tag:blogger.com,1999:blog-2198942534740642384.post5549694574768384514..comments2023-10-24T03:16:41.009-07:00Comments on Econometrics Beat: Dave Giles' Blog: Degrees of Freedom in RegressionDave Gileshttp://www.blogger.com/profile/05389606956062019445noreply@blogger.comBlogger15125tag:blogger.com,1999:blog-2198942534740642384.post-85295762089742389622015-10-21T05:49:55.628-07:002015-10-21T05:49:55.628-07:00thank you sir.thank you sir.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-2198942534740642384.post-54342956256021052062015-07-29T11:45:29.405-07:002015-07-29T11:45:29.405-07:00Well said in understandable words. Thank you. Well said in understandable words. Thank you. Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-2198942534740642384.post-89915485338983643702013-09-12T12:46:56.721-07:002013-09-12T12:46:56.721-07:00Absolutely - the "constant term" is a ve...Absolutely - the "constant term" is a vector of "ones", with a coefficient. That coefficient is just like the other regression coefficients - you count it. So k=4. This is the universal convention - not just in some books.Dave Gileshttps://www.blogger.com/profile/05389606956062019445noreply@blogger.comtag:blogger.com,1999:blog-2198942534740642384.post-7092565987471823572013-09-12T12:13:39.799-07:002013-09-12T12:13:39.799-07:00When you say "n-k+J" d.f. is used in cal...When you say "n-k+J" d.f. is used in calculation of AIC, what do you mean by k exacly?<br />That is to say, say, <br />Y ~ constant + B2*U + B3*V + B4*W then k=3 or k=4? Is the constant (intersection) thought as a regressor? In some books, it says so. Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-2198942534740642384.post-59614721757130597452013-09-12T12:06:27.447-07:002013-09-12T12:06:27.447-07:00Thank you very much.
Erdogan CEVHERThank you very much.<br /><br />Erdogan CEVHERAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-2198942534740642384.post-79480473519108343382013-02-15T13:22:10.779-08:002013-02-15T13:22:10.779-08:00Thank you!
DGThank you!<br /><br />DGDave Gileshttps://www.blogger.com/profile/05389606956062019445noreply@blogger.comtag:blogger.com,1999:blog-2198942534740642384.post-60781431403037942132013-02-15T13:17:46.799-08:002013-02-15T13:17:46.799-08:00Excellent explanation!Excellent explanation!Anonymoushttps://www.blogger.com/profile/04437108382893764666noreply@blogger.comtag:blogger.com,1999:blog-2198942534740642384.post-7996158718156236582012-10-23T21:58:43.863-07:002012-10-23T21:58:43.863-07:00Very good.Very good.Sinahttps://www.blogger.com/profile/07215169480944612100noreply@blogger.comtag:blogger.com,1999:blog-2198942534740642384.post-91210539478881614772012-10-13T08:41:33.988-07:002012-10-13T08:41:33.988-07:00John - thanks for both comments. Omission fixed - ...John - thanks for both comments. Omission fixed - thank you!<br />Second - it will be the number of "free" parameters. Consider restricted least squares, where there are "n" observations, "k" regressors, and "J" independent linear restrictions on the coefficients. Then the d.o.f. are (n-k+J), and (k-J) would be the appropriate quantity to use when constructing AIC, BIC, etc.Dave Gileshttps://www.blogger.com/profile/05389606956062019445noreply@blogger.comtag:blogger.com,1999:blog-2198942534740642384.post-16127657726346681642012-10-13T08:38:05.839-07:002012-10-13T08:38:05.839-07:00Procyon - thank you.Procyon - thank you.Dave Gileshttps://www.blogger.com/profile/05389606956062019445noreply@blogger.comtag:blogger.com,1999:blog-2198942534740642384.post-17675274509687264352012-10-13T08:37:25.507-07:002012-10-13T08:37:25.507-07:00Thanks for the very kind comment.Thanks for the very kind comment.Dave Gileshttps://www.blogger.com/profile/05389606956062019445noreply@blogger.comtag:blogger.com,1999:blog-2198942534740642384.post-30670609620485773792012-10-12T23:49:38.200-07:002012-10-12T23:49:38.200-07:00Professor,
How simply you have explained that as ...Professor,<br /><br />How simply you have explained that as constraints to the system increase the number of independent information (degrees of freedom) come down, which is further reduced by the reduction in rank in the case of the matrix. <br /><br />This raises the doubt that when data is structured for proving a hypothesis, we are ignorant of the fact that actually less are independent sets of information as constraints tend to increase. Thus when the hypothesis is tested with more number of constraints, we have a diminishing nature of independence in the information sets.<br /><br />Procyon MukherjeeAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-2198942534740642384.post-56388684415926526402012-10-12T10:23:50.799-07:002012-10-12T10:23:50.799-07:00Brilliant explanation! I think most of the econome...Brilliant explanation! I think most of the econometrics professors don't know how to explain that. Thank you.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-2198942534740642384.post-39964263388934394832012-10-12T10:02:19.824-07:002012-10-12T10:02:19.824-07:00I slightly messed up that example, E would be nXm,...I slightly messed up that example, E would be nXm, B would be mXn. So the number of parameters in the first case would be n^2, 2nm in the second case, and nm in the third. Johnhttps://www.blogger.com/profile/01457388998903348000noreply@blogger.comtag:blogger.com,1999:blog-2198942534740642384.post-57135159747750372982012-10-12T09:59:40.243-07:002012-10-12T09:59:40.243-07:00Fantastic post, though there is a math error in th...Fantastic post, though there is a math error in the second bullet where you have e=y-Xb=M (essentially) when it should be My. <br /><br />As a follow up, when considering the AIC it asks for the number of parameters. Is this always the same as the k you use when thinking about degrees of freedom?<br /><br />I'm not sure I can think of a simple example... Consider m principal components, E, from X (which is TXn) to create F=XE. Suppose you regress X=FB+e=XEB+e. EB will be mXn, but presumably only has m+n free parameters since they can be used to reconstruct EB. If B=E', then there are only m parameters. Does this make sense?Johnhttps://www.blogger.com/profile/01457388998903348000noreply@blogger.com