Correlation analysis establishes relationships between two variables. The correlation coefficient, r, measures the linear relationship between variables on a scale from -1 to 1, where -1 is total negative correlation, 1 is total positive correlation, and 0 is no correlation. A scatterplot diagrams the relationship between two variables based on their x and y values, showing the strength, shape, direction, and outliers of the relationship to help interpret the correlation coefficient.

2. CorrelationAnalysis is a
process for establishing the relationships
between two variables.
The measure is best used in variables
that demonstrate a linear relationship
between each other..

3. CorrelationCoefficient ( R ) or
the Pearson’s product moment
correlation coefficient in honor
of its developer Karl Pearson ).
It is numerical measure of the
linear relationship between two
variables usually labeled x and
y.

4. Scattergram is composed of the points
plotted in the rectangular coordinate
system, where x and y are respectively the
values of the independent and dependent
variables. It is useful when there are a large
number of data sets. They provide the
following information about the
relationship between two variables:
•Strength
•Shape –linear, curved, etc.
•Direction
•Presence of outliers

12. Interpretationof “r”orcorrelation
coefficients:
Between ±0.80to ±0.99 High correlation
Between ±0.60to ±0.79 Moderately high correlation
Between ±0.40to ±0.59
Moderately correlation
Between ±0.20to ±0.39 Low correlation
Between ±0.01to±0.19
Negligible correlation

13. r

14. The correlation coefficient, r, has a
specific range of values:

15. Note that:
•r never lies outside this range, therefore r = 2 is a
nonsense answer whose only explanation can be "I
made an arithmetic error".
•r =1 is perfect positive correlation and all the data
points lie exactly on a straight line with positive
gradient.
•r = -1 likewise is perfect negative correlation.
•r is often measured or referred to as a percentage.
In this case, the range is from -100% to 100%
(remembering that 100% is the same as 1)

16. Steps you need to follow:
1.draw the scatterplot;
2.draw the trend line which describes
the direction of the data;
3.evaluate how closely the cloud of data
points clusters around the line;
4.determine what r value and what word
descriptor best suits the data cloud.

17. The following diagram has a number line of r
values to help you assigning the numbers
and the word descriptors.

18. x
y
x2 y2
Student Scores in
Scores
in
Statistic
s
1
English
(x)
36
(y)
21
2 42 18
3 37 15
4 31 11
5 25 15
6 28 9
7 33 10
8 28 20
9 42 16
10 39 11
11 38 21
12 40 14
N =12 ∑x= ∑y= ∑xy= ∑x2= ∑y2=

20. Studen
t
Scores
in
Scores
in
Statistic
s
x
y
x2 y2
English (x) (y)
1 36 21 756 1296 441
2 42 18 756 1764 324
3 37 15 555 1369 225
4 31 11 341 961 121
5 25 15 375 625 225
6 28 9 252 784 81
7 33 10 330 1089 100
8 28 20 560 784 400
9 42 16 672 1764 256
10 39 11 429 1521 121
11 38 21 798 1444 441
12 40 14 560 1600 196
SUM: 419 181 6384 15001 2931