation field on the Graph.
On the X-axis for the first value of the independent variable, mark a point on the Y-axis corresponding
to the value of the dependent variable. The resulting set of points is called the correlation field [38-45].
We analyze the received schedule and conclude the presence of communication or its absence.
Correlation coefficient is an indicator used to measure the density of the relationship between traits
in the correlation-regression model of linear dependence [46-52]. The absolute value of the correlation
coefficient ranges from -1 to +1.
The correlation ratio determines the correlation in any of its forms, namely in, straight or curved.
The correlation ratio can be determined to estimate the curvilinear relationship between the values of
X and Y. It always has a positive value and is in the range from 0 to + 1. The value of the zero ratios is
taken when the relationship between the features is absent [38-52].
Autocorrelation is the correlation of a function with itself shifted by a certain amount of independent
variable. The autocorrelation function graph can be obtained by plotting the correlation coefficient of
two functions along the ordinate axis and the value along the abscissa axis [38-45]. The autocorrelation
function measures the linearity of the relationship between the elements of the time series spaced apart
at x points in time. The Graph of an autocorrelation function is called a correlogram.
The correlation matrix is a table that represents the values of the correlation coefficients for different
variables. It shows the numerical value of the correlation coefficient for all combinations of variables.
It is generally used when we need to determine the relationship between more than two variables. It
consists of rows and columns that contain variables, and each cell contains coefficient values that inform
the degree of association and linear relationship between two variables [38-45]. In addition, it can be
used in specific statistical analyzes. Multiple linear regression, where we have several independent
variables and a correlation matrix, helps determine the degree of association.
The multiple correlation coefficient describes the correlation's intensity, or the relationship's degree
of closeness, between a dependent variable and several independent variables [38-45]. Its value cannot
be less than the absolute value of any partial or straightforward correlation coefficient. The primary
indicator of the closeness of the connection in multiple correlations is the coefficient of multiple
correlations, which has a value from 0 to +1.
4. Experiments
The structure of the dataset [24] is presented in the Table 1 and has ten fields, among which month,
NLTK (Natural Language Toolkit), spaCy, Stanford-NLP, Python, R, NumPy, SciPy, MATLAB,
Machine-Learning, and 132 rows for 12 years.
Table 1
The dataset structure of the programming language libraries based on StackOverflow queries
Stanford- Machine-
month NLTK spaCy NLP Python R NumPy SciPy MATLAB Learning
09-Jan 0 0 0 631 8 6 2 19 8
09-Feb 1 0 0 633 9 7 3 27 4
… … … … … … … … … …
19-Nov 72 79 14 23602 4883 1297 199 479 918
19-Dec 82 72 13 20058 4150 1118 159 349 983
Charts are used to represent data on a sheet graphically. There are several standard chart types in
Excel. Charts can be ¬placed directly on the sheet next to the data used to build the chart. Such charts
are called embedded. In addition, the chart can occupy a separate sheet in the book, which is called a
chart sheet. No matter how the chart was created, it is always linked to the sheet data. If the data changes,
the chart will be updated automatically [33]. The graphical form of data representation is called a chart.
In the form of a chart, you can provide sets of numbers, sums of money, percentages, dates, and time
values. Chart is created using the Chart Wizard, launched by the Chart Wizard button on the Standard
toolbar (Fig. 1). Output Range is a range of spreadsheet cells ¬that contains data that will be displayed
graphically or in the form of textual explanatory elements. A graphic representation of a single value is
called a data element in the chart. A row of data is a sequence of data arranged in a single row or column
of a spreadsheet and displayed graphically on a chart (Fig. 2). Typically, the value shown in the diagram
depends on another value or set of text values. Such independent values and text values are called data
categories [33].
