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【Econometrics】Ordinary Least Square (OLS)

The OLS Formula If you choose an option to add a trend line in excel or other programs like Python, SAS or R, they are essentially plotting OLS-dervied coordinates. In this section, I explain in detail what the computer does when it tries to find the line that best fits the data points. The basic idea is very simple. The computer decomposese the actual value of an observation ($Y$) into fitted v..

Study Note/Econometrics 2020. 7. 16. 16:24

【Econometrics】The Fitted Line : Estimation of Beta

The Fitted Line Estimation of $\beta$ It is important at this point to note that the value of our estimates depends on the particular sample we drew from the population (If drawn samples are significantly different from each other, the estimates will be different). Using another sample of $P$ points would have resulted in different estimates values. To make this point clear let's consider an exa..

Study Note/Econometrics 2020. 7. 10. 16:28

【Econometrics】The Fitted Line : Basic Idea

The Fitted Line Basic Idea In practice, we only see the observations plotted in Fig 5. In order to derive the shape of the line that might have generated these points, we can use $P_1$-$P_4$ points to draw a line which is an approximation to the $Y = \beta_1+\beta_{2}X + u$. We write this line as $\hat{Y} = b_1+b_{2}X$, where the hat ("^") represents the fitted variable, lower case $b$'s represe..

Study Note/Econometrics 2020. 7. 10. 15:32

【Econometrics】Data Generating Process

Data Generating Process Suppose that a variable $Y$ is a linear function of another variable $X$, with unkown parameters $\beta_1$ and $\beta_2$ that we wish to estimate, as displayed in Fig. 1. Suppose that we have 4 observations with $X$ values as shown. If the relationship were an exact one, the observations would lie on the straight line and we would have no trouble obtaining accurate estima..

Study Note/Econometrics 2020. 7. 10. 05:41

【Econometrics】Proof of Properties of Estimator

In the last post, we went through the properties of estimators. This post contains a mathematical proof of two properties: Unbiasedness and Consistency 【Econometrics】Estimator As "econometrics" means to "measure" "economics", our goal is to derive the best estimate on an economic relationship. Then, what is the "best" estimator? Properties of Estimator 1. Unbiased (불편;.. quant-curiosity.tistory...

Study Note/Econometrics 2020. 6. 27. 06:02

【Econometrics】Estimator

As "econometrics" means to "measure" "economics", our goal is to derive the best estimate on an economic relationship. Then, what is the "best" estimator? Properties of Estimator 1. Unbiased (불편; 편향되지 않은) Equation 1 $$ E(\bar{X}) = \mu $$ We prefer that estimator be "accurate" or "unbiased" : meaning the estimator will reflect the population parameter as closely as possible. Estimator reflects t..

Study Note/Econometrics 2020. 6. 27. 05:11

【Econometrics】Derivatives

Derivatives From today, we will delve into mathematics and statistics used for econometric analyses. First, we begin with a review of derivatives. Motivation Regression line, which represents the relationship between A and B, we need derivatives. Roughly, the idea is to find the line that best fits the actual observations and the predictions generated by your statistical model set-up. Definition..

Study Note/Econometrics 2020. 6. 17. 08:36

【Econometrics】Data Types

Data TypesIn the last post, we went through a couple of examples of econometric questions. In this post, we will walk through three major data types used for econometric analyses. I. Cross-Sectional DataCross-Sectional data is data which describes the activities of "entities" (individuals, firms, or other units) at a given point in time. Example 1. Data Format (Numbers are arbitrary) Example 2. ..

Study Note/Econometrics 2020. 6. 17. 08:15

【Econometrics】Econometric Questions

Econometric Questions In the last post, I laid out a broad overview of what consists an econometric analysis. As a start, this post cites a couple of examples of econometric studies and demonstrate what kind of questions and information are included and important. 2020/06/05 - [Studies/Econometrics] - Econometrics (0) :: What is Econometrics? Example 1. Breastfeeding and IQ."Based on data collec..

Study Note/Econometrics 2020. 6. 17. 06:47