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Unformatted text preview: Lecture Notes 4 Econ 410 Introduction to Econometrics 1 Linear Regression with One Regressor: Part II Regression When X is a Binary Variable Regression analysis can also be used when the regressor is a binary variable (that is, when it takes on only two values). In this case, the procedure for obtaining the OLS estimators and 1 is the same as if the regressor is a continuous variable. However, the interpretation of the regression coefficients is different and it is related to the fact that a regression with a binary variable is equivalent to a difference of means analysis. Suppose that Y is the random variable earnings and X is a binary random variable defined as: = female a is person i the if male a is person i the if X th th i 1 The population regression model is: n i u X Y i i i ,....., 1 1 = + + = In order to understand the meaning of the regression coefficients, we consider the two possible cases = i X and 1 = i X one at the time. When the observed person is a female, the linear regression model can be written as: i i u Y + = From the conditional mean assumption, we know that ( ) | = = i i X Y E , so is the population mean value of earnings for females. Let now consider the case in which the observed person is a male. The linear regression model is: i i u Y + + = 1 From the conditional mean assumption, we know that ( ) 1 1 | + = = i i X Y E , so that 1 + is the population mean value of earnings for males. Since 1 + is the population mean value of earnings for males and is the population mean value of earnings for females, then 1 is the difference in mean earnings in these two populations. This can be mathematically written as: ( ) ( ) 1 | 1 | = = = i i i i X Y E X Y E . Lecture Notes 4 Econ 410 Introduction to Econometrics 2 Hypothesis Testing and Confidence Intervals Hypothesis testing and confidence intervals use the sampling distribution of the OLS estimators and 1 to infer about the true value of the coefficients in the linear regression model....
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This note was uploaded on 07/28/2010 for the course ECON 410 taught by Professor Staff during the Fall '08 term at Wisconsin.
- Fall '08