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Thread: Linear and Non-Linear three parameter Regression Analysis questions.

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    Linear and Non-Linear three parameter Regression Analysis questions.

    Hello All

    A short warning for a very long post!

    Im currently working on my master thesis in mechanical engineering. I need to do, for me, an advanced regression analysis on some data - and i therefore seek the experience of you pro's

    I have some experimentally obtained motion data for a big container ship, which i compare to theoretical derived data. An example of such can be seen here:

    The uncertainty between the theoretical derived data compared to the experimental data can be defined as: H_{e} = \phi * H_{t} where H_{e} is experimental data and H_{t} is theoretical data, and \phi is the difference between the data.

    phi can then be a simple form \phi = a or and more advanced form \phi(\omega) = b+c*\omega , where omega is the frequency as seen on the photo above. a and b is then determined in both cases.

    The data is obtained for various wave headings (U), speed (V) and draft(D) of the ship, and i think therefore it's obvious to make an regression analysis to determine how a, b and c change when wave heading, speed and draft changes.

    I set up a simple linear regression model for the simple phi first, i.e.:

    y = a = \beta_0 + \beta_1 * U + \beta_2 * V + \beta_3 *D

    and an adjusted R^2 value of 0.33 and three not so good looking residual plots. I therefore change the model to a quadratic second order model, which i think is non-linear??, i.e:

    y = a = \beta_0 + \beta_1*U+\beta_2*V+\beta_3*D+\beta_4*U^2+\beta_5*V^2+\beta_6*D^2+ \beta_7*U*V+\beta_8*U*D+\beta_9*V*D+\beta_10*U*V*D

    and gets a adjusted R^2 value of 0.83 and great looking residual plots.

    I then tried to test the more advanced \phi(\omega) = b+c*\omega , but i fail to understand how to do it. Do i just set y = b+c*\omega and then do the calculation for various omega values??

    Il hope i made my self clear, if not please let me know

    Thank you very much
    Last edited by kbach; 01-31-2015 at 09:46 AM. Reason: Make equations easier to see

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