VIETNAM NATIONAL UNIVERSITY
UNIVERSITY OF LANGUAGES AND INTERNATIONAL STUDIES
SUBJECT: MANAGERIAL ECONOMICS
THEME: IRIS SETOSA SPECIES
Author: Nguyen Hong Nhung
Class : KTTC.SNHU22E6
Lecturer : Ph.D. Dang Ngoc Sinh
Name : Nguyen Hong Nhung
Student ID : 22043319
HANOI – 2024
Table of contents
Contents
1. ABSTRACT.................................................................................................................................................3
2. INTRODUCTION........................................................................................................................................3
3. LITERATURE BACKGROUND.......................................................................................................................4
3.1 Literature Review........................................................................................................................................4
3.2 Literature Question.....................................................................................................................................4
4. CONTENTS....................................................................................................................................................5
Economic significance of regression coefficients......................................................................................6
Statistical significance of regression coefficients......................................................................................6
Multicollinearity.......................................................................................................................................7
Testing multicollinearity phenomenon.....................................................................................................7
5. DISCUSSION..............................................................................................................................................7
6. CONCLUSION................................................................................................................................................8
7. REFERENCES.................................................................................................................................................8
2
1.ABSTRACT between other floral characteristics,
thereby improving not only the
This paper focuses on the correlation speed and reliability of taxonomic
of sepal width to that of sepal length work in botany but also contributing
in Iris setosa, a unique breed to the general understanding of
characterized by its morphology. plant structures.
Sepal width (X) and sepal length (Y)
are the two physical measurements
obtained in centimeters that are
most common as far as
distinguishing features within this
species are concerned. Biotic
attributes also show correlation with
these attributes and the knowledge 2.INTRODUCTION
of such correlations is vital to the
study of plant morphology and The species, known as iris setosa, is
taxonomy. from the well researched genus of
iris, greatly due to the unique
Through regression analysis, this structural form of the flower. Among
research determines the all the body features, Sepal width
quantitative correlation between this and Sepal length are considered the
specific metric, sepal width, to sepal most important one taking into
length in Iris setosa. The evidence consideration the structural
presented here does point to a differences among the plants and
positive linear relationship which their relation to growth and
indicates that as the width of the development. Sepal width is another
sepal expands the length of the important metric given in
sepal is inclined to also expand. The centimeters and characterizes the
derived regression equation serves width of the sepal, while sepal
as a basis for estimating sepal length shows the length of this
length from sepal width with a structure. Altogether, these traits
considerable level of confidence. are used as key reference
benchmarks required for plant
These results have profound
taxonomy and plant body shape
implications not just for botanical
analysis.
study, but for the classification of
plants as well. Through elucidating Providing an appreciation of how
specific information regarding the sepal width and length are related is
roles of expansion and insertion in significant in plant biology since
the plants under study, and by knowledge of the two helps in
placing these results within the body uncovering how the characteristics
of knowledge concerning plant affect and play a role in rendering
morphology, the study benefits the overall structure of the flower.
those who use morphology as a By investigating this relationship in
means of species identification. the context of Iris setosa given that
Besides, it offers the basis for the growth patterns are relatively
subsequent investigations stable this relationship adds onto
concerning potential interactions our understanding of the
3
morphological properties of this characteristic purple-blue color,
species as well as helping in which is used as a research object
comparative analysis with other by biologists and data scientists due
species of Iris. to its easily identifiable properties
and stable number patterns
In these research, the author wants
According to Smith et al. (1936), the
to determine whether sepal width
Iris data set, including Iris Setosa,
has a linear relationship with sepal
was generated from flower
length in Iris setosa specimens by
morphological measurements,
performing regression test. More
including the length and width of the
precisely, it aims at testing whether
sepals (petals) and sepals (sepals).
these two characteristics are linearly
This dataset has become a standard
related and, if so, to what extent the
in problem analysis, clustering, and
variation in sepal width affects sepal
online datafication.
