Equations without Regression?
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September 14, 2009 at 5:46 pm #52643
As I recall, regression assumes that the independent variable (Typically x) is assumed to have no error, that all of the error in in Y.
My data has uncertainity in x as well as Y, the uncertainity in x is around 5 minutes (8%) for each reading (taken about an hour from the previous one), and an uncertainity in Y (per hour drop is about 15 deg) with an estimated uncertainity in the value of about 1 or 2 deg of the absolute value measured. My current regression model is Y=(x,x^2,x^3)
I’m thinking I need a different tool than regression. Is that correct, and if so, then what is the right tool?
0September 14, 2009 at 6:55 pm #185432
Robert ButlerParticipant@rbutler Include @rbutler in your post and this person will
be notified via email.The problem you are facing is the common one of regression when both Y and X are subject to error and is called “errors in both variables model”.
A good starting point would be pp.171172 of Statistical Methods 7th Edition Snedecor and Cochran.
Montgomery and Peck Introduction to Linear Regression Analysis also has a section – 9.5 Effect of measurement errors in the X’s which is a concise summary of the issues involved.
A very general observation is that if the errors in the X’s and the Y’s are uncorrelated and if the variability in the measurement errors is “small” relative to the variability in the X’s then the measurement errors can be ignored and standard least squares methods can be used.0September 14, 2009 at 7:46 pm #185439Thanks for the reply — I was thinking that there was another whole system (other than regression) that I could not recall.
In my case the uncertainity in the recorded temperature is about the same as the uncertainity that the variation in time would also cause, so I wanted to be a tad bit more cautious in the analysis before I went on. I have a book that will help at home, so I’ll look more at regression with errors in both variables tonight.
Thanks again.
Eugene0September 14, 2009 at 9:31 pm #185442Hey Butler, double check….I believe the reference pages should be 181182 of Snedecor and Cochran.
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