A LITERATURE SURVEY ON MULTIVARIATE LINEER REGRESSION ANALYSIS (original) (raw)
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An econometric model for Linear Regression using Statistics
IRJET, 2023
This research paper discusses the econometric modeling approach of linear regression using statistics. Linear regression is a widely used statistical technique for modeling the relationship between a dependent variable and one or more independent variables. The paper begins by introducing the concept of linear regression and its basic assumptions. The univariate and multivariate linear regression models are discussed, and the coefficients of the regression models are derived using statistics. The matrix form of the Simple Linear Regression Model is presented, and the properties of the Ordinary Least Squares (OLS) estimators are proven. Hypothesis testing for multiple linear regression is also discussed in the matrix form. The paper concludes by emphasizing the importance of understanding the econometric modeling approach of linear regression using statistics. Linear regression is a powerful tool for predicting the values of the dependent variable based on the values of the independent variables, and it can be applied in various fields, including economics, finance, and social sciences. The paper's findings contribute to the understanding of the linear regression model's practical application and highlight the need for rigorous statistical analysis to ensure the model's validity and reliability.
I n Chapter 2, we learned how to use simple regression analysis to explain a dependent variable, y, as a function of a single independent variable, x. The primary drawback in using simple regression analysis for empirical work is that it is very difficult to draw ceteris paribus conclusions about how x affects y: the key assumption, SLR.4-that all other factors affecting y are uncorrelated with x-is often unrealistic. Multiple regression analysis is more amenable to ceteris paribus analysis because it allows us to explicitly control for many other factors that simultaneously affect the dependent variable. This is important both for testing economic theories and for evaluating policy effects when we must rely on nonexperimental data. Because multiple regression models can accommodate many explanatory variables that may be correlated, we can hope to infer causality in cases where simple regression analysis would be misleading. Naturally, if we add more factors to our model that are useful for explaining y, then more of the variation in y can be explained. Thus, multiple regression analysis can be used to build better models for predicting the dependent variable. An additional advantage of multiple regression analysis is that it can incorporate fairly general functional form relationships. In the simple regression model, only one function of a single explanatory variable can appear in the equation. As we will see, the multiple regression model allows for much more flexibility. Section 3.1 formally introduces the multiple regression model and further discusses the advantages of multiple regression over simple regression. In Section 3.2, we demonstrate how to estimate the parameters in the multiple regression model using the method of ordinary least squares. In Sections 3.3, 3.4, and 3.5, we describe various statistical properties of the OLS estimators, including unbiasedness and efficiency. The multiple regression model is still the most widely used vehicle for empirical analysis in economics and other social sciences. Likewise, the method of ordinary least squares is popularly used for estimating the parameters of the multiple regression model. We begin with some simple examples to show how multiple regression analysis can be used to solve problems that cannot be solved by simple regression. 89782_03_c03_p073-122.qxd 5/26/05 11:46 AM Page 73