kalbracht47

10-19-2007, 08:49 PM

Dear Biomech-L readers,

I have some problems fitting a linear regression to my measured data and

especially to determine the goodness of the fit. The regressions we

need, have two substantial differences to the simple linear regressions:

1) Due to some physical consideration we have a regression model with no

intercept term, i.e. through the origin (y = b*x)

2) Both variables are erroneous

My question is: How to calculate a 'valid' rsquare and the standard

error of such a regression ?

In the literature (Casalla, G. & Berger, R. L. 2002: Statistical

Inference, Duxbury, pp 581-583) we found for the sake that both

variables are erroneous, the orthogonal least square distance is used

instead of the ordinary least square distance to fit the regression. In

addition we found that the calculation of rsquare is different for the

no-intercept model compared to the common used intercept model (Hahn, G.

H. 1977: Journal of Quality Technology 9(2), pp 56-61; Eisenhauer, J. G.

2003: Teaching Statistics 25(3), pp 76-80).For the intercept model

rsquare is the proportion of the initial variation, as measured by the

sum of squares around the mean of Y, which is accounted for by the

regression. For the no-intercept model, the variation around the fitted

regression, however, could exceed the variation around the mean,

resulting in a negative value of rsquar. Therefore, for the intercept

model it is recommended to calculate rsquare as the variation around the

origin.

However, I am wondering whether I can apply this calculation also when I

used the orthogonal least square distance to fit the regression.

Any help would be greatly appreciated

Kirsten Albracht

--

Kirsten Albracht

Institute for Biomechanics and Orthopaedics

German Sport University Cologne

Carl Diem Weg 6

50933 Cologne

Email: albracht@dshs-koeln.de

Tel.: +49 221 4982-5680

Fax.: +49 221 4971598

I have some problems fitting a linear regression to my measured data and

especially to determine the goodness of the fit. The regressions we

need, have two substantial differences to the simple linear regressions:

1) Due to some physical consideration we have a regression model with no

intercept term, i.e. through the origin (y = b*x)

2) Both variables are erroneous

My question is: How to calculate a 'valid' rsquare and the standard

error of such a regression ?

In the literature (Casalla, G. & Berger, R. L. 2002: Statistical

Inference, Duxbury, pp 581-583) we found for the sake that both

variables are erroneous, the orthogonal least square distance is used

instead of the ordinary least square distance to fit the regression. In

addition we found that the calculation of rsquare is different for the

no-intercept model compared to the common used intercept model (Hahn, G.

H. 1977: Journal of Quality Technology 9(2), pp 56-61; Eisenhauer, J. G.

2003: Teaching Statistics 25(3), pp 76-80).For the intercept model

rsquare is the proportion of the initial variation, as measured by the

sum of squares around the mean of Y, which is accounted for by the

regression. For the no-intercept model, the variation around the fitted

regression, however, could exceed the variation around the mean,

resulting in a negative value of rsquar. Therefore, for the intercept

model it is recommended to calculate rsquare as the variation around the

origin.

However, I am wondering whether I can apply this calculation also when I

used the orthogonal least square distance to fit the regression.

Any help would be greatly appreciated

Kirsten Albracht

--

Kirsten Albracht

Institute for Biomechanics and Orthopaedics

German Sport University Cologne

Carl Diem Weg 6

50933 Cologne

Email: albracht@dshs-koeln.de

Tel.: +49 221 4982-5680

Fax.: +49 221 4971598