6 Modelling Scientific Systems Ė in development

 

You have already identified (step 1) your aims in relation to modelling the system that you are investigating.

 

ACTION: You now need to

The measurements are grouped under the headings of modelling -

Linear variation

Exponential variation

Non-linear variation

Variation with respect to more than one other variable

Any more?

 

 

Linear variation of a response variable, y, with respect to a single predictor variable, x - 'best-fit' straight line.

 

> Linear regression of y against x to derive slope and intercept of 'best-fit' straight line. Excel Minitab, SPSS

Note: Normal linear regression assumes that there is no uncertainty in the x values.

> Use Orthogonal regression when there is uncertainty in the values of both y and x.

> Use Logical regression when response variable, y, has binary values (e.g. Yes/No)

> Using 'best-fit' straight line (calibration line) to predict (read off) unknown values

 

Exponential variation of a response variable, y, with respect to a single predictor variable, x.

 

> Log transformation to ln(y) followed by linear regression against x

> Using non-linear regression in software.

 

Non-linear variation of a response variable, y, with respect to a single variable, x.

 

> Transformation of data followed by linear regression

> Using non-linear regression in software

> Using Excel Solver

 

Variation of a response variable with respect to two or more variables

 

> Stepwise regression

> ANOVA

 

Does the value of one variable change in ordered way with a change in the value of another variable?

Examples:

Does a measurement of body fat using skinfold thickness give the same results as using bioelectrical impedance?

Typical analyses: Pearsonís correlation (N), Linear Regression (N), Bland-Altman plot, Spearmanís correlation

 

Can I produce a mathematical model to show how certain factors affect the measured response variable(s)?

Examples:                                                                   

Producing an equation to predict lung function, based on physiological factors (e.g age, blood pressure, exercise, body fat, etc)?

Typical analyses: Stepwise linear (or multiple) regression,

 

What is the variation of a measured variable with respect to time?

Examples:                                                                   

How do cannabis samples degrade with heat and time?

Calculations based on exponential decay (or growth)

Typical analyses: Plot of log(data) against time, linear regression (N)

 

Does the measured variable change linearly with respect to a factor variable?

Examples:                                                                   

Using a linear calibration curve

Typical analyses: Linear regression (N)