deviation of IQ is about 15, which is pretty close to the population value of 15. CHAPTER 3 TEACHING NOTES

b. β 2 <0 and x 1 and x 2 are positively correlated c. β 2 =0 and x 1 and x 2 are negatively correlated d. β 2 =0 and x 1 and x 2 are negatively correlated xi fixed). But as x increases, the variance of βˆ 1 increases relative to Var(β% 1 ). The bias in β% 1yi) on (c 2 + xi), and β% 1 = βˆ 1. The intercept is β% 0 = ()cy 1 + – β% 1 (cx 2 + ) = (c 1 + y) – βˆ 1 (c 2 +

degree of collinearity between the explanatory variables in the sample, even if it is reflected in a Because statistical inference is no more difficult in multiple regression than in simple regression, issue is perfect collinearity in the population, but this is fairly easy to dispense with via examples. iv) Again, we can apply part (ii) with c 1 = 0 and replacing c 2 with log(c 2 ) and xi with log(xi). course, that this change prate is possible (if, say, prate is already at 98, this interpretation makes

Dev status

From (2), we obtain the intercept as β% 0 = (c 1 y) – β% 1 (c 2 x) = (c 1 y) – [(c 1 /c 2 )βˆ 1 ](c 2 x) = sampling distributions (conditional on the explanatory variables). I emphasize that the full set of First, make a scatter-plot of the two variables and look for possible patterns in the relationship between them. If β垐 0 and β 1 are the original intercept and slope, then β% 1 =βˆ 1 and β% 00 =−ββ垐 log( )c 21. SOLUTIONS TO COMPUTER EXERCISES