25000
20000
15000
10000
5000
0
19-MAY
09-MAY
10-MAY
11-MAY
12-MAY
13-MAY
09-SEP
10-SEP
11-SEP
12-SEP
13-SEP
14-MAY
15-MAY
16-MAY
17-MAY
18-MAY
14-SEP
15-SEP
16-SEP
17-SEP
18-SEP
19-SEP
09-JAN
10-JAN
11-JAN
12-JAN
13-JAN
14-JAN
15-JAN
16-JAN
17-JAN
18-JAN
19-JAN
nltk spacy stanford-nlp python r numpy scipy matlab machine-learning
Figure 1: Graphical data representation of queries by date in the Cartesian coordinate system
09-Jan
19-Nov
19-Sep 09-Mar
09-May
19-Jul
19-May 25000 09-Jul
09-Sep
19-Mar 09-Nov nltk
19-Jan 10-Jan
18-Nov 20000 10-Mar
18-Sep 10-May spacy
18-Jul 10-Jul
18-May 15000 10-Sep
18-Mar 10-Nov stanford-nlp
18-Jan 11-Jan
10000
17-Nov 11-Mar python
17-Sep 11-May
5000 r
17-Jul 11-Jul
17-May 11-Sep
0 numpy
17-Mar 11-Nov
17-Jan 12-Jan
scipy
16-Nov 12-Mar
16-Sep 12-May
matlab
16-Jul 12-Jul
16-May 12-Sep
16-Mar 12-Nov machine-
16-Jan 13-Jan learning
15-Nov 13-Mar
15-Sep 13-May
15-Jul 13-Jul
15-May 13-Sep
15-Mar
15-Jan 13-Nov
14-Jan
14-Nov
14-Sep 14-Mar
14-May
14-Jul
Figure 2: Graphical data representation of queries by date in the polar coordinate system
Descriptive statistics [25-29, 32-36] provide the basis for the formation of competencies for
choosing a measurement scale, automation of data processing using different formats at the stage of
their collection, presentation of results in various forms, graphical presentation of results, calculation
of statistical distribution parameters, and evaluation of general population parameters using information
technology. It selects quantitative information necessary (or interesting) for different people. Large data
sets must be generalized or collapsed before humans can study them. It is what descriptive statistics do,
which describes, summarizes, or reduces the properties of data sets to the desired type. Descriptive
statistics are used to analyze and interpret statistical data, construct statistical distributions and calculate
the relevant numerical parameters that characterize the study population. It is used to organize
information collection, check the quality of data and their interpretation, and the image of statistical
material [25-29, 32-37]. A result of descriptive statistics shows in the Table 2.
The construction of histograms interprets the distribution data more apparent [32]. It involves
dividing the entire range of possible values of X into a finite number of intervals (in the
multidimensional case - rectangular) and counting the number of implementations that fall into each of
them (Fig. 3).
Cumulate is the curve of the interval variation series's accumulated frequencies [34]. The Graph of
the integral distribution function F (x) is compared with the cumulative and is also considered in
probability theory [34]. The concepts of histograms and cumulates are associated with continuous data
and their interval variation series [34]. Their graphs are empirical estimates of the probability density
and distribution function (Fig. 3).
The methods of smoothing time series are the method of moving average, exponential smoothing,
adaptive smoothing, and their modifications [25-29, 32-36]. They are used to reduce the influence of a
random component (random fluctuations) in time series. They make it possible to obtain more "pure"
values, which consist only of deterministic components. Some of the methods aim to highlight some
components, such as trends [25-29, 32-36]. Smoothing methods can be divided into two classes based
on analytical and algorithmic approaches.
