note03 - 1 Chapter 3. Multiple Regression Analysis:...

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1 Chapter 3. Multiple Regression Analysis: Estimation Simple linear regression model: an intercept and one explanatory variable (regressor) Multiple linear regression model: an intercept and many explanatory variables (regressors) OLS estimation method is exactly same as in the simple linear regression model. OLS estimators are derived from minimizing the residual sum of squares ( SSR ) with respect to the parameters The predicted values of and the regression residuals are computed by and the unbiased estimator of the variance of error term is Note that the number of coefficients is subtracted from the sample size n in the denominator. Interpretation of the marginal effect If all explanatory variables are different, then represents the marginal effect of , holding all other explanatory variables constant. Example 3.2. Hourly wage in log-linear model An increase in education by one year increases by 0.092, which is equivalent to an increase in wage by 9.2%. An increase in labor market experience by one year increases the average wage by 0.41%, etc. Note: . This is based on the first order Taylor expansion
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2 A Measure of Goodness-of-fit We introduced the squared correlation coefficient ( ) between and as a measure of how well our model explains the dependent variable. A higher means a better model fitting. We showed We can use this in the multiple regression equation also. Statistical Properties of OLS Estimator in Multiple Regression Model OLS estimators are unbiased if (1) and they are BLUE if (1) (2) (3) Assumption (1) implies , for all i and j , for all i and j The formulas of variance of and covariance between and are quite complicated to write out, though it has a simple form in matrix form. We only need to know that the estimated variances and covariances use the unbiased estimator . What are the new issues in the multiple regression model?
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note03 - 1 Chapter 3. Multiple Regression Analysis:...

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