mathematical modeling of serial data modeling serial data differs from simple equation fitting in...
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Kin 304 Measurement & Inquiry in Kinesiology
Mathematical Modeling of Serial Data
Mathematical Modeling of Serial Data
Modeling Serial Data
Differs from simple equation fitting in that the parameters of the equation must have meaning
Can be used to smooth
Can explain phenomena
Can be used to predict
Mathematical Modeling of Serial Data
Steps in Mathematical Modeling
Identification of the mechanism
Translation of that phenomenon into a mathematical equation
Testing the fit of the model to actual data
Modification of the model according to the results of the experimental evaluation
Mathematical Modeling of Serial Data
Criteria of Fit of the Model
Least Sum of Squares
Shape of the curve
Mathematical Modeling of Serial Data
Examination of Residuals
Residual = Actual Y - Predicted Y
Ideally there is no pattern to the residuals.
In this case there would be a horizontal normal distribution of residuals about a mean of zero.
However there is a clear pattern indicating the lack of fit of the model.
Mathematical Modeling of Serial Data
Ideal Characteristics of a Model
Simple
Fits the experimental data well
Has biologically meaningful parameters
Modeling Growth Data
Mathematical Modeling of Serial Data
National Centre for Health Statistics (N.C.H.S.)1970srevamped asCenter for Disease ControlC.D.C. charts, 2001
Most often used clinical norms for height and weight
Cross-sectional
Clinical Growth Charts
Mathematical Modeling of Serial Data
Preece-Baines model I
where h is height at time t,
h1 is final height,
s0 and s1 are rate constants,
q is a time constant and
hq is height at t = q.
Smooth curves are the result of fitting Preece-Baines Model 1
to raw data
This was achieved using MS EXCEL rather than custom software
Examination of Residuals
Caribbean Growth Data
n =1697
X Line Fit Plot
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