8.1 Introduction to Multiple Linear Regression

In the previous chapter, we covered the concepts of multiple linear regression and polynomial linear regression. There, we defined regression as the prediction of continuous values; and in the case of multiple linear regression, there are multiple independent variables and a single dependent variable. If Y is a dependent variable whose value depends on X1, X2, X3,…, Xn independent variables, then mathematically, multiple linear regression is represented by Equation (8.1).

where b0 is the constant and b1, b2, …, bn are the coefficients. Each of the coefficients represents the change in the dependent variable due to the per unit change in the independent variable value. Let us move ahead and implement a multiple linear regression model in Python.

8.1.1 Understanding Dataset and Problem Statement

Let us consider the dataset of 50 advertisement agencies in India. A few instances of this dataset are shown in Table 8.1. The goal is to predict the agency's profit based on different parameters – Print Media Expenses, Social Media Expenses, Outdoor AD Expenses, and City or Location. All the figures mentioned in this dataset is in INR (Indian rupees).

The dataset used in this chapter is derived from the SuperDataScience dataset by Kirill Eremenko and his team. A big thanks to SuperDataScience for granting us permission to use and reference the dataset in this book. You can find it at https://www.superdatascience.com/pages/machine-learning.

1.1 Introduction

“Thermodynamics” is the branch of science that deals with the macroscopic properties of matter. In this branch of physics, concepts about heat and work and their inter-conversion, energy and energy conversion, and working principle of heat engines with their efficiency are mainly discussed. The name “thermodynamics” was originated from two Greek words: “therme” means “heat” and “dynamics” means “power” or “energy”. Thus, matter related to heat and energy is primarily paid attention in this subject. Further, it is believed that the term “thermodynamics” arises from the fact that the macroscopic thermodynamic variables used to describe a thermodynamic system depend on the temperature of the system.

Thermodynamics is the branch of physics in which the system under investigation consists of a large number of atoms and molecules contributing to the macroscopic matter of the system. The average physical properties of such a thermodynamic system are determined by applying suitable conservation equations such as conservation of mass, conservation of energy, and the laws of thermodynamics in equilibrium. The equilibrium state of a macroscopic system is achieved when the average physical properties of the system do not change with time and the system is not driven by any external driving force during the course of investigation. The interrelationships among the various physical properties are established with the help of associated thermodynamic relations derived from the laws of thermodynamics. These average (macroscopic) properties of thermodynamic systems are determined from the macroscopic parameters such as volume 𝑉 , pressure 𝑃 , and temperature 𝑇 , which do not depend on the detailed positions and ocities of the atoms and molecules of the macroscopic matter in the system. These macroscopic quantities are called thermodynamic coordinates, variables or parameters. Further, these macroscopic properties depend on each other. Therefore, from the measurements of a subset of these properties, the rest of them can be calculated using the associated thermodynamic relations.

The ideology of Marxism–Leninism seemingly contradicts competition, yet competition was prevalent in former communist countries to foster productivity and economic growth. The Stakhanovite movement, originating in the Soviet Union, incentivized laborers to excel as an economic propaganda tool, while also honoring them as socialist heroes but also penalizing dissent as a political propaganda tool. Competition extended to managers of state-owned enterprises (SOEs) vying for government resources. Consumer competition arose from pervasive shortages, driving black market economies. Underground enterprises, which were protected from competition, resisted economic reform from a planned economic system to a more market-oriented system to maintain their privileged status. Post-World War II, some SOEs adopted market-based approaches, competing domestically and globally. This chapter argues that such forms of competition emerge when humans struggle for survival amid perceived inequalities in the existing system, prompting them to seek opportunities and thrive.

Machine learning (ML) is one of the most upcoming knowledge areas transforming the world. It is a dynamic and transformative field that has the potential to reshape the way we interact with technology and the world around us. In the book, Machine Learning with Python: Principles and Practical Techniques, author Parteek Bhatia offers an insightful and hands-on approach to demystifying this complex subject.

In a world where ML plays an increasingly central role in our lives, understanding its principles and practical applications is essential. In this book, numerous algorithms are explained in detail, assuming no previous knowledge of readers. All these algorithms are widely used in the practicing world and research areas. This book is an invaluable resource for beginners and those looking to deepen their knowledge in the field.

Parteek Bhatia takes the reader on an engaging journey, starting from the basics and gradually building up to more advanced concepts. What sets this book apart is its focus on practicality. The book covers various ML techniques, from data pre-processing and regression to classification, clustering, and association mining. Each concept is illuminated with detailed Python implementations, allowing you to see firsthand how these algorithms work and how they can be applied to real-world problems. It also delves into more advanced topics like artificial neural networks, deep learning, convolutional neural networks, recurrent neural networks, and genetic algorithms. This comprehensive approach equips you with the tools and knowledge to tackle complex ML challenges.