length. In this way, the study further
advances the knowledge of plant
morphology and taxonomy, of great B, Biological characteristics of Iris
utility for botanists, horticulturalists Setosa
and anyone interested in the Geometry:
structural behaviour of flowering Research by Anderson (1935) has
plants. shown that Iris Setosa is clearly
different from species of the same
Furthermore, this study fits within genus such as Iris Versicolor and Iris
the emerging paradigm of Virginica by the following
quantitative approaches in botany characteristics:
because of the need for quantitative - Petals are shorter (usually less
techniques for enhancing the than 1.9 cm).
- The sepal is narrower, ranging from
identification and classification
2.0–4.0 cm.
precision of species. The emphasis
Geographic distribution:
of this study on Sep setosa This species is mainly distributed in
underlines the significance of the North America and Europe, where it
morphological traits as quantitative often grows on moist soil or along
indices of plant attributes for riversides. According to research by
subsequent studies on related Mabberley (2008), Iris Setosa is
species and floral characters to build highly adaptable to changing
environments, which explains its
3.LITERATURE wide distribution. This research
BACKGROUND highlights the significance of sepal
width and sepal length in
3.1 Literature Review morphological and taxonomic
studies, particularly for *Iris setosa*.
These traits are critical for
Introduction to Iris Setosa: understanding developmental
Iris Setosa, belonging to the Iris processes, environmental
genus and Iridaceae family, is a influences, and species
flower with diverse biological and differentiation. Prior studies have
structural characteristics, often utilized regression models to explore
growing in the Northern correlations between sepal
Hemisphere. This stands out for its characteristics and other plant
4
traits. Despite advancements in data across populations of Iris Setosa.
analysis, species-specific studies on Another critical question is the
*Iris setosa* remain essential to efficacy of traditional regression
provide precise insights into its models compared to modern data
morphology and taxonomy.. analysis tools, such as machine
learning techniques, in identifying
3.2 Literature Question associations between traits and
estimating fluctuations within plant
genotypes. By addressing these
It seeks to investigate how sepal questions, the research aims to
width and sepal length correlate in contribute new insights into the
Iris Setosa across varying morphological and taxonomic
environmental conditions and understanding of Iris Setosa, with
genotypic variations. The study also broader implications for plant
aims to explore the extent to which morphology studies in angiosperms.
these two morphological traits
influence and predict other plant
features such as petal size, plant
height, and overall floral structure.
Furthermore, it examines the impact
of environmental factors on the
stability of sepal dimensions and
whether these influences differ
4. CONTENTS
4.1. Data
X Y
3.5 5.1
3 4.9
3.2 4.7
3.1 4.6
3.6 5
3.9 5.4
3.4 4.6
3.4 5
2.9 4.4
3.1 4.9
3.7 5.4
3.4 4.8
3 4.3
4 5.8
4.4 5.7
3.9 5.4
3.5 5.1
5
3.8 5.7
3.8 5.1
3.4 5.4
3.7 5.1
3.6 4.6
3.3 5.1
3.4 4.8
3 5
3.4 5
3.5 5.2
3.4 5.2
3.2 4.7
3.1 4.8
3.4 5.4
4.1 5.2
4.2 5.5
3.1 4.9
3.2 5
3.5 5.5
3.6 4.9
3 4.4
3.4 5.1
3.5 5
2.3 4.5
3.2 4.4
3.5 5
3.8 5.1
3 4.8
3.8 4.6
3.7 5.3
3.3 5
Variables: Suppose we have a regression
model:
X represents the sepal width.
Y = β1 + β2X
Y represents the sepal length.
