Correlation: Understanding the Basics, Study notes of Statistics

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Correlation

• Correlation is the relationship that exists between two or more variables.
• If two variables are related to each other in such a way that change increases a corresponding change in other, then variables are said to be correlated.

Uses of Correlation

• Economic theory and business

studies relationship between

variables like price and quantity

demand.

• Correlation analysis helps in

deriving precisely the degree and

the direction of such relationships.

• The effect of correlation is to

reduce the range of uncertainty of our prediction.

• The prediction based on

correlation analysis will more reliable and near to reality.

Negative correlation

• If both the variables are vary in the opposite direction ,correlation is said to be Negative.
• If one variable increases ,the other decrease or ,if one variable decreases ,the other also increases ,then the two variables are said to be Negative.

Types of Correlation

• Simple correlation
• Multiple correlation
• Partial Multiple correlation

Scatter Diagram Method

• Scatter diagrams are used to

demonstrate correlation

between two quantitative

variables.

Quantitative Aptitude & BusinessStatistics: Correlation 11

Scatter Plots of Data with Various Correlation Coefficients

Y

X

Y

X

Y

X

Y

X

Y

X

r = -1 r = -Ve r = 0

r = +Ve r = 1

The value of r lies between - 1 and +

• If r=0 There exists no relationship

between the variables

• If +0.75 ≤r ≤ +1 There exists high

positive relationship between the

variables.

• If -0.75 ≥ r ≥ -1 There exists high

negative relationship between the

variables

• If +0.5 ≤r ≤ 0.75 There exists Moderate positive relationship between the variables.
• If -0.50 ≥ r >-0.75 There exists moderate negative relationship between the variables.
• If r > -0.50 There exists low negative relationship between the variables
• If r <0.5 There exists low positive relationship between the variables.

Properties of Co-Variance

• Independent of Choice of origin
• not Independent of Choice of Scale.
• Co-variance lies between negative infinity to positive infinity.
• In other words co-variance may be positive or negative or Zero.

From the following Data

Calculate

Co-Variance

X 1 2 3 4 5

Y 10 20 30 50 40

Quantitative Aptitude & BusinessStatistics: Correlation 19

• N= number of pairs =

3 5

15 = = =

N

X X (^) 30

N

Y

Y

N

xy

N

X X Y Y

Cov X Y

Karl Pearson's Correlation

• The most widely used

mathematical method for

measuring the intensity or the

magnitude of linear

relationship between two

variables was suggested by

Karl Pearson's