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Equations without Regression?

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  • #52643

    Lee
    Participant

    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?
     

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    #185432

    Robert Butler
    Participant

      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.171-172 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.

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    #185439

    Lee
    Participant

    Thanks 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.
    Eugene

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    #185442

    Darth
    Participant

    Hey Butler, double check….I believe the reference pages should be 181-182 of Snedecor and Cochran.

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