Regression model (1) using Stata,
Summarize x y:
we obtain the following rerult:
Variable Obs Mean Std. Dev. Min Max
x
y
48
48
3.441667
5.008333
.3802761
.3583849
2.3
4.3
4.4
5.8 Table 1: regression model Y = β1 +
The value of X will range from 2.3 to β2X
5.8 and 4.3 to 5.8 for Y with
standard deviations of 0.35 shows a Dependent variable: Y
fairly high level of point
Method: Least Squares
concentration
6
Date:16/11/2024 4.3. Confidence interval
Time:9:14 am for regression
Included observation: 48
coefficients
The confidence interval for the
Source SS df MS Number of obs
F( 1, 46)
=
=
48
44.57
regression coefficients is given by
Model
Residual
2.97057974
3.06608637
1
46
2.97057974
.066654052
Prob > F
R-squared
=
=
0.0000
0.4921
the following formula:
Adj R-squared = 0.4810
^β i – t a/ 2 Se( ^β i) < βi < ^β i + t a/ 2
Total 6.03666611 47 .128439705 Root MSE = .25817
n−k n−k
y Coef. Std. Err. t P>|t| [95% Conf. Interval]
x
_cons
.6611083
2.733019
.0990297
.3428582
6.68
7.97
0.000
0.000
.461772
2.042881
.8604447
3.423157
Se( ^β i)
The confidence interval for the
From the above estimation results
we obtain: intercept is calculated as:
(PRF): E(Y/X1,X2,X3)= β1 + β2X ^β 1 - t (n−2) Se( ^β 1 ) < β1 < ^β 1 + t (n−2)Se( ^β 1 )
a/ 2 a/ 2
(SRF): Y = 2.73 + 0.66X
2.73-1.95*0.34 < β1 <
4.2. Analyze regression
2.73+1.95*0.34
results
Economic significance of regression 2.067< β1 < 3.393
coefficients
- B1 = 2.73 > 0 That means that when other factors
Shows that the best price has a remain constant, the Best price is in
constant amount of 2.73 the range (2.067;3.393)
- B2 = 0.66 > 0
Similarly we have:
Inverse ratio shows that every 1 unit
0.48< β2 < 0.83
increases will increase 0.66 unit of
best price That means, other things being
equal, X1 is in the range (0.48;0.83)
Statistical significance of regression 4.4. Test the
coefficients
appropriateness of the
Test pair of hypotheses:
model.
{ β J =0
βJ ≠ 0
(j=2) Test pair of hypotheses:
H0: R2 = 0
Inspection standards: T=
^β −β
J j
T ( n−2 ) H1: R2 ≠ 0
Sⅇ ( β^ )
2
R /(2)
w α =(T :|T |>t
45
=1.95) F¿ F (2 ; 45)
0.025
(1−R 2)/(46)
Tqs2 = 6.68 → Reject H0, accept
H1→ B2 is statistically significant Domain rejected Wa = (F: F >
F0.05(2;45) = 4.977)
7
We have: F = 44.57 ∈ Wa dimensions are known to have
positive relationships. In Iris setosa
Reject H0, accept H1 these results may mean that the
Suitable model dimensions of sepals are controlled
during growth in a coordinated
R2 = 0.478 shows that the manner by genetic and
environmental influences. For
independent variable explains example, the large sepals would
47.8% of the variation in the mean stronger support of the sepals,
which, in turns, would enhance the
dependent variable
flower’s harmony and practical use.
4.5. Check the model The intercept value of means that,
for defects when the sepal width is equal to
zero, the sepal length would be 2.73
Multicollinearity
respectively. This is actually out of
Testing multicollinearity bound for Iris setosa in so far as
phenomenon sepal width is concerned, and hence
So this model is appropriate and logically not possible, but its
there is no multicollinearity presence in the context of
phenomenon because there is only 1 regression analysis is significant to
independent variable. We have cover the overall variation of the
overcome the multicollinearity different variables.
