Correlation explained

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Correlation explains Relation between two

variables

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X Y

Correlation

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X

Y

NEGATIVE CORRELATION

When X increases

Y decreases

-

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X

Y

NEGATIVE CORRELATION

When X decreases

Y increases

-

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X Y

POSITIVE CORRELATION

When X decreases Y also decreases

+

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X Y

POSITIVE CORRELATION

When X Increases Y also Increases

+

Confused?

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Got it!

Correlation When?

+ X and Y move in same direction

_ X and Y move in opposite direction

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Correlation coefficient

Measures

Correlation

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Correlation coefficient is always between -1

and +1

Because, it is just a

scale and it is defined like that.

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0 +1 -1

X and Y move in opposite direction

X and Y move in same

direction

Correlation coefficient between variables X and Y

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0 +1 -1

Correlation coefficient between variables X and Y

NO Correlation

Scatterplots – Positive correlation

X Y 1 2 4 3 6 5 7 7 9 2

11 11

0

2

4

6

8

10

12

0 5 10 15

Variable Y

Variable X

Graph of Y plotted against X

Linear (Y)

Trend line has positive slope -

Positive correlation

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Scatterplots – Negative correlation

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X Y 1 10 4 8 6 5 7 3 9 2

11 11

0

2

4

6

8

10

12

0 5 10 15

Variable Y

Variable X

Graph of Y plotted against X

Linear (Y)

Trend line has negative slope -

Negative correlation

Scatterplot – zero correlation

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X Y 1 100 2 99 3 98 4 99 5 100

97.5

98

98.5

99

99.5

100

100.5

0 1 2 3 4 5 6

Y

Y

Linear (Y)

Trend line has zero slope – Zero correlation

Scatterplot – zero correlation

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X Y 1 100 2 100 3 100 4 100 5 100

0

20

40

60

80

100

120

0 1 2 3 4 5 6

Y

Y

Linear (Y)

Trend line has zero slope – Zero correlation

= Interpretation of correlation coefficient

‘Correlation does not mean causation’. That means if two variables have high correlation

then an inference CAN NOT be made that one is dependent on another or one is the cause of

other.

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Correlation Causation

Mathematically!

n*(∑XY) – (∑X)*(∑Y) SQRT[ (n*∑X^2 – (∑X)^2) * (n*∑Y^2 – (∑Y)^2)]

Corr. Coefficient =

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Pearson correlation (What we discussed till now) represents only a linear relationship

between two variables although the actual relationship between two variables may or

may not be linear.

Thanks!

For more information refer to

https://stats2analytics.wordpress.com/2016/05/12/correlation-explained/

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