The Implementation of Machine Learning and Deep Learning Algorithms for Crop Yield Prediction in Agriculture

Bulletin of TUIT: Management and Communication Technologies
Nodir Rahimov, Dilmurod Khasanov 
2023.Vol-2(4) 
values of the dependent variable and the actual 
values of the dependent variable. In multivariate 
regression, the number of independent variables can 
vary, and the number of dependent variables can be 
more than one. In cases where there are multiple 
dependent variables, the regression equation takes 
the form: 
Y
1
= β
01
+ β
11
X
1
+ β
12
X
2
+ β
13
X
3
+ ... + ε
1
Y
2
= β
02
+ β
21
X
1
+ β
22
X
2
+ β
23
X
3
+ ... + ε
2
Y
3
= β
03
+ β
31
X
1
+ β
32
X
2
+ β
33
X
3
+ ... + ε
3
... 
Y
n
= β
0n
+ β
n1
X
1
+ β
n2
X
2
+ β
n3
X
3
+ ... + ε
n
where Y
1
, Y
2
, Y
3
, ..., Y
n
are the n dependent variables, 
X
1
, X
2
, X
3
, ... are the independent variables, β
01
, β
11
, 
β
12
, β
13
, ..., β
n1
, β
n2
, β
n3
, ... are the coefficients or 
regression weights, and ε
1
, ε
2
, ε
3
, ..., ε
n
are the error 
terms. 
Overall, the structure of multivariate 
regression involves fitting a linear equation to the 
data to model the relationship between multiple 
independent variables and a single or multiple 
dependent variables, and estimating the coefficients 
using the OLS regression method. 
2.2. Multiple Linear Regression (MLR) 
Multiple linear regression (MLR), also referred 
to as multiple regression, is a statistical approach that 
employs several explanatory variables to forecast the 
outcome of a response variable. The objective of 
MLR is to establish a linear relationship between the 
independent or explanatory variables and dependent 
or response variables. Essentially, multiple 
regression is an extension of ordinary least-squares 
(OLS) regression, as it involves more than one 
explanatory variable [8].
In the context of publishing an article, MLR can 
be a powerful tool for analyzing data and drawing 
conclusions that are supported by statistical evidence. 
For example, MLR can be used to investigate the 
relationship between various demographic factors 
and a specific health outcome, or to analyze the 
relationship between different types of marketing 
strategies and sales outcomes. To use MLR 
effectively, researchers must carefully choose their 
independent and dependent variables and ensure that 
they are measuring each variable accurately and 
consistently. They must also ensure that they have a 
sufficient sample size to achieve statistically 
significant results. Once the data is collected, 
researchers can use MLR to determine the strength 
and direction of the relationships between the 
independent variables and the dependent variable. 
They can also use MLR to create predictive models 
that can be used to estimate the value of the 
dependent variable based on specific values of the 
independent variables [8]. 
Multiple linear regression is a statistical method 
that aims to model the relationship between a 
dependent variable and multiple independent 
variables. The structure of a multiple linear 
regression model can be represented as follows: 
Y = β
0
+ β
1
X
1
+ β
2
X
2
+ ... + β
n
X
n
+ ε 
Where: 
Y is the dependent variable; 
X
1
, X
2
, ..., X
n
are the independent variables; 
β
0
is the intercept or constant term; 
β
1
, β
2
, ..., β
n
are the regression coefficients, which 
represent the expected change in Y for a one-unit 
change in X
1
, X
2
, ..., X
n
, while holding all other 
independent variables constant; 
ε is the error term, which represents the unexplained 
variability in Y that is not accounted for by the 
independent variables; 
The multiple linear regression model aims to 
estimate the values of the regression coefficients that 
best fit the data, in order to make predictions about 
the dependent variable based on the independent 
variables. The quality of the model fit can be 
assessed using measures such as the R-squared value, 
which indicates the proportion of variance in the 
dependent variable that is explained by the 
independent variables [8]. 
In practice, multiple linear regression 
models can be complex and may involve interactions 
or nonlinear relationships between the independent 
variables and the dependent variable. However, the 
basic structure remains the same, with the aim of 
modeling and predicting the relationship between a 

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Bulletin of TUIT: Management and Communication Technologies
Nodir Rahimov, Dilmurod Khasanov 
2023.Vol-2(4) 
dependent variable and multiple independent 
variables. 
2.3. Deep Neural Network (DNN) 
A deep neural network (DNN) is a particular 
type of artificial neural network (ANN) that includes 
multiple hidden layers situated between the input 
and output layers, as depicted in Figure 1. The 
process of learning in DNNs involves a repetitive 
error backpropagation procedure, which modifies 
weights to minimize the loss function's value 
through optimization functions such as pure 
propagation and stochastic gradient descent [1].
Nonetheless, increasing the depth of a neural 
network can lead to gradient vanishing or exploding, 
while increasing the number of neurons may lead to 
overfitting. To tackle the issue of gradient vanishing 
or exploding, an appropriate weight initialization 
technique that is based on the type of activation 
function can be employed. Additionally, overfitting 
can be reduced by utilizing techniques such as 
dropout and batch normalization. Furthermore, 
advancements in hardware, such as improved 
graphics processing units (GPUs), have significantly 
reduced the computation time of complex matrices 
in deep learning. DNNs that address these challenges 
can perform complex nonlinear modeling. Therefore, 
these techniques are highly effective in developing 
highly accurate machine learning models capable of 
handling complex, high-dimensional data. In 
conclusion, DNNs are a powerful tool for addressing 
complex machine learning problems, and their 
ability to learn complex non-linear mappings from 
high-dimensional data makes them highly effective 
in various fields [1]. 
Figure 1. Construction of the deep neural 
network (DNN) model [9]. 
2.4.Gradient Boosting Regressor Tree (GBRT) 
Boosting is a type of ensemble machine learning 
technique that combines multiple weak learners to 
create a strong learner, as demonstrated in Figure 2. 
Gradient boosting is one of the most popular and 
commonly utilized boosting algorithms, which 
focuses on improving the accuracy of the model by 
enhancing the predictions made by prior models [1]. 
Figure 2. The typical structure of GBRT model 
[16]. 
To start the gradient boosting algorithm, the first 
model calculates the average prediction value of the 

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Bulletin of TUIT: Management and Communication Technologies
Nodir Rahimov, Dilmurod Khasanov 
2023.Vol-2(4) 
target variables across the entire dataset and 
computes the residual. This residual is then utilized 
to train multiple decision trees that create a stronger 
model. The process of enhancing the model 
iteratively continues by obtaining the gradient of the 
residual and using it to reduce the residual even 
further in the next model. 
Gradient boosting has been found to be highly 
effective in improving the accuracy of machine 
learning models [15-17]. It can be applied to a broad 
range of data types and has been extensively utilized 
to address regression problems. Therefore, gradient 
boosting is a robust and powerful ensemble 
technique that can significantly enhance the 
prediction accuracy of machine learning models.