problem in the original model
As the given data shows, these
5.DISCUSSION conclusions have some implications
for morphological and taxonomical
The findings of this research are a
study of plants. Awareness of
positive linear relationship between
correlation between sepal width and
sepal width and sepal length in the
sepal length is important in species
Iris setosa since the regression
identification since shape is an
equation is Y = 2.73 + 0.66 X. It also
important factor when identifying
indicates that sepal width is directly
species in botany. In addition, this
related to sepal length since the
will offer a better understanding of
variables have tendencies to
how different Iris setosa might exist
proportionally rise as the other
or sustain itself under various
varies. More precisely, with each
environmental conditions with
increase in sepal width by 1 cm,
regard to the physical dimensions
sepal length expands by 0.66 cm.
that could in one way or the other
Concerning the two morphological
be subjected to soil factors such as
characters, the relatively high slope
type and quality, availability of light
coefficient (0.66) confirms the fact
or water ratio.
that there is a relatively strong
positive relationship between them. However, the present study has its
limitations also. The analysis is also
The positive correlation observed for
limited to a first-order contingent
this characteristic agrees with other
model, which means that it
researches carried out on plants
presupposes that changes in sepal
morphometry where floral
width are paralleled by changes in
8
sepal length in proportion. Although The study also indicates that sepal
the above assumption accords with width has some effect on sepal
the data, non-linear relationships length proving the close relationship
may be present under some between or within these attributes.
circumstances or in other species of This kind of relationship is very
Iris. However, the sepal size may important especially for researchers
also be affected by other factors not and botanists because it gives
addressed in this study including comprehensive data on patterns of
variation in genes, or change of plant growth, classification type and
environment. Future work could plant morphological aspects relating
build on this by using multivariate to different species.
analysis to include other factors
Therefore, the outcomes of this
affecting the dimensions of the
paper dovetail with knowledge
Sepal.
about the morphology of Iris setosa
Thus, the work clearly evidences and show that regression analysis
that there is a very high correlation can be valuable in discovering
between sepal width and sepal correlations between dimensions of
length in Iris setosa. Therefore, the the physical characteristics of
studies extend the knowledge of the plants. The research conducted to
morphology of the species and join support the current study can be
the global discourse on plant taken further and applied to explore
development. Molecular equation other factors which could help to
following studies are suggested, have better insight of plant
which may bring further light to morphology; for instance,
genetic and environmental factors environmental factors and genetic
that might contribute to the floral differences..
formation.
7. REFERENCES
6. CONCLUSION
UCI Machine Learning
Y = 2.73 + 0.66X Repository - Iris Data Set: This
dataset, originally compiled by
This equation shows that there is
Fisher in 1936, is widely used in
positive linear relationship between
statistics and machine learning for
sepal width and the sepal length. In
classification methods. It includes
other words, increase of the sepal
data on Iris setosa among other iris
width by 1 cm means the increase of
species. Available at:
the sepal length by about 0.66 cm
https://archive.ics.uci.edu/ml/datase
on average. The constant term,
ts/Iris
2.73, is the estimated sepal length
when sepal width is zero, although Oxford Academic - The Iris Data
such a value is not borne out of Set: In Search of the Source of
reality since it is an outlier of the Virginica: This paper discusses the
range of actual biological data of Iris historical significance and usage of
setosa. the Iris data set in statistical
research. Available at:
9
https://academic.oup.com/jrssig/arti
cle/18/6/26/7038520
International Journal of Scientific
Research in Research Paper.
Mathematical and Statistical
Sciences
https://www.researchgate.net/profile
/Shohal-Hossain-2/publication/
367220930_Classification_of_Iris_Flo
wer_Dataset_using_Different_Algorit
hms/links/
63c7bf9b6fe15d6a572a5497/
Classification-of-Iris-Flower-Dataset-
using-Different-Algorithms.pdf
U.S. Forest Service
Caring for the land and serving
people. Introduce:
https://www.fs.usda.gov/wildflowers/
beauty/iris/Blue_Flag/iris_setosa.sht
ml
Floria of North America.
Introduce the size,cm,..:
http://www.efloras.org/florataxon.as
px?flora_id=1&taxon_id=200028212
10