Parteek Bhatia's passion for the subject and dedication to making it accessible shines through every chapter. This book is not just a collection of information; it is a learning adventure. It takes the reader from a beginner to a confident practitioner, ready to take on the exciting and everevolving world of ML.

Whether you are a student, a professional, or simply someone eager to explore the possibilities of ML, this book will be your trusted guide. Machine Learning with Python is your gateway to unlocking the potential of this fascinating field.

I commend Parteek Bhatia for his commitment to creating this educational masterpiece. As you embark on your journey through the captivating realm of ML, I encourage you to embrace the concepts, put them into practice, and let your curiosity and creativity flourish.

5A Saha ionization equation

At a high enough temperature and/or density, the atoms in a gas suffer collisions due to their high thermal energy, and some of the atoms get ionized, making an ionized gas. In this process, a number of electrons that are normally bound to the atom in orbits around the atomic nucleus become free and thus form an independent electron gas cloud coexisting with the surrounding gas of atomic ions and neutral atoms. These ionized atoms and electrons generate an electric field that causes motion of the charges, and a current is generated in the gaseous medium. This current produces a localized magnetic field. The state of matter thus created is called plasma. In thermal equilibrium, the ionization state of such a gaseous system is related to the ionization potential, temperature, and pressure of the system. Thus, the Saha ionization equation. expresses how the state of ionization of any particular element in a star changes with varying temperatures and pressures. This equation takes into account the combined ideas of quantum mechanics and statistical mechanics for its derivation and is used to explain the spectral classification of stars. This equation was developed by the Indian astrophysicist Prof. Meghnad Saha in 1920. 5A.1 Derivation of Saha ionization equation According to Prof. M. N. Saha, the temperatures in the interior of stars are extremely high, and the elements present there are mostly in the atomic state. Saha argued that under the prevailing conditions inside the stars, atoms move very rapidly and undergo frequent collisions. In the process of such collisions, valence electrons are stripped off from their orbits. This is referred to as thermal ionization and is accompanied by electron recapture to form neutral atoms. The degree of such thermal ionization depends on the temperature of the star. Using the Saha ionization equation, a general relation between the degree of thermal ionization and the temperature can be obtained from the statistical description of plasma in thermodynamic equilibrium.

This chapter aims to provide conceptual clarity on animals’ current legal status by addressing the long-debated question of whether they can have legal rights. By taking a legal positivist approach to legal rights, I suggest that there are no conceptual barriers to animal legal rights – whether we draw on the interest or the will theory of rights. Furthermore, by considering an example of animal welfare legislation that recognises the ‘intrinsic value’ of animals, we see evidence that certain animals already have legal rights. Nevertheless, even the strongest animal welfare laws are replete with exemptions that protect the interests of human individuals and industries that subject animals to poor levels of welfare or outright cruelty. As such, the legal rights that animals do have are weak. Finally, the chapter addresses three counters to the claim that animals have legal rights: welfare, enforcement, and personhood objections. With none of these objections posing a fatal challenge to animals’ legal rights, we can move on to the next chapter to consider what, precisely, is in the way of animals’ greater legal inclusion if not their rightlessness per se.

9.1 Introduction to Classification

We rely on machine learning (ML) to make critical decisions or predictions in the modern world. It is very important to understand how computers by using ML make these predictions. Usually, the predictions made by ML models are classified into two types, i.e., classification and regression. The ML models use various techniques to predict the outcome of an event by analyzing already available data. As machines learn from data, the type of training or input data plays a crucial role in deciding the machine's capability to make accurate decisions and predictions. Usually, this data is available in two forms, i.e., labeled and unlabeled. In label data, we know the value of the output attribute for the sample input attributes, while in unlabeled data, we do not have the output attribute value.

For analyzing labeled data, supervised learning is used. Classification and regression are the two types of supervised learning techniques used to predict the outcome of an unknown instance by analyzing the available labeled input instances. Classification is applied when the outcome is finite or discrete, while the regression model is applied when the outcome is infinite or continuous. For example, a classification model is used to predict whether a customer will buy a product or not. Here the outcome is finite, i.e., buying the product or not buying. In this case, the regression model predicts the number of products that the customer may buy. Here the outcome is infinite, i.e., all possible numbers, since the term quantity refers to a set of continuous numbers.

