Linear Regression

THIS GOOD FOR READ AND PRACTICE

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.

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.

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.

IZA World of Labor, 2017

Causal relationships are most valuable for policy advice and interventions, but interpreting a linear regression model as a causal relationship is challenging and requires strong assumptions. Specification of a linear regression model is not always straightforward because there is no simple, hard rule that prescribes how to choose an appropriate specification. Specification of a regression model requires care and statistical testing, particularly if estimates of interest appear very sensitive to the specification used or to the set of explanatory variables included. Using linear regression to establish empirical relationships Linear regression is a powerful tool for estimating the relationship between one variable and a set of other variables

Critical Care, 2003

The most commonly used techniques for investigating the relationship between two quantitative variables are correlation and linear regression. Correlation quantifies the strength of the linear relationship between a pair of variables, whereas regression expresses the relationship ...

Rachev/Probability, 2010

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.