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giordandue
Italy
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 Posted - 01/12/2012 : 07:22:15 AM
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Origin Ver. and Service Release (Select Help-->About Origin):
Operating System: Origin 8.6 and Win7
Hi,
performing a multiple regression analysis (n.3 independent variables), I observe that if I fix the intercept at 0, I get (a strange) R value of 0.997;
on the contrary, if I do not fix any intercept (i.e. free fitting), I get (a more reasonable) R=0.868. I do not understand why I get a lower R for the free fitting option: could you help me?
Thank you in advance
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giordandue
Italy
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Posted - 01/12/2012 : 5:15:26 PM
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From the Linear Regression tutorial, I have realized that if any intercept is accepted, the so-called "corrected" equation for fitting is applied, while if intercept=0 the so-called "uncorrected" equation is applied. I suppose that the observed difference is related to this, despite my concern/doubt about the results remain..
I profit of such a reply to my-self  to add a question to the same topic. I have observed as well that the resulting correlation matrix is different from the scatter matrix. I know that in the ellipse matrix the adjusted R^2 is applied (incidentally, is it for this reason that some absurd Adj R^2 negative values occur?), while in the correlation matrix not. Anyway, why some correlations appear of different sign? Let you see for example in the attached image the highligthed case "thrust vs torque": in the correlation matrix is signed -0.346, while in ellipse matrix Adj R^2=0.118. Thank you for some explanation. Kind Regards  |
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Echo_Chu
China
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Posted - 01/13/2012 : 03:38:26 AM
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Hi, Giordano
As for the R value when fix intercept, you are right. : If intercept is fixed, the total sum of squares is uncorrected. R value is computed from total sum of square so you got a high value when intercept is fixed.
You can also see the details of the algorithm in this page.
http://www.originlab.com/www/helponline/Origin/en/UserGuide/Multiple_Regression_Results.html#ANOVA_Table
As for the second question, the result in correlation coefficent matrix (-0.34635) is a Pearson't correlation coefficient, which is computed by equation
And the Adj R^2 (0.118) is the same as what you got in the linear fit result. It is computed by equation
They are different measurement so different value.
Thanks, Echo |
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giordandue
Italy
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Posted - 01/13/2012 : 03:51:15 AM
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Hi, Echo_Chu,
thank you for your detailed answer. What is not clear for me is why in the two linear correlations (i.e. in the correlation matrix and in the ellipse matrix) present in some case different sign. As I said (see the image), for example the correlation between the parameters "thrust" and "torque" is -0.346 (i.e. negative correlation), while the correspondent case in the ellipse matrix shows a positive correlation.
Kind Regards |
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giordandue
Italy
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Posted - 01/13/2012 : 04:06:21 AM
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| Please, let you observe in addition that using the Pearson correlation coefficient equation I get +0.346 and not -0.346 as reported in the correlation matrix.. |
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multiple regression