3A Temperature in Thermodynamics

For an infinitesimal reversible process, a combination of first and second laws of thermodynamics results

where 𝑌 𝑑𝑋 denotes the generalized expression for work done by the system, 𝑑𝑆 is the change in entropy, and 𝑑𝑈 is the change in internal energy of the system. Equation (16) leads to the definition of temperature 𝑇 as

Thus, equation (17) indicates that the temperature at any point depends on the slope of the 𝑆 − 𝑈 curve. If the slope of this curve (point 𝐴 in Figure 3A.1) is positive, the temperature will be positive. On the other hand, the temperature will be negative for the negative slope of the curve (point 𝐶 in Figure 3A.1).

The book Heat and Thermodynamics: Theory, Problems, and Solutions is an informal, readable introduction to the basic ideas of thermal physics. It is aimed at making the reader comfortable with this text as a first course in Heat and Thermodynamics. The basic principles and phenomenological aspects required for the development of the subject are discussed at length. In particular, the extremum principles of entropy and free energies are presented elaborately to make the content of the book comprehensive. The book provides a succinct presentation of the material so that the student can more easily determine the major objective of each section of a particular chapter. In fact, thermal physics is not the subject in physics that starts with its epigrammatic equations—Newton’s, Maxwell’s, or Schrodinger’s, which provide accessibility and direction. Instead, it (thermodynamics) can be regarded as a subject formed by the set of rules and constraints governing interconversion and dissipation of energy in macroscopic systems. Further, the syllabus of statistical mechanics for graduate students has changed significantly with the introduction of National Education Policy 2020.

Thermal physics has established the principles and procedures needed to understand and explain the properties of systems consisting of macroscopically large numbers of particles, typically of the order of 1023 or so. Examples of such collections of systems include the molecules in a closed vessel, the air in a balloon, the water in a lake, the electrons in a piece of metal, and the photons (electromagnetic wave packets) emitted by the Sun. By developing the macroscopic classical thermodynamic descriptions, the book Heat and Thermodynamics: Theory, Problems, and Solutions provides insights into basic concepts and relationships at an advanced undergraduate level. This book is updated throughout, providing a highly detailed, profoundly thorough, and comprehensive introduction to the subject. The laws of probability are used to predict the bulk properties like stiffness, heat capacity, and the physics of phase transition, and magnetization of such systems.

8.1 INTRODUCTION [LO1]

In simple words, the application of a torque on a prismatic member causes twisting or torsion. This causes shear stress if a torque alone is applied. However, this is rarely true in practical cases. A circular bar, used to transmit torque between a prime mover and a machine, is a typical example of a torsion member. However, in many applications, a torque along with a bending moment and axial loading are applied, and there we need to combine these effects and find the principal stresses. A typical example of such combined stresses is a propeller shaft. Torsional problems are important in many applications both in industry and in our daily life. Therefore, we consider torsion alone in this chapter in some detail.

Torsional problems for circular members are generally solved assuming that plane sections normal to the axis of the bar remain plane even after twisting. This assumption was first made by Coulomb intuitively in 1784, and he came up with a correct usable equation for members with circular sections. However, this assumption does not apply to bars with a noncircular cross-section. Navier attempted to solve torsional problems with noncircular sections using Coulomb's assumption and came up with an erroneous solution. The correct solution was provided by St. Venant in 1853 using a warping function. Much later, in 1903, Prandtl came up with a membrane analogy method that could solve problems with any complicated cross-section. First, we shall consider torsional problems with circular cross-sections.

8.2 TORSION OF MEMBERS WITH CIRCULAR CROSS-SECTION [LO2]

The torsion analysis of members with a circular cross-section starts with simplified assumptions made by Coulomb. In order to establish a relation between the applied torque and shear stress developed and the angle of twist in such cases, the following assumptions are made:

• 1. Material is homogeneous and isotropic.

• 2. Plane sections perpendicular to the axis of a circular member remain plane after twisting. No warping or distortion of the parallel planes occurs.

11.1 INTRODUCTION [LO1]

Stresses developed at the contact between two loaded elastic bodies are generally localized and most machine parts or structures are designed based on the stresses in the main body. However, there are many important machine members where the localized stresses developed at the contact between curved surfaces with initially limited contact area play an important role in their design. Ball or roller bearings, gears, cams, and valve tappets of internal combustion engines are some of the examples of machine parts where contact stresses must be taken into account in order to predict their failure probability.

