This document defines and explains different types of correlation between two variables: positive correlation, negative correlation, no correlation, perfect correlation, strong correlation, and weak correlation. It provides examples of scatter plots that illustrate positive and negative correlation, and includes formulas to calculate the correlation coefficient (r) between two variables from their data values.

1. Saira Kazim
sairakazim@gmail.com

2.  Correlation is a statistical measure that
indicates the extent to which two or more
variables fluctuate together.

3.  Positive Correlation
 Negative Correlation
 No Correlation
 Perfect Correlation
 Strong Correlation
 Weak Correlation

4.  Positive correlation occurs when an increase
in one variable increases the value in
another.
 The line corresponding to the scatter plot is
an increasing line.

5.  Negative correlation occurs when an increase
in one variable decreases the value of
another.
 The line corresponding to the scatter plot is
a decreasing line.

6.  No correlation occurs when there is no linear
dependency between the variables.

7.  Perfect correlation occurs when there is a
functional dependency between the
variables.
 In this case all the points are in a straight
line.

8.  A correlation is stronger the closer the points
are located to one another on the line.

9.  A correlation is weaker the farther apart the
points are located to one another on the
line.

10. Formula No. 1
r=∑xy/√∑x2∑y2
Formula No. 2

11. X Y
4 4
9 7
11 11
7 5
4 3

12. X Y x y x2 y2 xy
4 4 3 2 9 4 6
9 7 -2 -1 4 1 2
11 11 -4 -5 16 25 20
7 5 0 1 0 1 0
4 3 3 3 9 9 9
∑x=35 ∑y=30 ∑x2 =38 ∑y2 = 40 ∑xy=37
Mean=7 Mean=6
r=∑xy/√∑x2∑y2
=37/√38*40
=37/√1520
=37/38.98
r=0.949
answer

13. x y X2 Y2 xy
4 4 16 16 16
9 7 81 49 63
11 11 121 121 121
7 5 25 25 35
4 3 9 9 12
∑x=35 ∑y=30 ∑x2 =283 ∑y2 =220 ∑xy=247
= 5*247-35*30/√ [5*283-(35)2][5*220-(30)2]
=1235-1050/√[1415-1225][1100-900]
=185/√[190][200]
=185/√38000
=185/194.93
r=0.949 answer