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Unit 10: Correlation: Scatter Diagram Method, Karl Pearson's Coefficient of Correlation

of very little relationship between the variables—correlation shall be positive if the points are rising Notes
from the lower left-hand corner to the upper right hand corner (diagram V) and negative if the points
are running from the upper left-hand side to the lower right-hand side of the diagram (diagram VI).
If the plotted points lie on a straight line parallel to the x-axis or in a haphazard manner, it shows the
absence of any relationship between the variables, (i.e., r = 0) as shown by diagram VII.

HIGH DEGREE OF HIGH DEGREE OF
POSITIVE NEGATIVE
CORRELATION CORRELATION

Y Y

X X

V VI

NO CORRELATION ( = 0)
r

Y

X

VII
Example 1: Given the following pairs of value of the variables X and Y:

X: 2 3 7 6 8 9
Y: 6 5 5 8 12 11

(a) Make a scatter diagram.
(b) Do you think that there is any correlation between the variables X and Y ? Is it
positive or negative ? Is it high or low ?
(c) By graphic inspection, draw an estimating line.
Solution: By looking at the following scatter diagram we can say that the variables X and Y are
correlated. Further, correlation is positive because the trend of the points is upward
rising from the lower left-hand corner to the upper right-hand corner of the diagram.
The diagram also indicates that the degree of relationship is high because the plotted
points are near to the line which shows perfect relationship between the variables.

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