The localized contact stresses that develop between two curved bodies as they are loaded with small deformations are often referred to as Hertzian stresses, following the work of H. Hertz (1881), who first solved these contact problems elegantly more than a century ago. Since then the topic has received a good deal of attention by the researchers due to its importance in engineering practice and science. Much work has been done on the stress distribution at the Hertzian contact surfaces and sub-surfaces. Ball bearings and gear teeth often fail by pitting. Hertzian stress analysis can precisely locate the depth at which maximum shear stress occurs where cracks may initiate and propagate leading to failure. Thus, a remedy to such failures may be prescribed in terms of limiting stresses. In many rolling contact problems, failure occurs with the initiation of a tiny crack that eventually grows due to repeated contacts. Analysis of crack initiation and growth is often based on Hertzian stress analysis. In this chapter, we shall consider the basics and application of contact stress analysis, beginning with some basic elasticity theory necessary for such analyses.

Legal personhood is the status accorded those, like humans, who are recognised as the subjects of the legal system. As such, many argue that we can address animals’ weak legal position by having them recognised as legal persons. This chapter first considers what legal personhood is and highlights how this concept has been heavily influenced by metaphysical accounts of personhood that privilege characteristics associated with the ‘archetypal’ human. Through a discussion of cases involving animal plaintiffs, the chapter shows how a range of different – and, at times, conflicting – conceptions of personhood have influenced the courts’ understanding of legal personhood. In addition to the judicial inconsistency that legal personhood seems to invite, we see evidence of how particular conceptions of personhood have been operationalised to exclude animals (conceptions that also serve to further marginalise vulnerable human groups). This leads the chapter to conclude that legal personhood is not a desirable solution to animals’ lack of legal inclusion. More than this, the chapter argues that a concept like personhood should nor underpin legal subjecthood for any being, human or otherwise.

Through this chapter, I explored life in a competitive arena during socialist mass movements in North Korea. Since liberation from Japanese rule at the end of World War II, North Korea has implemented mass movements to increase labor productivity, known as "Socialist Efforts toward Competition Movements." These movements have permeated various settings, including individuals, workplaces, enterprises, and cooperative farms. The Chollima movement, initiated in December 1956, symbolizes North Korea’s path toward economic development. It has promoted labor competition through mass movements such as "Speed War" and "Learning to Follow Hidden Heroes." Socialist mass movements influenced my daily life, fostering competition in schools and workplaces. Through the lens of my lived experiences, I share stories covering my life journey from North to South Korea, historical backgrounds of North Korea’s competition movements, a comparison analysis before and after the North Korean Famine in the mid-1990s, and characteristics of competition in North Korean society.

2.1 MATHEMATICAL PRELIMINARIES [LO1]

In any scientific or engineering field of study, knowledge of some mathematical techniques and methods are essential. Solid mechanics is no exception. To develop proper formulation methods and solution techniques for elasticity problems, it is necessary to have an appropriate mathematical background. In this chapter, we shall discuss Cartesian tensors, which have a special significance in the discussion of stress, strain, and displacement fields, and their manipulation. Other mathematical details will be discussed as and when they are required in solving different problems.

Tensors may be defined in a number of ways. One simple definition is that a tensor is a physical quantity that is governed by certain transformation laws when the coordinate system is changed. A tensor is invariant under any change of coordinate system, but its components along the coordinate axes change with the changed coordinate system. Tensors of order zero are called scalars. Common examples of scalars are temperature, density, Young's modulus, or Poisson's ratio. They have a single magnitude at each point in space, and they are invariant with coordinate transformations. A typical example of scalars is often taken as temperature T at a point in space with coordinates (x, y, z) represented as T(x, y, z). Temperature at the same point does not change if we choose a different coordinate system (x′, y′, z′) represented as T′(x′, y′, z′) and we may say

T=T′. (2.1.1)

Tensors of first order are vectors, and we know that a vector has a magnitude and a direction. A typical example of a vector is a velocity vector V. It is sometimes taken as a convention to represent a vector by a bold letter. Consider the velocity vector V in (x, y, z) coordinate system.

Little attention has been paid to competitive dynamics from a political perspective, despite numerous instances of political competition across cultures and systems. In liberal democratic societies, political competition is legalized, allowing citizens to elect leaders who represent their ideas. Conversely, in totalitarian societies, citizens lack voting rights, and political authority is not challenged through democratic means. However, political competitions still occur among ruling elites, often through purges to seize power. This chapter explores political competition, particularly in totalitarian regimes, where purges eliminate rivals among ruling elites. The collapse of such regimes has marked an evolution toward freedom and equal opportunities for all individuals, regardless of background, which aligns with Darwin’s theory of evolution. Highlighting the lack of research on political competitions from an evolutionary psychology perspective, this chapter underscores the need for future research on human emotions and competitive behaviors in the political arena.