The degree to which one variable can be predicted
from another linearly related variable is given by a
statistic called the coefficient of determination.
The coefficient of determination is = r2
 The coefficient of determination is found by squaring
the correlation coefficient r
 It tells us how well the values of the DV can be
predicted by the values of the IV
 We usually convert r2 into % form and state “___% of
the variation in the DV can be explained by the
variation in the IV”
Examples
1.
If the correlation coefficient r = -0.451, calculate r2
and convert into % form
ANSWER:
r2 = -0.451 x -0.451 = 0.2034
0.2034 x 100% = 20.34%
Examples
2. For the scatterplot shown, the coefficient of
determination r2 = 0.789.
Calculate the correlation coefficient r.
Examples
ANSWER:
r=
The scatterplot shows a NEGATIVE correlation so we
choose the negative option (-0.8883)
Interpreting the results
3. Data relating number of accidents (DV) and years of
driving experience (IV) has the correlation coefficient r
= -0.242. Calculate the coefficient of determination
and interpret the results.
ANSWER:
r2 = -0.242 x -0.242 = 0.0586
0.0586 x 100% = 5.86%
Interpreting the results
 “5.86 % of the variation in number of accidents can be
explained by the variation in the years of driving
experience”
4.8 Correlation and causality
 A correlation is a relationship between two variables.
 Causality is when the outcome of one variable is
directly caused by another variable.
 Even for strong correlations, it is incorrect to conclude
that one variable CAUSES another to change. There
may be a high dependence but there are almost always
other factors involved.
Example
 There is a strong positive correlation between heights
and weights of 200 surveyed people aged 12-25. Does
this mean that all taller people are also heavier? What
other factors may be involved?
Solution:
 We CANNOT say that weight is CAUSED by height,
though there is an obvious correlation between the
two. Other factors may include diet, metabolism,
exercise, stress levels, genetics etc...
4.9 Which graph?
 When investigating relationships between variables,
use the table below to determine the most appropriate
graphical representation.
 Insert table from page 122
Questions
• Ex 4G Q1, 2, 3 (a,b)
• Ex 4H Q1-4
• Ex 4I (copy table from pg 122 and use it to answer all of
Q1)
• From chapter review read through skills check pg 124.
If you are unsure of any skills from ch4, now is the best
time to ask for help.
• Chapter review: Multiple choice Q1-15, Short answer
Q1-5