From: Bob Wheeler Subject: Re: Statistically significant? Date: Mon, 18 Jan 1999 14:52:26 -0500 Newsgroups: sci.math Keywords: What is R^2 (in statistics)? Yes, you err. The absolute magnitude of R^2 is not in general very informative. You can, for instance, make it arbitrarily small simply by adding extraneous noise -- i.e. increase the residual variance by increasing the variety of low Ph soils sampled. The fact that it was significant, means that the odds are long against 0.1415 being due to chance, and hence, the slope coefficient has long odds against being zero. R^2 is not a very useful statistic, and as in this case causes confusion. -- Bob Wheeler --- (Reply to: bwheeler@echip.com) ECHIP, Inc. petrovitch@my-dejanews.com wrote: > > Not my data. The equation was presented as the relationship (cause and > effect) of phosphorus fertilizer applied to low Ph soils and the return on > crop yeild. The speaker was demonstrating that when this fertilizer was > applied to low Ph soils it had an negative relationship to yield. The graph > was stunning. A sharp regression line was displayed on the slide using > bright red on black. But then I remembered reading HOW TO LIE WITH > STATISTICS, and didn't accept the relationship as presented. On the same > slide the equation was presented: > > y = 120 - 2.2 x > r2 = 0.1415 > > So, the slope is negative and the slope coefficient is very large for the > data, but the r2 tells me there is no relationship between the variables. > Using a multiple regression a partial coefficient of determination between > these variables would be significant, but I did not think it should be used > in a simple regression. > > I just wanted to know if there was an error in my interpretation. At first, I > thought it was a simple mistake, but then the guy said, "The relationship is > significant even with an r2 of 0.1415" I'm not concerned with winning an > argument ... just want to know the right answer for my sake. > > In article <19990117234242.10425.00000008@ng124.aol.com>, > kschmidt10@aol.com (KSchmidt10) wrote: > > >I was at a meeting recently where the speaker introduced a simple regression > > >equation: y = 120 - 2.2 x with r2 = 0.1415 > > > > > >One on one I challenged the speaker ... with an r2 of 0.1415 I said the > > >equation was insignificant, but the speaker disagreed sharply saying even > > >with > > >this low r2 the relationship between x and y is significant. > > > > > >r2, or the coefficient of determination, demonstrates how much of the > > >variation from the mean is explained by the relationship ... and r2 is the > > >coefficient of correlation squared ... isn't that a measure of significance? > > > > > > > Yes. Approximately 14% of the y-value can be attributed to a change in the > > x-value with a coefficient of .14. > > Whether or not this amount is significant for your purposes is more a matter of > > semantics, but this is a fairly low r. > > Have you tried a chi-square test on the data to determine its statistical > > significance? > > > > > > -----------== Posted via Deja News, The Discussion Network ==---------- > http://www.dejanews.com/ Search, Read, Discuss, or Start Your Own ============================================================================== From: Joel Bonagua Subject: Re: Statistically significant? Date: Tue, 19 Jan 1999 12:29:26 +0800 Newsgroups: sci.math petrovitch@my-dejanews.com wrote: [as above -- djr] The r2 is the % of the total variation that is accounted for by the regression model.  An r2 of 0.1415 indicates that given the current model being used, only 14% of the original variability is being accounted for.  That should indicate that there might be some other factors aside from phosphorus fertilizer that  could affect crop yield.   In short, it is possible that phosphorus fertilizer is a significant factor but given the low value of r2, the generated model is not adequate enough to be used for prediction purposes. Regards, Joel