Table 2
The dataset structure of the programming language libraries based on Stack Overflow queries
Machi
Stan- ne-
ford- MAT- Learni
Index NLTK spaCy NLP Python R NumPy SciPy LAB ng
Mean 42,70 11,85 25,54 9856,70 2411,86 514,20 112,45 651,68 264,40
Standar
d Error 2,53 1,83 1,99 541,47 149,25 34,20 6,06 34,46 21,73
Median 44,50 0,00 17,50 9651,50 2613,50 486,00 130,50 581,00 154,50
Mode 0,00 0,00 0,00 - 139,00 6,00 2,00 99,00 8,00
Standar
d
Deviatio
n 29,02 21,07 22,82 6221,07 1714,76 392,88 69,68 395,95 249,66
Sample 842,4 443,8 38701728 294039 154357, 4855,4 156776, 62327,
Variance 2 1 520,80 ,16 9,25 03 1 11 85
Kurtosis -1,23 2,15 -0,79 -1,15 -1,51 -1,32 -1,33 -1,04 -0,57
Skewnes
s 0,05 1,80 0,66 0,17 -0,06 0,22 -0,28 0,13 0,80
106,0
Range 0 79,00 79,00 22971,00 5136,00 1306,00 227,00 1516,00 981,00
Minimu
m 0,00 0,00 0,00 631,00 2,00 4,00 2,00 19,00 2,00
Maximu 106,0
m 0 79,00 79,00 23602,00 5138,00 1310,00 229,00 1535,00 983,00
5637, 1564, 3371,0 1301085, 318365, 67875,0 14844, 86022,0 34901,
Sum 00 00 0 00 00 0 00 0 00
132,0 132,0
Count 0 0 132,00 132,00 132,00 132,00 132,00 132,00 132,00
Largest
(2) 94,00 79,00 79,00 23414,00 5117,00 1297,00 223,00 1433,00 918,00
Smallest
(2) 0,00 0,00 0,00 633,00 4,00 6,00 2,00 24,00 3,00
Confide
nce
Level
(95.0%) 5,00 3,63 3,93 1071,17 295,25 67,65 12,00 68,18 42,99
The simplest way of forecasting is considered to be the approach that determines the forecast
estimate from the achieved level using the average level, average growth, and average growth rate—
extrapolation based on the average level of the series [25-29, 32-36]. When extrapolating socio-
economic processes based on the average level of the series, the predicted value is taken as the
arithmetic mean of the previous levels of the series. The reliability interval considers the uncertainty
hidden in the estimate of the mean. However, the projected indicator is assumed to be equal to the
average sample value. The approach doesn't consider that individual indicator values fluctuated around
the average in the past [25-29, 32-36]. It will also happen in the future.
Methods of analytical smoothing include regression analysis and the method of least squares and its
modifications [25-29, 32-36]. To identify the primary trend by the analytical method means to give the
studied process the same development throughout the observation period. Therefore, for 4 of these
methods, choosing the optimal function of the deterministic trend (growth curve) is essential, which
smooths out several observations.
250 Frequency Cumulative %
25,00%
200 20,00%
150 15,00%
Frequency
100 10,00%
50 5,00%
0 0,00%
9,01 9,11 10,09 11,07 12,05 13,03 14,01 14,11 15,09 16,07 17,05 18,03 19,01 19,11 Bin
Figure 3: The diagrams of the distribution data of queries – frequency and cumulate
Forecasting methods based on regression methods are used for short-term and medium-term
forecasting. They do not allow adaptation: the forecasting procedure must be repeated first with the
receipt of new data. The optimal length of the lead period is determined separately for each economic
process, taking into account its statistical instability.
5. Results
The most commonly used method is smoothing time series using moving averages [25-29, 32-36].
The algorithm for calculating the moving average is as follows [25-29, 32-36].
(1)
Algorithm for calculating the weighted average is as follows [25-29, 32-36].
(2)
5.1. Smoothing according to Kendel formulas - simple moving average
Smooth the data using the dimensions of the smoothing interval w = 3, 5, 7, 9, 11, 13, 15 are
presented in Fig. 4-Fig. 6. The smoothed data for queries about MatLab are calculated using to Kendel
formulas for the smoothing interval w = 3 (Fig. 4, a), w = 5 (Fig. 4, b), w = 7 (Fig. 4, c), w = 9 (Fig. 5,
a), w = 11 (Fig. 5, b), w = 13 (Fig. 5, c), w = 15 (Fig. 6).
