{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

ECON301_Handout_10_1213_02

If r 2 is high but the partial correlations are low

Info iconThis preview shows pages 9–13. Sign up to view the full content.

View Full Document Right Arrow Icon
If R 2 is high but the partial correlations are low, multicollinearity is a possibility. Here one or more variables may be superfluous. But if R 2 is high and the partial correlations are also high, multicollinearity may not be readily detectable. Although a study of the partial correlations may be useful, there is no guarantee that they will provide an infallible guide to multicollinearity.
Background image of page 9

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

View Full Document Right Arrow Icon
ECON 301 - Introduction to Econometrics I May 2013 METU - Department of Economics Instructor: Dr. Ozan ERUYGUR e-mail: [email protected] Lecture Notes 10 4. Variance-Inflating Factor (VIF) Recall that for the case of two explanatory variables (X’s):     2 2 2 1 22 2 2 2 2 12 12 1 ˆ var( ) . . 11 tt t t VIF xx x r r   (7)     2 2 2 2 2 2 2 2 12 12 1 ˆ var( ) . . t VIF x r r (8) When there are more than two explanatory variables, multicollinearity produces similar effects. The VIF takes the form: 2 1 1 i i VIF P (12) where 2 i P is the coefficient of multiple determinations from the regression of i th independent variable on the remaining independent variables. VIF tells us how much the variance of ˆ j is being inflated by its correlation with the other variables, that is why, it is called variance- inflating factor.
Background image of page 10
ECON 301 - Introduction to Econometrics I May 2013 METU - Department of Economics Instructor: Dr. Ozan ERUYGUR e-mail: [email protected] Lecture Notes 11 Note that 2 1 ii P VIF    (VIF does not have an upper-bound) 2 01 P VIF   (VIF does have a lower-bound) 2 0 i P means that, there is no linear relationship between its associated explanatory variable and the remaining explanatory variables, or when a vector of the X matrix is orthogonal to the remaining vectors. The VIF for each term in the model measures the combined effect of the dependences among the regressors (explanatory variables) on the variance of that term. Practical experience indicates that if any of the VIFs exceeds 10, it is an indication that the associated regression coefficients are poorly estimated because of serious multicollinearity. Thus in practical work: 10 i VIF serious multicollinearity (due to that exp. variable). Note that VIF>10 implies 2 0.90 i P Example Consider the model 0 1 1 2 2 3 3 tt t t t Y a a X a X a X u . 1 0 1 2 2 3 t t t t X b b X b X v , 2 1 0.95 P 2 0 1 1 2 3 t t t t X c c X c X w , 2 2 0.80 P 3 0 1 1 2 2 t t t t X d d X d X z , 2 3 0.75 P
Background image of page 11

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

View Full Document Right Arrow Icon
ECON 301 - Introduction to Econometrics I May 2013 METU - Department of Economics Instructor: Dr. Ozan ERUYGUR e-mail: [email protected] Lecture Notes 12 1 1 20 10 1 0.95 VIF serious MC 1 1 5 10 1 0.80 VIF   no serious MC 1 1 4 10 1 0.75 VIF   no serious MC 5. Condition number The characteristic roots or eigenvalues of * * XX say λ 1 , λ 2 , λ k , can be used to measure the extent of the multicollinearity in the data.
Background image of page 12
Image of page 13
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Page9 / 18

If R 2 is high but the partial correlations are low...

This preview shows document pages 9 - 13. Sign up to view the full document.

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