3-1 Chapter 3 a brief overview of the Iwom classical linear regression model
3-1 Chapter 3 A brief overview of the classical linear regression model
3-2 1 Regression Regression is probably the single most important tool at the econometricians disposal. What is regression analysis It is concerned with describing and evaluating the relationship between a given variable (usually called the dependent variable) and one or more other variables ( usually known as the independent variable(s). 回归是试图用自变量的变动来解释因变量的变化
3-2 1 Regression • Regression is probably the single most important tool at the econometrician’s disposal. What is regression analysis? • It is concerned with describing and evaluating the relationship between a given variable (usually called the dependent variable) and one or more other variables (usually known as the independent variable(s)). • 回归是试图用自变量的变动来解释因变量的变化
3-3 Some notation Denote the dependent variable by y and the independent variable(s) by x1 x2,., xk where there are k independent variables Some alternative names for the y and x variables: dependent variable Independent variables regressand regressors effect variable causal variables explained variable explanatory variable Note that there can be many x variables but we will limit ourselves to the case where there is only one x variable to start with In our set-up, there is only one y variable
3-3 Some Notation • Denote the dependent variable by y and the independent variable(s) by x1 , x2 , ... , xk where there are k independent variables. • Some alternative names for the y and x variables: y x dependent variable independent variables regressand regressors effect variable causal variables explained variable explanatory variable • Note that there can be many x variables but we will limit ourselves to the case where there is only one x variable to start with. In our set-up, there is only one y variable
3-4 2 Regression is different from Correlation If we say y and x are correlated, it means that we are treating y and x in a completely symmetrical way. In regression, we treat the dependent variable v) and the independent variable(s('s)very differently. The y variable is assumed to be random or "stochastic" in some way, i.e. to have a probability distribution. The x variables are. however. assumed to have fixed (non-stochastic)values in repeated samples Regression as a tool is more flexible and powerful than correlation
3-4 2 Regression is different from Correlation • If we say y and x are correlated, it means that we are treating y and x in a completely symmetrical way. • In regression, we treat the dependent variable (y) and the independent variable(s) (x’s) very differently. The y variable is assumed to be random or “stochastic” in some way, i.e. to have a probability distribution. The x variables are, however, assumed to have fixed (“non-stochastic”) values in repeated samples. • Regression as a tool is more flexible and powerful than correlation
3-5 3 Simple regression For simplicity, say k-l. This is the situation where y depends on only one x variable. Examples of the kind of relationship that may be of interest include: How asset returns vary with their level of market risk Measuring the long-term relationship between stock prices and dividends. Constructing an optimal hedge ratio(套期比)
3-5 3 Simple Regression • For simplicity, say k=1. This is the situation where y depends on only one x variable. • Examples of the kind of relationship that may be of interest include: – How asset returns vary with their level of market risk – Measuring the long-term relationship between stock prices and dividends. – Constructing an optimal hedge ratio（套期比）