1800
matlab w=3
1600
1400
1200
1000
800
600
400
200
0
16
21
1
6
11
26
31
36
41
46
51
56
61
66
71
76
81
86
91
96
101
106
111
116
121
126
131
a
1800 matlab w=5
1600
1400
1200
1000
800
600
400
200
0
101
1
6
11
16
21
26
31
36
41
46
51
56
61
66
71
76
81
86
91
96
106
111
116
121
126
131 b
1800
matlab w=7
1600
1400
1200
1000
800
600
400
200
0
101
1
6
11
16
21
26
31
36
41
46
51
56
61
66
71
76
81
86
91
96
106
111
116
121
126
131
c
Figure 4: The smoothed data for queries about MatLab using the smoothing interval w = 3 (a), w = 5
(b), w = 7 (c)
We smoothed the data using the smoothing interval w = 3, then we smoothed the obtained smoothed
data again, but use the size of the smoothing interval w = 5. We continued smoothing the obtained data
with a smoothing interval w = 7 and so on to w = 15.
1800 matlab w=9
1600
1400
1200
1000
800
600
400
200
0
101
1
6
11
16
21
26
31
36
41
46
51
56
61
66
71
76
81
86
91
96
106
111
116
121
126
131
a
2000
matlab w=11
1500
1000
500
0
101
1
6
11
16
21
26
31
36
41
46
51
56
61
66
71
76
81
86
91
96
106
111
116
121
126
131
b
1800
matlab w=13
1600
1400
1200
1000
800
600
400
200
0
101
1
6
11
16
21
26
31
36
41
46
51
56
61
66
71
76
81
86
91
96
106
111
116
121
126
131
c
Figure 5: The smoothed data for queries about MatLab using the smoothing interval w = 9 (a), w = 11
(b), w = 13 (c)
The smoothed data for queries about MatLab obtained by the smoothing data again. In Fig. 7 there
are presented the smoothed data for queries about MatLab using the smoothing interval w = 5 (w = 3)
(a), w = 7 (w = 5) (b). Fig. 8 shown the smoothed data for queries about MatLab for w = 9 (w = 7) (a),
w = 11 (w = 9) (b), w = 13 (w = 11) (c), w = 15 (w = 13) (d) according to Kendel formulas.
1800
matlab w=15
1600
1400
1200
1000
800
600
400
200
0
46
131
1
6
11
16
21
26
31
36
41
51
56
61
66
71
76
81
86
91
96
101
106
111
116
121
126
Figure 6: The smoothed data for queries about MatLab using the smoothing interval w = 15 according
to Kendel formulas
1600
matlab w=5(w=3)
1400
1200
1000
800
600
400
200
0
69
89
1
5
9
13
17
21
25
29
33
37
41
45
49
53
57
61
65
73
77
81
85
93
97
101
105
109
113
117
121
125
129
a
1600
1400
1200
1000
800
600
400
200
0
121
1
5
9
13
17
21
25
29
33
37
41
45
49
53
57
61
65
69
73
77
81
85
89
93
97
101
105
109
113
117
125
matlab w=7(w=5)
b
Figure 7: The smoothed data for queries about MatLab using the smoothing interval w = 5 (w = 3) (a),
w = 7 (w = 5) (b)
In both cases, we find for each smoothing the number of turning points and correlation coefficients
between the original values and the smoothed ones.
1500 1500
1000 1000
500 500
0 57 0
105
1
9
17
25
33
41
49
65
73
81
89
97
113
121
89
1
9
17
25
33
41
49
57
65
73
81
97
105
113
121
matlab w=9(w=7) matlab w=11(w=9)
a b
1500 1500
1000 1000
500 500
0 0
1
9
17
25
33
41
49
57
65
73
81
89
97
105
113
121
65
1
9
17
25
33
41
49
57
73
81
89
97
105
113
121
matlab w=13(w=11) matlab w=13(w=11)
c d
Figure 8: The smoothed data for queries about MatLab using the smoothing interval w = 5 (w = 3) (a),
w = 7 (w = 5) (a), w = 9 (w = 7) (a), w = 11 (w = 9) (a), w = 13 (w = 11) (a), w = 15 (w = 13) (a) according
to Kendel formulas
The correlation coefficients between the original values and the smoothed ones are calculated in
Table 3.
