eChapters

Fundamentally toposheet represents a kind of map in which topographic features of particular area is given details on the map features in two dimensional land surfaces. It shows both horizontal and vertical portion of the terrain with a combination of contour lines, contours, symbols, labels and related representation together in one piece of paper. Toposheet portray the shapes, location of mountains, many natural and manmade features, and the toposheet combinedly uses for extracting accurate information about particular area containing land surface features.

Q.1 In addition to the assumption of ANOVA, the other point which is given due consideration by the statistician is “The stability of variance.”

Q.2 In any investigation, if it is possible to incorporate the “randomisation procedure” then it is customary to rely on “ Randomisation” to break up any “correlation among experimental errors”

Square-Root Transformation for Counts

stabilizes the variance more effectively.

Counts of rare events, such as number of defects or of accidents tend to be distributed approximately in poisson fashion.

This chapter begins by providing an essential overview of different data transformation methods and their importance. It primarily concentrates on exploring three crucial transformation techniques: the square root transformation, log transformation, and arc sine transformation. Additionally, this chapter explores the practical application and analysis of these transformations using the R programming language.

Data Transformation

Data transformation is often needed in statistical analysis and data processing for several key reasons:

• Assumption of homogeneity of variances: ANOVA requires that the variances within each group being compared are equal. When this assumption is violated, i.e., when variances are significantly different across groups, data transformation can help stabilize these variances.

• Normality assumption: ANOVA assumes that the residuals (the differences between observed and predicted values) are normally distributed. However, real-world data often deviates from this normal distribution. Data transformation, such as log or square root transformations, can help in reshaping the distribution of data.

• Handling skewed data: In situations where the data is highly skewed, the results of ANOVA can be misleading. Transformations can reduce skewness, making the distribution more symmetric and suitable for ANOVA.

• Proportional or percentage data: When dealing with data in the form of proportions or percentages, certain transformations (like the arc sine transformation) are necessary. This is because proportions have a bounded scale (0–1 or 0–100%) and their variances are not constant across the range, which can violate ANOVA assumptions

Raster transformations involve mathematical manipulation of raster layers to generate new raster images. These transformed raster images either contain the information of interest or highlight the features which are not discernible in the original image. Transformations are also performed to preserve the essential information in reduced number of dimensions or layers. In this chapter, we are going to discuss few most commonly used transformation tools listed below:

Introduction

A vision of the industrial landscape of the future that emphasises safeguarding society and the environment has lately surfaced as the “Industry 5.0” idea. People collaborating with robotics and intelligent machines are referred to as “Industry 5.0.” By utilising cutting-edge technologies like big data, Internet of Things (IoT) and robots can help people operate more efficiently and quickly. The Industry 4.0 pillars of efficiency and automation are given a more human touch through this. It aims to combine the inventiveness and problem solving abilities of human employees with the powers of mechanisation and artificial intelligence, ultimately producing a more productive and adaptable production environment. This paradigm shift emphasises the value of human decision-making and intervention in the industrial context while addressing the drawbacks of complete automation. By fusing the strengths of both robots and humans, Industry 5.0, which is still in its early stages, has the potential to revolutionise several industries. In 1987, the United Nations Commission defined sustainability as addressing the requirements of the present without compromising the capacity of people in the future to address their issues. Sustainability is essential in Industry 5.0, the next stage of industrial development characterised by growing digitization and automation. Within this paradigm, sustainable practices reduce resource consumption, trash, and emission levels, leading to more effective utilisation of resources like materials and energy. Industry 5.0’s commitment to sustainability reduces waste, carbon dioxide emissions, and environmental impacts. Utilising green technologies and eco-friendly practices helps reduce environmental impact

• In statistics, best linear unbiased prediction (BLUP) is used in linear mixed models for the estimation of random effects. BLUP was derived by Charles Roy Henderson in 1950 but the term “best linear unbiased predictor” (or “prediction”) seems not to have been used until 1962 (Henderson, 1975, 1985).

• “Best linear unbiased predictions” (BLUPs) of random effects are similar to best linear unbiased estimates (BLUEs) of fixed effects. The distinction arises because it is conventional to talk not about estimating fixed effects but rather about predicting random effects, but the two terms are otherwise equivalent.

BLUE and BLUP are both acronyms used in statistics

• BLUE stands for Best Linear Unbiased Estimates and refers to the solutions (or estimates) associated with the fixed effects of a model.

• BLUP stands for Best Linear Unbiased Predictions and refers to the solutions (but identified as predictions) associated with the random effects of a model.

• Both BLUEs and BLUPs are linear functions of the data and have the lowest variance.

• The expected value of a mean estimate for an individual equals its true value for BLUEs.

• BLUPs are similar to BLUEs, but it is conventional to talk about estimating fixed effects but predicting random effects.

• BLUP is the standard selection method in animal breeding where the breeding values of sires are estimated based on progeny performance to select superior genotypes and to breed superior families.

