Case Study Regression

We consider the problem of regression when study variable depends on more than one explanatory or independent variables, called as multiple linear regression model. This model generalizes the simple linear regression in two ways. It allows the mean function () E y to depend on more than one explanatory variables and to have shapes other than straight lines, although it does not allow for arbitrary shapes.

Regression models form the core of the discipline of econometrics. Although econometricians routinely estimate a wide variety of statistical models, using many different types of data, the vast majority of these are either regression models or close relatives of them. In this chapter, we introduce the concept of a regression model, discuss several varieties of them, and introduce the estimation method that is most commonly used with regression models, namely, least squares. This estimation method is derived by using the method of moments, which is a very general principle of estimation that has many applications in econometrics. The most elementary type of regression model is the simple linear regression model, which can be expressed by the following equation: y t = β 1 + β 2 X t + u t. (1.01) The subscript t is used to index the observations of a sample. The total number of observations, also called the sample size, will be denoted by n. Thus, for a sample of size n, the subscript t runs from 1 to n. Each observation comprises an observation on a dependent variable, written as y t for observation t, and an observation on a single explanatory variable, or independent variable, written as X t. The relation (1.01) links the observations on the dependent and the explanatory variables for each observation in terms of two unknown parameters, β 1 and β 2 , and an unobserved error term, u t. Thus, of the five quantities that appear in (1.01), two, y t and X t , are observed, and three, β 1 , β 2 , and u t , are not. Three of them, y t , X t , and u t , are specific to observation t, while the other two, the parameters, are common to all n observations. Here is a simple example of how a regression model like (1.01) could arise in economics. Suppose that the index t is a time index, as the notation suggests. Each value of t could represent a year, for instance. Then y t could be household consumption as measured in year t, and X t could be measured disposable income of households in the same year. In that case, (1.01) would represent what in elementary macroeconomics is called a consumption function.

The following technical paper presents two case studies pertaining to Linear Regression analysis. Case study 1 presents the use regression analysis in the form of simple regression and multiple regression and elaborates the practical use of regression analysis in the decision making process of which predictor variables should be used in the analysis. Case study 2 presents the use of linear regression techniques in studying the September Sea Ice extent in the Arctic Ocean from year 1979 – 2012. This case study also shows the use of quadratic regression to represent the data with a continuously variable slopes in the regression equation.

Statistics for Biology and Health, 2010

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it also appears as one of the default data sets in Minitab software). The response variable is y (that is, "quality") and we wish to find the "best" regression equation that relates quality to the other five parameters.

Journal of Applied Mathematics and Physics, 2023

The development of prediction supports is a critical step in information systems engineering in this era defined by the knowledge economy, the hub of which is big data. Currently, the lack of a predictive model, whether qualitative or quantitative, depending on a company's areas of intervention can handicap or weaken its competitive capacities, endangering its survival. In terms of quantitative prediction, depending on the efficacy criteria, a variety of methods and/or tools are available. The multiple linear regression method is one of the methods used for this purpose. A linear regression model is a regression model of an explained variable on one or more explanatory variables in which the function that links the explanatory variables to the explained variable has linear parameters. The purpose of this work is to demonstrate how to use multiple linear regressions, which is one aspect of decisional mathematics. The use of multiple linear regressions on random data, which can be replaced by real data collected by or from organizations, provides decision makers with reliable data knowledge. As a result, machine learning methods can provide decision makers with relevant and trustworthy data. The main goal of this article is therefore to define the objective function on which the influencing factors for its optimization will be defined using the linear regression method.

An important objective in scientific research and in more mundane data analysis tasks concerns the possibility of predicting the value of a dependent random variable based on the values of other independent variables, establishing a functional relation of a statistical nature. The study of such functional relations, known for historical reasons as regressions, goes back to pioneering works in Statistics.

Data collected from Kelly Blue Book for several hundred 2005 used General Motors (GM) cars allows students to develop a multivariate regression model to determine car values based on a variety of characteristics such as mileage, make, model, engine size, interior style, and cruise control. Students learn to look at residual plots to check for heteroskedasticity, normality, autocorrelation, and multicollinearity as well as explore techniques for variable selection and develop specially constructed variables.