CORRELATION
•To be able to plot scattergraphs accurately
•To be able to describe and interpret correlation
•To be able to calculate Sxx, Syy, Sxy and the
product moment correlation coefficient (r)
•To understand the limitation of product
moment correlation
Scattergraphs
Vehicles (x)
Millions
8.6
13.4
12.8
9.3
1.3
9.4
13.1
Accidents (y)
thousands
33
51
30
48
12
23
46
4.9
13.5
9.6
7.5
9.8
23.3
21
19.4
18
36
50
34
35
95
99
69
Scattergraphs
Accidents (thousands)
Number of vehicles v number of accidents
100
95
90
85
80
75
70
65
60
55
50
45
40
35
30
25
20
15
10
5
0
0
5
10
15
Vehicles (millions)
20
25
Describe and interpret correlation
2nd 1st
3rd 4th
Positive correlation – mainly in the 1st and 3rd quadrants
Negative correlation – mainly in the 2nd and 4th quadrants
No correlation – equally spread in all 4 quadrants
Describe and Interpret Correlation
Describe Correlation
•State whether the correlation is strong or
weak, positive, negative or no correlation
Interpret Correlation
•Explain and analyse what the correlation
actually means
•E.g. as an athlete trains for longer their
active heartbeat reduces
Product Moment Correlation Coefficient
Calculates the variation between bivariate data
Variance = Σ(x – x)² , Σ(y – y)² , Σ(x – x)(y – y)
n
n
n
Sxx = Σ(x – x)²
Syy = Σ(y – y)²
Sxy = Σ(x – x)(y – y)
Notice that variance = Sxx therefore
n
variance x n = Sxx
Product Moment Correlation Coefficient
Notice that variance = Sxx therefore
variance x n = Sxx
n
Sxx = variance x n
Sxx = n Σx² - x ²
Sxx = Σx² - Σx ²
n
n
Sxx = Σx² - nx ²
Sxx = Σx² - n Σx ²
n
Sxx = Σx² - n Σx ²
n²
Syy = Σy² - Σy ²
n
Sxy = Σxy - ΣxΣy
n
Product Moment Correlation Coefficient
r=
Sxy
√Sxx Syy