Statistics has originated as a science of statehood and found applications slowly and steadily in Agriculture, Economics, Commerce, Biology, Medicine, Industry, planning, education and so on. Sir Ronald A. Fisher, (1890 – 1962), who is called “the Father of Statistics”, drew many solid conclusions

1.2 Definition

Statistics is the science which deals with the collection of data, organisation of data (or) classification of data, presentation of data, analysis of data and interpretation of data, which are known as the statistical methods.

“Statistics is the science, technology and art of creating new knowledge.”

–RA Fisher.

“By statistics we mean, aggregate of facts affected to a marked

extent by multiplicity of causes numerically expressed enumerated or

estimated according to reasonable standard of accuracy collected in a

systematic manner for a predetermined purpose and placed in relation

to each other.”

– Professor Horace Secrist

Number line

Every real number occupies a position on the number line and conversely,

every point of the line can be matched with a real number.

Absolute value

The absolute value of modules of a number is equivalent to the value of that

number ignoring the sign. For example, the absolute value for -1 is 1, and the

absolute value of +1 is also 1.The absolute value is defined by the symbol

?x?.

Computers: Input and Output Devices

3.1 Input Device

Input devices are the pieces of hardware that allow to enter or input data into

a computer.

Keyboard

• A computer keyboard serves as a data input device.

• A keyboard is a device containing keys, each of which denotes an

alphabet, number, or number instruction that may be served to a computer

to do multiple tasks.

• The keyboard is a significant input device, both computers and laptops

use keyboards to enter commands into the computer.

Mouse

• Mouse is a pointing device.

• The mouse is used to open various files and programs by directly clicking

on the various icons on the system.

• A mouse has three buttons on top and one trackball on the bottom, which

are used to select and move the mouse.

• A touchpad is provided as an alternative for the mouse on laptops, which

aids in mouse pointer movement.

4.1 Principles of Economics

• ‘Economics’ word derived from two Greek words, oikos (a house) and

nemein (to manage) means ‘managing an household’

• Microeconomics: Study of the behavior of individual, small, isolated

and disaggregated units.

• Macroeconomics: Study of groups and broad aggregates of the economy.

• Adam Smith wrote the book- “An Enquire into the Nature and Causes of

Wealth of

• Nations” or in short “Wealth of Nations” in 1776.

• Adam Smith is known as father of modern economics.

4.2 Wealth Definition - Adam smith

• Adam smith (1723 - 1790), in his book “An Inquiry into Nature and

Causes of Wealth of Nations” (1776)

4.3 Welfare Definition - Alfred Marshall

• Alfred Marshall (1842 - 1924) wrote a book “Principles of Economics”

(1890)

• Alfred Marshall defined “Political Economy” or Economics is a study

of mankind in the ordinary business of life; it examines that part of

individual and social action which is most closely connected with the

attainment and with the use of the material requisites of well being”.

4.4 Scarcity Definition - Lionel Robbins

• Lionel Robbins published a book “An Essay on the Nature and

Significance of Economic Science” in 1932.

• Robbins defined, “economics is a science which studies human behaviour

as a relationship between ends and scarce means which have alternative

uses”.

Unsupervised classification is the technique of classification of raster data in which no prior information is provided by the user. Raster data is classified based on their spectral characteristics such that the pixels having similar spectral properties in the multispectral feature space are grouped together in one class. Unsupervised classification is mainly performed by clustering algorithms. The purpose of these algorithms is to minimize within cluster variability and maximize between clusters variability. The user must interpret and label the classes after performing unsupervised classification. This method of classification requires minimum data which makes it easy and quick, but user has toput efforts in identification of the classes. This method could be useful when user doesn’t have any prior knowledge about the study area. This method removes subjectivity and enables us to get the unique classes which might be unrecognized by the user. K-means is the most commonly used method for performing unsupervised classification. In this chapter, we have discussed K- means, CLARA and unsupervised random forest method for classification of raster data in R.

Introduction

The technology behind Internet search engines is advancing quickly, and this has an impact on how individuals find the information they need online as well as how search engines improve their algorithms (N. Zafar et al. 2022). Search engines are playing a prime role in generating leads for businesses (Olbrich and Schultz, 2014), Because of this, search engines are regarded as the most recent online communication channels for dynamic marketing (Olbrich and Schultz, 2014). To examine how academic institutions (in higher education) use the web to facilitate student relations and identify how prospective students are using the Internet to research academic institutions, Will et al. conducted a study that involved the analysis of more than 3000 university websites. The web continues to be the primary research resource for prospective students, counselors, and parents. The research was undertaken (Sampath Kumar and Kumar, 2013) to determine whether or not academics utilized search engines to access scholarly content from the internet. 285 (95%) of the 300 respondents used search engines to find academic content, compared to just 5% who didn’t. To access the Ed-tech companies that are playing a role in academia, comparable assessment is crucial.