Table 3
The correlation coefficients between the original values and the smoothed ones
Interval w 3 5 7 9 11 13 15 5 (3) 7 (5) 9 (7) 11 (9) 13 (11) 15 (13)
Correlat.
coeffic. 0,980 0,962 0,953 0,939 0,925 0,916 - 0,977 0,971 0,965 0,958 0,953 0,950
Number of
correct
36 30 24 23 16 14 14 20 8 4 4 2 2
turning
points
5.2. Smoothing according to Pollard formulas
John Pollard's algorithm, proposed by him in 1975, is used to factorize integers [28]. It is based on
Floyd's algorithm for finding the length of the cycle in the sequence and some consequences of the
paradox of birthdays. The algorithm most effectively factored composite numbers with relatively minor
factors in the decomposition. All of Pollard's ρ-methods construct a numerical sequence, the elements
of which form a loop, starting with some number n, which can be illustrated by the arrangement of
numbers in the Greek letter ρ. It was the name for a family of methods [28].
We smooth the data for queries about R using the same dimensions of the smoothing interval (w =
3, 5, 7, 9, 11, 13, 15). It is presented in Fig. 9-Fig. 11. The smoothed data for queries about R are
calculated using Pollard formulas for the smoothing interval w = 3 (Fig. 9, a), w = 5 (Fig. 9, b), w = 7
(Fig. 9, c), w = 9 (Fig. 10, a), w = 11 (Fig. 10, b), w = 13 (Fig. 10, c), w = 15 (Fig. 11).
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Figure 9: The smoothed data for queries about R using the smoothing interval w = 3 (a), w = 5 (b), w =
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Figure 10: The smoothed data for queries about R using the smoothing interval w = 9 (a), w = 11 (b),
w = 13 (c) according to Pollard formulas
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Figure 11: The smoothed data for queries about R using the smoothing interval w = 15 according to
Pollard formulas
We smooth the data using the size of the smoothing interval w = 3, then we smooth the obtained
smoothed data again, but we use the size of the smoothing interval w = 5.
The smoothed data for queries about R obtained by the smoothing data again. In Fig. 12 there are
presented the smoothed data for queries about R using the smoothing interval w = 5 (w = 3) (a), w = 7
(w = 5) (b). Fig. 13 shown the smoothed data for queries about R for w = 9 (w = 7) (a), w = 11 (w = 9)
(b), w = 13 (w = 11) (c), w = 15 (w = 13) (d) according to Pollard formulas.
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Figure 13: The smoothed data for queries about R using the smoothing interval w = 9 (w = 7) (a), w =
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5.3. Exponential smoothing
We add all sample elements to construct exponential smoothing and multiply by a factor (1 - α). The
α takes values from zero to one, and the last element of the already created table of values for a certain
α is multiplied by α (the Sum of coefficients should be equal to 1). The following is a graph of
exponential smoothing for all required α.
Exponential smoothing queries about Machine Learning for а=0.1 (a), а=0.15 (b), а=0.2 (c), а=0.25
(d), а=0.3 (e) are presented in the Fig. 14.
We find the number of turning points and coefficients for each smoothing correlation between
original and smoothed values. The correlation coefficients between the original values and the
smoothed ones are calculated in the Table 4.
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Figure 14: Exponential smoothing queries about Machine Learning for а=0.1 (a), а=0.15 (b), а=0.2 (c),
Table 4
The correlation coefficients between the original values and the smoothed ones
Factor α 0.1 0.15 0.2 0.25 0.3
Correlation coefficient 0,958867 0,964152 0,96739 0,969568 0,971129
Number of correct
26 32 38 38 42
turning points
5.4. Median smoothing
Median smoothing queries about Python for w=3 (a), w=5 (b), w=7 (a), w=9 (a), w=11 (a), w=13
(a), w=15 (a) are presented in the Fig. 15-Fig. 17.
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Figure 15: Median smoothing queries about Python for w=3 (a), w=5(b)
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6. Discussions
6.1. Data correlation
Correlation analysis is a group of methods that can detect the presence and degree of relationship
between several parameters that change randomly [24]. Two samples (data sets) are studied in the
simplest case. Their multidimensional complexes (groups) are studied in the general case. The purpose
of correlation analysis is to determine whether one variable has a significant dependence on another
[25]. The main tasks of correlation analysis are the definition and expression of the form of analytical
dependence of the resultant trait y on the factor traits хі.
