Page 21 - Math SL HB Sem 3

Scatter Diagrams, Correlations and

Line of best fit

- whether two variables are related and how strong the relationship is...

Scatter diagrams:
Adata set that consists of two variables in each observation is called bivariate data.

\. Example:

Nine students ioined an investigation in which their head circumferences and their body heights
are measured.
Stude nts B C D E F G H
/
Circumferences of heads (x) cm 44.3 48.7 47 .5 45.0 43.1 44.2 48.0 42.6 47 .0
Heights (y)/cm IOJ 170 165 160 toz 164 151 '167

To see whether and to what extent the two variables (the circumferences of head and heights of
students) are related, a scatter diagram is plotted. The pattern of points shows us to which types of
correlation, if at all, the two variables belong.

s.rtter di.gram 5howlng helghts et.ln3t head drcumter€nces
175
170
165
i,*
E
155
-E
150
145
t40
42 43 44 45 45 47 48 49 50
Head cimc!mleren.e' /.m

Types of correlation:

v v v

x
lt
I
It x
x
T
x x x
High positive linear correla6on No correlation Hlgh n tive linear correlation

imply asI I v t imply a5 .t t v I

v v v
tx tt,

x .x x

Low positive linear correlation No linear correlation Low negative linear correlation

Jb