Econometrics Chapter Summaries
2) Basic Ideas of Linear Regression: The Two-Variable Model
In this chapter we introduced some fundamental ideas of regression analysis. Starting with the key concept of the population regression function (PRF), we developed the concept of linear PRF. This book is primarily concerned with linear PRFs, that is, regressions that are linear in the parameters regardless of whether or not they are linear in the variables. We then introduced the idea of the stochastic PRF and discussed in detail the nature and role of the stochastic error term u. PRF is, of course, a theoretical or idealized construct because, in practice, all we have is a sample(s) from some population. This necessitated the discussion of the sample regression function (SRF).
We then considered the question of how we actually go about obtaining the SRF. Here we discussed the popular method of ordinary least squares (OLS) and presented the appropriate formulas to estimate the parameters of the PRF. We illustrated the OLS method with a fully worked-out numerical example as well as with several practical examples.
Our next task is to find out how good the SRF obtained by OLS is as an estimator of the true PRF. We undertake this important task in Chapter 3.
3) The Two-Variable Model: Hypothesis Testing
In Chapter 2 we showed how to estimate the parameters of the two-variable linear regression model. In this chapter we showed how the estimated model can be used for the purpose of drawing inferences about the true population regression model. Although the two-variable model is the simplest possible linear regression model, the ideas introduced in these two chapters are the foundation of the more involved multiple regression models that we will discuss in ensuing chapters. As we will see, in many ways the multiple regression model is a straightforward extension of the two-variable model.
4) Multiple Regression: Estimation and Hypothesis Testing
In this chapter we considered the simplest of the
In this chapter we introduced some fundamental ideas of regression analysis. Starting with the key concept of the population regression function (PRF), we developed the concept of linear PRF. This book is primarily concerned with linear PRFs, that is, regressions that are linear in the parameters regardless of whether or not they are linear in the variables. We then introduced the idea of the stochastic PRF and discussed in detail the nature and role of the stochastic error term u. PRF is, of course, a theoretical or idealized construct because, in practice, all we have is a sample(s) from some population. This necessitated the discussion of the sample regression function (SRF).
We then considered the question of how we actually go about obtaining the SRF. Here we discussed the popular method of ordinary least squares (OLS) and presented the appropriate formulas to estimate the parameters of the PRF. We illustrated the OLS method with a fully worked-out numerical example as well as with several practical examples.
Our next task is to find out how good the SRF obtained by OLS is as an estimator of the true PRF. We undertake this important task in Chapter 3.
3) The Two-Variable Model: Hypothesis Testing
In Chapter 2 we showed how to estimate the parameters of the two-variable linear regression model. In this chapter we showed how the estimated model can be used for the purpose of drawing inferences about the true population regression model. Although the two-variable model is the simplest possible linear regression model, the ideas introduced in these two chapters are the foundation of the more involved multiple regression models that we will discuss in ensuing chapters. As we will see, in many ways the multiple regression model is a straightforward extension of the two-variable model.
4) Multiple Regression: Estimation and Hypothesis Testing
In this chapter we considered the simplest of the