There are the following stages of correlation analysis [24, 25].
• Identifying the relationship between the signs;
• Determining the form of communication;
• Determination of strength (tightness) and direction of communication.
Advantages of correlation analysis are as following.
• Ability to create a new rule of the interaction of functions with each other;
• Estimation of the interaction of functions received strangely.
Disadvantages are as following. The results obtained using the technique can be used only in the
field of this study or close to it.
A correlation occurs when a series of values of a function (dependent variable) corresponds to the
same value of an argument (independent variable) [24].
To construct a correlation field, we considered the definition of the concept of correlation field. The
correlation field (scatter plot) is a graphical representation of the relationship between the two studied
sequences [24, 25]. Thus, it is a set of points in a rectangular coordinate system, the abscissa of each of
which corresponds to the value of the factor feature (x), and the ordinate - the value of the resultant
feature (y) of a particular unit of observation. The number of points on the Graph corresponds to the
number of observation units. The location of points on the correlation field allows you to judge the
nature of the dependence, for example, linear, parabolic, hyperbolic, logistical, logarithmic,
exponential, exponential, or no dependence [24].
Fig. 18 shows the behavior of the correlation field for queries about the python programming
language for only one month for each day. From Fig. 18 it is seen that the nature of the dependence is
linear. The dependence is described by an equation y = 1932x - 17317 with a high coefficient of
determination R² = 0,972.
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Figure 18: The correlation field for queries about Python to days during one month
The correlation field is built from the input data (x and game) in the form of a scatter plot. Analyzing
the location of points on the correlation field, we can judge the nature of the dependence, namely that
it is linear. Request dates start from 2009 and are collected until 2019 inclusive, broken down by all
months. The lowest number of requests for Python was one month of 2009 and increased with each
passing month, indicating the language's growing popularity and increased number of users. Data from
2019 to 2021 are not collected in the network date. However, analyzing the statistics, we can predict
even more significant growth in the popularity of the programming language, as there are requests for
its library. That is, the data has a growing trend.
We are determining the value of the correlation coefficient. A sample correlation coefficient is used
to quantify the closeness of the connection. The correlation coefficient characterizes the degree of
closeness of the linear dependence. In general, when some stochastic dependence relates the X and Y
values, the correlation coefficient may have a value in the range of -1 ≤ r ≤ +1 [24].
The formula for calculating the correlation coefficient is as following.
(3)
The statistical scientific sources [24-29] are recommended to use the following expression to
calculate the correlation coefficient.
(4)
The calculated correlation coefficient for queries about Python is equal to R2=0,98588536. It is a
good correlation coefficient, and it shows that there is a dependence; it is linear and quite close.
The correlation ratio is used in cases where there are following case [24-29].
• Between a pair of studied features, there is a nonlinear relationship;
• The nature of the sample data (number, density of location on the correlation field) allows their
grouping on the y-axis, and secondly, the ability to calculate "individual" mathematical expectations
within each grouping interval.
According to the preliminary construction of the correlation field, we see that the Graph is linear, so
it is impractical to calculate the correlation ratio.
To divide one of the sequences into three equal parts we divide the sequence, corresponding to the
number of queries about the python in the programming language library (Table 5).
Table 5
The divided sequence of the queries about python in the programming language libraries into three
equal intervals
1st part 2nd part 3rd part
Interval (1; 45) (45; 89) [89; 132]
Number of sample items 44 44 44
As we can see the partition is performed so that the number of sample elements at each interval is
the same, and it is equal 44. In the case of many observations, when the correlation coefficients need to
be calculated sequentially for several samples, for convenience, the obtained coefficients are
summarized in tables, which are called correlation matrices.
The correlation matrix is a square table where the correlation coefficient between the corresponding
parameters is located at the corresponding row and column intersection [24-29].
Dividing the sample into three equal parts, we build a correlation matrix (Table 6).
