硕士计量1-02-SimpleRegressionModel.ppt

* PowerClickAnswer0/AnswerOption3/OptionPoint1/Point/PowerClick * * PowerClickAnswer0/AnswerOption4/OptionPoint1/Point/PowerClick * * PowerClickAnswer0/AnswerOption4/OptionPoint1/Point/PowerClick * PowerClickAnswer0/AnswerOption2/OptionPoint1/Point/PowerClick * 78 * Stopped here Summary of OLS slope estimate The slope estimate is the sample covariance between x and y divided by the sample variance of x If x and y are positively correlated, the slope will be positive If x and y are negatively correlated, the slope will be negative Only need x to vary in our sample Test Your Understanding Which of the following is not true? If cov(x,y)0, then ?1 0 cov(x,y)=0, then ?1 =0 cov(x,y)0, then ?1 0 cov(x,y)0, then ?1 0 ^ ^ ^ ^ TestScore = 698.9 – 2.28×STR Interpretation of the estimated slope and intercept is: Districts with one more student per teacher on average have test scores that are 2.28 points lower. To increase the test score by one, the student teacher ration has to go down by 2.28 The true interpretation is, = –2.28 The intercept (taken literally) means that, according to this estimated line, districts with zero students per teacher would have a (predicted) test score of 698.9. This interpretation of the intercept makes no sense – it extrapolates the line outside the range of the data – in this application, the intercept is not itself economically meaningful. More terminology We can think of each observation as being made up of an explained part, and an unexplained part. Given yi=?i+?i, we then define the following: is the total sum of squares (SST) is the explained sum of squares (SSE) ∑(yi-?i)2=∑?i2 is the residual sum of squares (SSR) Then, SST=SSE+SSR Total sum of squares (Yi -?)2 Unexplained sum of squares (Yi –?i)2 Explained sum of squares (?i -?)2 Yi SST=SSE+SSR Proof that SST = SSE + SSR Why? for algebraic properties of OLS showed that ∑?ixi=0 and ∑?i=0 Goodness-of-Fit How do we think about how well our sample regression line fi