文档介绍：Chapter 3
A brief overview of the
classical linear regression model
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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。
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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.
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2 Regression is different from Correlation
If we say y and x are correlated, it means that we are treating y and x in pletely 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, . 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
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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)
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Simple Regression: An Example
Suppose that we have the following data on the excess returns on a fund manager’s portfolio (“fund XXX”) together with the