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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】 What is Econometrics?

What is Econometrics? Econometrics is the quantitative analysis of actual economic phenomena based on concurrent development of theory and observation, related by appropriate methods of inference. To simply put, it is a study process of mathematical statistics and statistical theory to extract simple economic relationships. The most basic tool is linear regression model. The Econometric Society ..

Study Note/Econometrics 2020. 6. 5. 02:52