Cambridge International Mathematics

Consider again theOpening problem.

After plotting the mean on the scatter diagram, we draw in the line of best fit by eye.

As this line is an estimate only, lines drawn by eye will vary from person to person.

Having found our line of best fit, we can then use this linear model to estimate a value ofyfor any given

value ofx.

Example 1 Self Tutor

Ten students were surveyed to find the number of marks they received in a pre-test for a module of

work, and a test after it was completed.

The results were: Pre-test (x) 40 79 60 65 30 73 56 67 45 85

Post-test (y) 48 91 70 71 50 85 65 75 60 95

a Find the mean point (x,y).

b Draw a scatter diagram of the data. Mark the point (x,y) on the scatter diagram and draw in the

line of best fit.

c Estimate the mark for another student who was absent for the post-test but scored 70 for the

pre-test.

a x=

40 + 79 + 60 +::::::+85

10

=60

y=

48 + 91 + 70 +::::::+95

10

=71 So, (x,y)is( 60 , 71 ).

B LINE OF BEST FIT BY EYE [11.9]

75

80

85

90

95

100

105

175 180 185 190 195 200 205

Weight versus Height

height (cm)

weight (kg)

For the , the mean point is

approximately ( , ).

Opening problem

187 88

The scatter diagram for this data is shown

alongside. We can see there is a moderate

positive linear correlation between the variables,

so it is reasonable to use a line of best fit to

model the data.

One way to do this is to draw a straight line through the data points which:

² includes themean point(x,y)

² has about as many points above

the line as are below it.

75

80

85

90

95

100

105

175 180 185 190 195 200 205

Weight versus Height

height (cm)

weight (kg)

Two variable analysis (Chapter 22) 459

IGCSE01

cyan magenta yellow black

(^05255075950525507595)
100 100
(^05255075950525507595)
100 100
Y:\HAESE\IGCSE01\IG01_22\459IGCSE01_22.CDR Monday, 27 October 2008 2:14:45 PM PETER