计量经济学导论电子教案ch03章节幻灯片.pptVIP

Economics 20 - Prof. Anderson * Multiple Regression Analysis y = b0 + b1x1 + b2x2 + . . . bkxk + u 1. Estimation Economics 20 - Prof. Anderson * Parallels with Simple Regression b0 is still the intercept b1 to bk all called slope parameters u is still the error term (or disturbance) Still need to make a zero conditional mean assumption, so now assume that E(u|x1,x2, …,xk) = 0 Still minimizing the sum of squared residuals, so have k+1 first order conditions Economics 20 - Prof. Anderson * Interpreting Multiple Regression Economics 20 - Prof. Anderson * A “Partialling Out” Interpretation Economics 20 - Prof. Anderson * “Partialling Out” continued Previous equation implies that regressing y on x1 and x2 gives same effect of x1 as regressing y on residuals from a regression of x1 on x2 This means only the part of xi1 that is uncorrelated with xi2 are being related to yi so we’re estimating the effect of x1 on y after x2 has been “partialled out” Economics 20 - Prof. Anderson * Simple vs Multiple Reg Estimate Economics 20 - Prof. Anderson * Goodness-of-Fit Economics 20 - Prof. Anderson * Goodness-of-Fit (continued) How do we think about how well our sample regression line fits our sample data? Can compute the fraction of the total sum of squares (SST) that is explained by the model, call this the R-squared of regression R2 = SSE/SST = 1 – SSR/SST Economics 20 - Prof. Anderson * Goodness-of-Fit (continued) Economics 20 - Prof. Anderson * More about R-squared R2 can never decrease when another independent variable is added to a regression, and usually will increase Because R2 will usually increase with the number of independent variables, it is not a good way to compare models Economics 20 - Prof. Anderson * Assumptions for Unbiasedness Population model is linear in parameters: y = b0 + b1x1 + b2x2 +…+ bkxk + u We can use a random sample of size n, {(xi1, xi2,…, xik, yi): i=1, 2, …, n}, from the population model, so that the sample model is yi = b0 +