Table 6
The correlation matrix of the queries about python
1st part 2nd part 3rd part
1st 1
2nd 0,92230619 1
3rd 0,8602376 0,86988678 1
The formula for calculating the autocorrelation coefficient is as following [24-29].
(5)
To calculate the autocorrelation coefficient according to the formula (5). We used the CORREL
function. The autocorrelation coefficient for queries about Python is presented in Table 7. The sequence
of autocorrelation coefficients of the levels of the first, second, third, etc. orders is called the
autocorrelation function. The Graph of the autocorrelation function is called the correlogram [25-29].
Table 7
Multiple correlation coefficients for the queries about python
Lag Autocorrelation coefficients
1 0,98701089
2 0,98096642
3 0,98308662
4 0,9783225
5 0,9783225
6 0,97742187
7 0,97709153
The correlogram for the queries about python is presented in Fig. 19. The pattern of the correlogram
shows that the studied series is not stationary because in the case of a stationary time series, the
correlogram must decline rapidly.
0,988 0,987
0,986
0,984 0,983
0,982 0,981
0,980
0,978 0,978
0,978 0,977 0,977
0,976
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0,972
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Figure 19: The correlogram for queries about Python vs each lag
6.2. The cluster data analysis
To form an "object-property" table from our data, let's split the data so that the 2nd, 3rd, 4th, and 5th
columns can be considered objects. The first column will then be considered a property. To calculate
each of the properties, we use the standard formulas [53-62]. To calculate the properties in column
2016, we used only the data for queries collected from this 2016 (Table 8). The term "average" in the
Table 8 means the average number of queries in the NumPy library overall 12 months. Accordingly,
"minimum" shows the lowest number of requests during the year (for a month), and "maximum" - the
most. "Volume" - the number of lines for a given year. There are 12 of them every year, because of 12
months a year. "Fashion" is the value of a certain quantity, which occurs most often in all observations.
Since the statistics on queries changed every month and there was never one repeated for at least two
months, cannot talk about fashion, it is impossible to determine. "Median" is a number that divides the
list of attribute values into two equal parts so that there is the same number of units on both sides.
"Standard error" is the approximate standard deviation of the statistical sample. The more data points
involved in calculating the mean, the smaller the standard error [63-79]. "Standard deviation" is the
deviation of all characteristic values from their average value.
Table 8
The Normalized table "object-property"
Index 2016 2017 2018 2019
Average 13259.25 16678.92 17191.67 19861.33
Standard error 0.037773 0.026568 0.037599 0.027778
Median 13108 16620 17334.5 20047.5
Fashion #N/A #N/A #N/A #N/A
Standard deviation 580.6382 1304,687 894.8652 1939,741
Sampling variance 367789.8 1856955 873582.2 4104650
Kurtosis -0.63691 -0.25216 -1.25289 0.25504
Asymmetry 0.396782 0.09637 -0.39425 0.7177
Interval 328,5209 738.1827 506.3083 1097,492
Minimum 12424 14388 15537 17167
Maximum 14296 18935 18329 23602
Sum 159111 200147 206300 238336
Amount 12 12 12 12
Reliability level (95%) 0.083137 0.058476 0.082755 0.061138
It is one of the essential methods to help determine how much a particular value change [74-79].
The larger the standard deviation, the more comprehensive the range of changes in the values of this
value "Amount" - the total number of requests to the library for twelve months for each described year.
The "level of reliability" is the ability to reject the null hypothesis when it is correct. It is a good
possibility of error of the first kind for this task. "Sampling variance" - allows you to measure how far
random values are distributed from their average value. Larger variance values indicate more significant
deviations of the values of the random variable from the center of the distribution. "Excess" is a
numerical characteristic of the probability distribution of an objective random variable. The excess
coefficient characterizes the "steepness," i.e., the rate of increase of the distribution curve compared to
the standard curve. "Asymmetry" measures how asymmetric the distribution (skew) can be. If we talk
about the opposite concept of symmetry, the distribution relative to the center on the right and left is
ideal mirror images of each other. "Interval" - the interval between the extreme values of the feature in
the group of units. To construct a matrix of similarities (Table 9) we used formula (6) by analogy with
the previous Table 8 [53-73].
