ECON301_Handout_05_1213_02

5 whenever x and z are orthogonal to one another have

Info iconThis preview shows pages 14–15. Sign up to view the full content.

View Full Document Right Arrow Icon
5 Whenever X and Z are orthogonal to one another (have zero collinearity) they do not overlap as in Figure 2 and the red area disappears. Because there is no red area in this case, regressing Y on X alone or on Z produces the same estimates of x and z , as if Y were regressed on X and Z together. Whenever X and Z are higly collinear and therefore overlap a lot, the blue and green areas become very small, implying that when Y is regressed on X and Z together very little information is used to estimate x and z . This causes the variances of these estimates to be very large. Thus, the impact of multicollinearity is to raise the variances of the OLS estimates. Perfect collinearity causes the X and Z circles to overlap completely, the blue and green area disappear and estimation is impossible. Multicollinearity will be discussed in detail later in this semester. In Figure 1 the blue area represents the variation in Y explained by X . Thus R 2 is given as the ratio of the blue area to the entire Y circle. In Figure 2 the blue+red+green area represents the variation 5 As is invariably the case in econometrics, the price of obtaining unbiased estimates is higher variances.
Background image of page 14

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
ECON 301 (01) - Introduction to Econometrics I April, 2012 METU - Department of Economics Instructor: Dr. Ozan ERUYGUR e-mail: [email protected] Lecture Notes 15 in Y explained by X and Z together. Thus, the R 2 resulting from the multiple regression is given by the ratio of the blue+red+green area to the entire Y circle. The yellow area represents variation in Y attributable to the error (disturbance) term, and thus the magnitude of the yellow area represents the magnitude of 2 , the variance of the error term. This implies, for example, that if, in the context of Figure 2, Y had been regressed on only X, omitting Z, 2 would be estimated by the yellow+green area, an overestimate.
Background image of page 15
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Page14 / 15

5 Whenever X and Z are orthogonal to one another have zero...

This preview shows document pages 14 - 15. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online