GCSE Statistics Scatter Graphs Fitting a line of

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

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

700 600 Area, y (mm²) 500 400 300 200 100 0 0 5 10 15 20 25 30 35 40 45 50 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.

700 Area, y (mm²) 600 500 400 300 200 100 0 0 5 10 15 20 25 30 35 40 45 50 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.

X X X X X X X X In an exam you will need to recognise these models X

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.

Your turn Exercise 5 G page 194