Regression analysis is a quantitative research tool that is used to model and analyse multiple variables in a dependent-independent relationship in order to create the most accurate forecast. These models do not forecast the real value of the data due to uncertainty. As a result, fuzzy regression is critical in overcoming or addressing this type of problem. In this chapter, the authors presented a comparative study of LR models and LR models using fuzzy data and real experimental data. The computational results demonstrate the best linear models for the data set.
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The collection of statistical methods for evaluating the degree to which one variable is related to another is referred to as regression analysis. It comprises a variety of approaches to demonstrating and assessing multiple variables, with the primary concentration placed on the relationship that exists between dependent variables and one or more independent variables (or “predictors”) (Bhoi et al., 2022; Mekala et al., 2022a; Yadav et al., 2022). To be more explicit, regression analysis explains why the average value of the dependent variable, also known as the “criterion variable”, shifts when only one of the independent factors is altered while the others remain the same. In the fields of prediction and forecasting, regression analysis is a technique that is frequently utilized. In addition, regression analysis can be used to study the nature of the relationship between an independent variable and the dependent variables, as well as to assess whether or not the independent variable is related to the dependent variables (Sumathy et al., 2022; Alferaidi et al., 2022a; Viriyasitavat et al., 2022; Dhiman et al., 2022a). In the nineteenth century, Francis Galton is credited with coming up with the term “regression” to describe a process that occurs in biological systems. The characteristic observed was that the heights of people whose ancestors had been tall tended to regress towards the normal average as their descendants grew older (a phenomenon that is also k/a regression to the mean). Galton only thought about regression in this biotic way. However, Uday Yule and Karl Pearson later used regression in a more general statistical way in Galton's work. Galton's work inspired them (Gupta et al., 2022; Sharma et al., 2022a; Dinesh Kumar et al., 2022).
Regression can be calculated using the equations Y = a + b or X = a¢ + b¢ Y (depending on whether we're looking at Y on X, where Y depends on X, or X on Y, where X depends on Y). The value of the unknown parameters (a, b, a’, b’) can be calculated by,
Where b=
and a=Y-bX
In an environment characterized by uncertainty, fuzzy regression models are utilized in order to regulate a suitable linear relationship between a dependent variable and a number of independent variables. At first, mathematical programming methods were used to try to figure out what the parameters of an FR model were. Many years ago, various fields made extensive use of the technique of regression analysis. Tanaka, Uejima, and Asai (1980) were the ones who first presented the concept of fuzzy linear regression. The majority of our lives have been spent playing with crisp sets (Sharma et al., 2022b; Ding et al., 2022; Mekala et al., 2022b). A crisp set is one in which each component is either a member of the set or not. As an illustration, a jellybean is an example of the category of food known as confectionery. Not mashed potatoes, however. On the other hand, fuzzy sets enable elements to only be partially included in a set. The fact that the crisp set-in regression mostly does not convey any idea-related uncertainty is the primary drawback of using this method in regression. In an environment of fuzzy specificity, these kinds of problems can be dealt with in the right way. A piece of information is said to be in a fuzzy state when it does not have a distinct or well-defined border at any point in its presentation (Alferaidi et al., 2022b; Dhiman et al., 2022b; Kanwal et al., 2022).