Positive and Negative Correlation

Introduction on positive and negative correlation:

The term correlation deals with the connection between two or more variables. If modify in one variable the result will affect another variable, the variables are said to be correlated.

There are basically three type of correlation, namely,

Positive correlation
Negative correlation
Zero correlation.

Types of correlation:

Positive correlation:

If the value of two variables diverge (change) in the same direction i.e. If the increment (or decrement) in one variable results in a corresponding increment (or decrement) in the order, the correlation between them is said to be positive.

Negative correlation:

If the value of two variables diverge (change) in the opposite direction i.e. If the increment (or decrement) in one variable results in a corresponding decrement (or increment) in the order, the correlation between them is said to be negative.

Zero correlation:

There is no relationship between two variable means such a correlation is a zero correlation

Formula of Correlation Coefficient: Positive and Negative Correlation

Correlation Co-Efficient:
Correlation(r) =    `(N sum XY -sum xsum y )/(sqrt[Nsum x^2 - (sum x)^2][Nsum y^2 - (sum y)^2 ] )`
where
N = Number of values or elements
X = First Score
Y = Second Score
SXY = Sum of the product of first and Second Scores
SX = Sum of First Scores
SY = Sum of Second Scores
SX2 = Sum of square First Scores
SY2 = Sum of square Second Scores

Example Problem for Positive and Negative Correlation:

Example problem on positive correlation :-

x:        5             10            15         20

y:        2              4              6           8

Solution:

Here the value of the variable x is increase and the corresponding variable y will be increase manner. So it’s a positive correlation

From the formula we need to find (SX), (SY), SXY, SX2, SY2    4 N=4

X          Y         X2           Y2               XY

5          2         25             4                 10

10         4         100          16                40

15         6         225          36                90

20         8         400          64                160

-------    ------       -------       ------              -------

50        20         750          120                300

Understanding easy math problems for kids is always challenging for me but thanks to all math help websites to help me out.

Substitute the value in the formula we get,

R=`(4* 300 - 50*20 )/(sqrt(4*750 - (50)^2 (4*120) - (20)^2))`

R=`(1200-1000)/(sqrt((3000-2500)(480-400)))`

R = `(200)/(sqrt(500*80))`

R=200/ 200

R= 1

Practice problem on negative correlation:

x:        15             12            10         8

y:        13              11             9         6