(6)
Table 9
The proximity matrix for four clusters
Cluster 1 2 3 4
1 0 1489747 508047.4 3737727
2 1489747 0 983393.4 2248031
3 508047.4 983393.4 0 3231234
4 3737727 2248031 3231234 0
The resulting proximity matrix (Table 9) is a symmetric diagonal matrix that indicates the amount
of proximity between objects. Agglomerative hierarchical cluster analysis is performed based on such
a matrix. The choice of integration strategy is determined by the approach. We chose the strategy of the
nearest neighbor. In it, the distance between two groups is defined as the distance between the two
closest elements of these groups.
After performing the cluster analysis procedure sequentially, we obtained proximity matrices for 3
(Table 10) and 2 clusters (Table 11).
Table 10
The proximity matrix for 3 clusters
Cluster 1.3 2 4
1.3 0 983393,4 3231234
2 983393,4 0 2248031
4 3231234 2248031 0
Table 11
The proximity matrix for 2 clusters
Cluster 1.3.2 4
1.3.2 0 2248031
4 2248031 0
The cluster analysis procedure starts with the proximity matrix. In it, we determine the smallest
number. It is 508047.4, located at the 1st and 3rd objects intersection. Therefore, we group the 1st and
3rd objects and create a new table. Now determine the minimum number again. This time it is at the
intersection of objects (1.3) and (2). We are grouping them again. We built a table "union-node-metric"
(Table 12).
Table 12
The union-node-metric table for programming language libraries
Step Association Node Metrics
1 1+3 d5 508047.4
2 1+3+2 d6 983393.4
3 1+3+2+4 d7 2248031
Our union-node-metric table is formed in 3 steps. In the first, there is a union of objects 1 and 3. In
the second step of objects (1,3) and 2. In the third (1,3,2) and 4. According to the steps, nodes are
formed, named d 5, d 6, and d 7, because there are four objects, and the next numbering begins after
the 4th. And the representation of the metric is the minimum value at each stage of the construction of
the table.
The constructed dendrogram for programming language libraries can help us to visualize the results
of cluster analysis in the Fig.20. We construct the dendrogram of clustering several objects manually in
the draft version and then implement it in a graphical environment. Indicators on the dendrogram on
the left represent the metric, the bottom objects, and the top point to each node separately. Drawing
horizontal lines in the plane of the dendrogram at a given height, in this case, allows you to select
individual clusters.
When interpreting the results of cluster analysis, we observe 3 clusters at level 2248031, among
which cluster 1 includes objects 1.3, the second cluster - only one object 2, and the third - only object
4. At level 983393,4 we observe 2 clusters, among which the first cluster includes three objects 1,3,2,
and the second - only one object 4. At the level of 508047,4 we observe one cluster of all elements.
7. Conclusions
In this work, we learned the basic visualization methods, graphical display, and primary statistical
processing of numerical data represented by a sample of time series.
We got acquainted with the main methods of highlighting the trend of the behavior of the studied
indicator, which is represented by the nature of its trend, using methods of smoothing time series and
presenting the results using an MS Excel spreadsheet.
Figure 20: The constructed dendrogram of programming language libraries
We also got acquainted with the methods of correlation analysis of experimental data presented by
time sequences. We learned to build a correlation field, determine the value of the correlation
coefficient, calculate the correlation ratio, plot autocorrelation functions, divide one of the sequences
into three equal parts, build a correlation matrix for them and find multiple correlation coefficients. We
also divided a given set of objects, each characterized by the same set of specific features, into separate
groups using hierarchical agglomerative cluster analysis.
A library rating system has been created, i.e., the most significant number of queries has been
identified, and the most popular language has been identified. In ranking queries in language libraries,
where the first is Python, the least popular - is spacy. The tendency of the growing popularity of all
language libraries characterizes the active development of programming and, most importantly,
people's interest in the work. The obtained data will allow experts to assess the decline, growth, and
invariability of the popularity of languages in the recent period (2009-2019) and offer their vision of
the possible development of specific programming languages.
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