Correlation and correlation coefficient are explained in detail.

1. Correlation explained
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2. Correlation explains
Relation between two
variables
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X Y
Correlation

3. https://stats2analytics.wordpress.com/
X
Y
NEGATIVE CORRELATION
When X increases
Y decreases
-

4. https://stats2analytics.wordpress.com/
X
Y
NEGATIVE CORRELATION
When X decreases
Y increases
-

5. https://stats2analytics.wordpress.com/
X Y
POSITIVE CORRELATION
When X decreases Y also decreases
+

6. https://stats2analytics.wordpress.com/
X Y
POSITIVE CORRELATION
When X Increases Y also Increases
+

7. Confused?
See Next....

8. Got it!
Correlation When?
+ X and Y move in same
direction
_ X and Y move in opposite
direction

9. https://stats2analytics.wordpress.com/
Correlation
coefficient
Measures
Correlation

10. https://stats2analytics.wordpress.com/
Correlation coefficient
is always between -1
and +1
Because, it is just a
scale and it is defined
like that.

11. https://stats2analytics.wordpress.com/
0 +1-1
X and Y move in
opposite
direction
X and Y move
in same
direction
Correlation coefficient
between variables X and Y

12. https://stats2analytics.wordpress.com/
0 +1-1
Correlation coefficient
between variables X and Y
NO
Correlation

13. 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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14. 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

15. 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

16. 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

17. =
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

18. 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.

19. Thanks!
For more information refer to
https://stats2analytics.wordpress.com/20
16/05/12/correlation-explained/
https://stats2analytics.wordpress.com/