tag:blogger.com,1999:blog-2198942534740642384.post8809036026928898747..comments2023-10-24T03:16:41.009-07:00Comments on Econometrics Beat: Dave Giles' Blog: More on the Distribution of R-SquaredDave Gileshttp://www.blogger.com/profile/05389606956062019445noreply@blogger.comBlogger10125tag:blogger.com,1999:blog-2198942534740642384.post-9934197284493666992016-01-06T10:28:38.991-08:002016-01-06T10:28:38.991-08:00In that case the F statistic will be non-central F...In that case the F statistic will be non-central F in distribution. R-squared should then be able to be written in terms of a non-central Beta statistic. The mean and variance could then easily be established.Dave Gileshttps://www.blogger.com/profile/05389606956062019445noreply@blogger.comtag:blogger.com,1999:blog-2198942534740642384.post-66720622489685071492016-01-06T03:40:30.286-08:002016-01-06T03:40:30.286-08:00Nice. Are there any results for the distribution o...Nice. Are there any results for the distribution of $R^2$ for nonzero $\beta$?Anonymoushttps://www.blogger.com/profile/15353085826653165029noreply@blogger.comtag:blogger.com,1999:blog-2198942534740642384.post-66514874144990648732015-07-02T13:15:20.898-07:002015-07-02T13:15:20.898-07:00Thank you - yes it should be, and I have now corre...Thank you - yes it should be, and I have now corrected it.Dave Gileshttps://www.blogger.com/profile/05389606956062019445noreply@blogger.comtag:blogger.com,1999:blog-2198942534740642384.post-99903233886734612015-07-01T20:59:30.881-07:002015-07-01T20:59:30.881-07:00I am not sure about the derivation of the variance...I am not sure about the derivation of the variance: shouldn't it be (2(k-1)(n-k) ) / ( (n-1)^2(n+1) ) . Thank you Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-2198942534740642384.post-20145788626661888502014-05-12T10:41:39.143-07:002014-05-12T10:41:39.143-07:00See http://davegiles.blogspot.ca/2013/10/in-what...See http://davegiles.blogspot.ca/2013/10/in-what-sense-is-adjusted-r-squared.htmlDave Gileshttps://www.blogger.com/profile/05389606956062019445noreply@blogger.comtag:blogger.com,1999:blog-2198942534740642384.post-79844763227673868342014-05-09T10:57:50.116-07:002014-05-09T10:57:50.116-07:00If the null hypothesis is true, then the variance ...If the null hypothesis is true, then the variance of the adjusted R-squared is (k - 1) / [n(n - k)], and this is greater than or equal to the variance of the R-squared itself in this case. I'll prepare s short post on this.Dave Gileshttps://www.blogger.com/profile/05389606956062019445noreply@blogger.comtag:blogger.com,1999:blog-2198942534740642384.post-16153878842819378352014-05-07T10:23:19.727-07:002014-05-07T10:23:19.727-07:00What would be the estimate of the variance of R-sq...What would be the estimate of the variance of R-sq-adj? KM Stationhttps://www.blogger.com/profile/07073428434100070526noreply@blogger.comtag:blogger.com,1999:blog-2198942534740642384.post-209530620084148352013-10-04T07:00:09.299-07:002013-10-04T07:00:09.299-07:00I see. Thanks.I see. Thanks.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-2198942534740642384.post-35271954832979923222013-10-02T09:55:53.472-07:002013-10-02T09:55:53.472-07:00No - you have misunderstood. In that case, k=2 (se...No - you have misunderstood. In that case, k=2 (see the definition of k), and var. (R^2)=(n-2)/[n(n-1)^2] > 0.Dave Gileshttps://www.blogger.com/profile/05389606956062019445noreply@blogger.comtag:blogger.com,1999:blog-2198942534740642384.post-84466453147224239172013-10-02T06:45:48.266-07:002013-10-02T06:45:48.266-07:00Very interesting. I think the result doesn't a...Very interesting. I think the result doesn't apply to the case of univariate regression or simple scatter plot. Otherwise, it suggests var(R-squared) equals zero!Anonymousnoreply@blogger.com