1. Graphical Analysis of Data
Details on website
select “Res/Sci” method on main menu

2. Graphical Analysis
Pictorial representation of a mathematical relationship
Two main approaches
Analytical
Based on theory
Empirical
Based on observation and experience

3. The straight line (1) Most graphs based on numerical data are curves.
The straight line is a special case
Data is often manipulated to yield straight line graphs as the straight line is relatively easy to analyse

4. The Straight line (2) Straight line equation y = mx + c Intercept = c
slope = m

5. Linearisation (1)
Many functions can be manipulated mathematically to yield a straight line equation.
Some examples are given in the next few slides

6. Linearisation (2)

7. Linearisation (3)

8. Polynomials These are functions of general formula
y = a + bx + cx2 + dx3 + …
They cannot be linearised
Techniques for fitting polynomials exist
for example using Excel

9. Functions involving logs (1)
Some functions can be linearised by taking logs
These are
y = A xn and
y = A ekx

10. Functions involving logs (2)
For y = Axn, taking logs gives
log y = log a + n log x
A graph of log y vs. log x gives a straight line, slope n and intercept log A.
To find A you must take antilogs (= 10x)

11. Functions involving logs (3)
For y = Aekx, we must use natural logs
ln y = ln A + kx
This gives a straight line slope k and intercept ln A
To find A we must take antilogs (= ex)

12. Special Graph Paper (1)
It is possible to plot graphs of y=Axn and y=Aekx without taking logs
This involves the use of graph paper in which the scale has been adjusted to give the intervals for logs.
The next two slides give examples

13. Special Graph paper (2) Log - Log graph paper for y = Axn Slope = n =
The intercept is at
log x = 0 i.e. the value of y at x = 1.0

14. Special Graph Paper (3) Log-linear graph paper for y = Aekx
Take logs to base 10
log y = log A + kx.log10e
Intercept = A
Slope
=k log10e

15. Using a spreadsheet Excel has tools to fit lines
Lines can be fitted on the graph
Slope and gradient can be found from data in tabular form
For more details see website

16. Finish
For now ...