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



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


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)?


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?


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?


Using a linear calibration curve

Typical analyses: Linear regression (N)