Introduction

Artificial intelligence (AI) became one of the 21st century’s most technologically disruptive innovations very quickly. The effort to be at the leading edge of AI discovery and development is becoming more intense as the field develops. The rapid advancement of artificial intelligence (AI) technology has sparked significant interest and debate across various sectors, including higher education. From personalized learning experiences to data-driven insights, AI offers a multitude of opportunities for optimizing educational processes and enriching student outcomes. In this reframed exploration, we delve into the transformative potential of AI within higher education and its multifaceted utilization across various domains. AI accelerates scientific research and knowledge discovery by analyzing vast datasets, identifying patterns, and generating insights that fuel innovation. Natural language processing (NLP) algorithms facilitate literature reviews, automate data analysis, and assist in hypothesis generation, empowering researchers to make breakthroughs across disciplines. AI-driven tools empower educators with innovative methods for teaching and assessing student progress. Automated grading systems, virtual tutors, and intelligent tutoring systems streamline administrative tasks, provide real-time feedback, and enable instructors to focus more on personalized instruction. AI streamlines administrative processes within higher education institutions, from admissions to alumni engagement. Chatbots handle inquiries, virtual assistants aid in course scheduling, and predictive analytics optimize resource allocation, enhancing operational efficiency and cost-effectiveness.

Reliability aims at assessing the accuracy and consistency of whatsoever the measuring instrument measures irrespective of whether we are measuring what we are supposed to measure or not. Whereas the validity emphasises on the question “are we measuring what we were supposed to measure?”

To clarify the difference between reliability and validity, let us take an example of instruments that measure colour intensity. Assume, an expert develops two separate instruments X and Y to measure the intensity of green and red colour, respectively. But, the commercial manufacturer wrongly tags the red colour measuring instrument as X. When someone uses this wrongly tagged instrument for measuring the green colour intensity, whatever intensity values the instrument yields are reliable but not valid. It is so because the instrument is measuring red colour intensity accurately (hence data is reliable) but it is not measuring what it was supposed to measure –the green colour intensity (hence data is not valid).

5.1 Introduction
One of the main methods for cost avoidance and prevention is value engineering/ value analysis. “Society of American Value Engineers (SAVE)” states that value Analysis is the systematic use of known procedures which determine the function of a product or service, define a monetary value for the function, and provide the essential function reliably at the lowest overall cost. If these are applied to a new product, it is called value engineering. By analysing the function of any product, material part, component, system, or service, it is possible to find extraneous expenditures connected with them and effectively remove them without compromising the product’s quality, functional dependability, or ability to provide services. The principles and steps of value analysis/ value engineering will supplement the effort of design thinking.
5.2 Symptoms for Introducing Value Analysis (VA)
If one or more of the following symptoms exist, starting a VA programme is expected to yield very positive effects.
i. Sales of the company’s products are declining.
ii. The prices of the products of the company are greater than those of the products of its rivals.

Variable is any character or attribute of the given object/set of objects which varies from object to object or from one point of time to another point of time. For example height of individuals is a variable; it varies from person to person.  Kerlinger (1973) defined variable as a symbol to which numerals or values are assigned.

Importance of variables: In previous sections, we discussed about formulating the research problem and development of research hypothesis. Variables are the building blocks of any scientific research problem and research hypothesis. When we consider a hypothesis to be relational hypothesis, we mean that it make claims about relationship between two or more variables. When we test hypothesis, as such we do not test the hypothesis, rather we test the significance of hypothesised relationship between two or more variables. Since variables play central role in observation, measurement and testing of relationship, it is of prime importance to understand the meaning of variables, different types and the way we define these variables.

Q.1 A sampling procedure in which the units are selected with probability proportional to their some size measure, is known as sampling procedure with probability proportional to size (P.P.S.) Notations: Let there be a population of N units say Yi , (i = 1,2, ......... N), YN with their selection probabilities Pi (i=1, 2........... , N). Here Pi ? Pj V i ? J. = 1, 2, .............. N. Let yi , (i = 1, 2, ...................n) be the sample drawn from the population with probability of selection pi (i = 1, 2 -, n).

Vector data analysis is performed to convert raw input vector data to output that provides new and meaningful information which ultimately supports decision making and disclose hidden patterns. There are various techniques to analyse vector data like buffering, intersect, union, and so on. Some of the most commonly used techniques with their R-code examples are explained in this chapter.

First of all, you need to import all the packages which are required for performing this exercise. These packages include rgdal and sp for importing and re-projecting vector data as well as raster and rgeos for performing vector analysis operations.

Vector data consists of points, lines and polygons with x, y coordinates known as vertices representing the geographic location i.e. latitude and longitude. Vector data depicts the shape of the spatial feature. Points consist of single x, y locations. Examples of points are tower location, sampling location, etc. Lines represent 1 – dimensional features like roads, streams, etc., and are composed of many or at least two connected points or vertices. Polygons denote 2 – dimensional features like boundaries with three or more vertices that are connected and closed. The vector data are represented in the following figure (fig. 5.1).