1. Scatter Graphs Fitting a line of best fit to a non-linear model
GCSE Statistics
Scatter Graphs
Fitting a line of best fit to a
non-linear model

2. Non Linear Models
Sometimes a straight line is not the best fit for an association between two variables

3. Area, y (mm²)
Length, x (mm²)
An investigation into the length and area of nine leave produced this scatter graph.
A straight line is not the best model for the association between these two variables. A curve is better, so these data fit a non linear model.

4. Area, y (mm²)
Length, x (mm²)
The curve is of the form y =axn +b
The look of the curves of the form y =axn +b vary according to n. It is important to recognise and use values for n or 2, -1 or ½.

5. In an exam you will need to recognise these models
These values give the following equations
n=2 n= -1 n=½
y = ax² + b y = ax-1 + b y = ax½ + b
y = a x + b y = a 𝑥 + b X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X
In an exam you will need to recognise these models

6. When we look at the way things decay and grow we usually get what is called an exponential function. This is one in the form y = kax.
exponential growth is in the form y = kax (a > 1)
exponential decay is in the form y = kax (0 <a < 1)
In an exam you will be told which model y = kax or y = ax² + b you should consider.

7. Your turn
Exercise 5G page 194