Cambridge International Mathematics

Using a graphics calculator we can obtain a scatter diagram. We then find the equation of the least squares

regression line in the form y=ax+b. For instructions on how to do this, see page 26 of the graphics

calculator instructions.

So, the linear regression model is y¼ 5 : 64 x¡ 28 : 4 or N¼ 5 : 64 t¡ 28 : 4.

THE CORRELATION COEFFICIENT AND COEFFICIENT OF DETERMINATION

Notice in the screen dump above that it also contains r^2 ¼ 0 : 631 and r¼ 0 : 795.

risPearson’s correlation coefficientandr^2 is called thecoefficient of determination.

These values are important because they tell us how close to linear a set of data is. There is no point in

fitting a linear relationship between two variables if they are clearly not linearly related.

All values ofrlie between¡ 1 and+1.

Ifr=+1, the data isperfectly positively correlated. This means

the data lie exactly in a straight line with positive gradient.

If 0 <r 61 , the data is positively correlated.

If r=0, the data showsno correlation.

If ¡ 16 r< 0 , the data is negatively correlated.

Ifr=¡ 1 , the data isperfectly negatively correlated. This means

the data lie exactly in a straight line with negative gradient.

Scatter diagram examples for positive correlation:

The scales on each of the four graphs are the same.

Scatter diagram examples for negative correlation:

rrand are not required

for this course, but they are

useful and easily available

from a calculator or

statistics software.

2

y

x

O r=+1

y

x

O r=+0.8

y

x

O r=+0.5

y

x

O r=+0.2

y

x

O r=-0.2

y

x

O r=-0.5

y

x

O r=-0.8

y

x

O r=-1

462 Two variable analysis (Chapter 22)

IGCSE01

cyan magenta yellow black

(^05255075950525507595)
100 100
(^05255075950525507595)
100 100
Y:\HAESE\IGCSE01\IG01_22\462IGCSE01_22.CDR Monday, 27 October 2008 2:14:55 PM PETER