Correlation refers to statistical relationships between two random variables. The correlation coefficient r ranges from -1 to 1, indicating the direction and strength of the relationship. Karl Pearson and Spearman methods can be used to calculate r. While correlation indicates an association, it does not imply causation. Correlation is used in business, government, education, medicine, and agriculture to study relationships and make predictions.

1. Correlation and
Regression
-Aakriti Agarwal
Roll No. 13004
BMS 1A

2. Correlation
•
•
•
Correlation refers to statistical relationships
involving two random variables or sets of
data
The correlation coefficient is denoted by ‘r’
and ranges from -1 to +1
Tells the Direction and Measure of the
Relationship between two variables

3. Coefficient of Correlation
The coefficient of correlation can be:
perfectly negative
r=-1
strong negative
-1<r<0 and r closer to 1
weak negative
-1<r<0 and r closer to 0
independent
r=0
strong positive
0<r<1 and r closer to 1
weak positive
0<r<0 and r closer to 0
perfect positive
r=1
•
•
•
•
•
•
•

4. Methods to calculate
Correlation
Coefficient
Karl
Pearson
Spearman

5. Karl Pearson
𝑟=
𝑛
𝑖=0(𝑥1
𝑥1 − 𝑥
− 𝑥 )(𝑦1 − 𝑦)
2
𝑦1 − 𝑦
n - number of pairs of
observations
2

6. Data for Calculation in MS Excel
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
Sales
(in Unit Lakhs)
9.1
10.1
9.3
9.9
11.3
10.9
11.6
12.5
14
14.5
15
15.6
16.2
18
16
14
12
Lakhs
Year
Marketing
Expenditure
(In Rs. Lakhs)
8
10.5
11
12
12.9
13.5
11.6
10.9
13
14
15.3
16
17
10
8
Expenditure In Lakhs
6
Sales in Lakhs
4
2
0
2000
2005
2010
Year
2015

7. Pearson in MS Excel
2
2
Year
x
y
2001
8
9.1
-4.746153846 22.52598 -3.20769 10.28929
15.2242
2002
10.5
10.1
-2.246153846 5.045207 -2.20769 4.873905
4.958817
2003
11
9.3
-1.746153846 3.049053 -3.00769 9.046213
5.251893
2004
12
9.9
-0.746153846 0.556746 -2.40769 5.796982
1.796509
2005
12.9
11.3
0.153846154 0.023669 -1.00769 1.015444
-0.15503
2006
13.5
10.9
0.753846154 0.568284 -1.40769 1.981598
-1.06118
2007
11.6
11.6
-1.146153846 1.313669 -0.70769 0.500828
0.811124
2008
10.9
12.5
-1.846153846 3.408284 0.192308 0.036982
-0.35503
2009
13
14
0.253846154 0.064438 1.692308 2.863905
0.429586
2010
14
14.5
1.253846154 1.57213 2.192308 4.806213
2.748817
2011
15.3
15
2.553846154 6.52213 2.692308 7.248521
6.87574
2012
16
15.6
3.253846154 10.58751 3.292308 10.83929
10.71266
2013
17
16.2
4.253846154 18.09521 3.892308 15.15006
16.55728
𝒙
12.74615
∑
∑
∑
𝒚
12.30769
73.33231
74.44923
63.79538
𝑥1 − 𝑥
𝑥𝑖 − 𝑥
𝑦𝑖 − 𝑦
𝑦𝑖 − 𝑦
(𝑥 𝑖 − 𝑥 )(𝑦 𝑖 − 𝑦)
r=$H$16/($E$16*$G$16)^0.5
∑(𝑥 𝑖 − 𝑥 )(𝑦 𝑖 − 𝑦)
∑ 𝑥𝑖 − 𝑥
Square
root
2
∑ 𝑦𝑖 − 𝑦
2
R= 0.863399

8. Spearman
𝑟 =1−
6
2
𝐷
+
1
𝑛
𝑖=0 12
𝑛3 − 𝑛
3
𝑚𝑖
− 𝑚𝑖
m=no. of times a pair of
observations is repeated
D=Rank 1- Rank 2

9. Spearman in MS Excel
Year
x
y
Rank 1
Rank 2
D(R1-R2)
𝐷2
2001
8
9.1
1
1
0
0
2002
10.5
10.1
2
4
-2
4
2003
11
9.3
4
2
2
4
2004
12
9.9
6
3
3
9
2005
12.9
11.3
7
6
1
1
2006
13.5
10.9
9
5
4
16
2007
11.6
11.6
5
7
-2
4
2008
10.9
12.5
3
8
-5
25
2009
13
14
8
9
-1
1
2010
14
14.5
10
10
0
0
2011
15.3
15
11
11
0
0
2012
16
15.6
12
12
0
0
2013
17
16.2
13
13
0
0
=SUM(F3:F15)
=64
∑𝐷2
=1-(6*F17)/($A$1*($A$1^2-1))
∑𝐷 2
squaring
No. of pairs of
observations
R=0.824176

10. Are Correlation and Causation the same?

11. Correlation ≠ Causation
If it were, these would be true...

12. Practical
Applications

13. Practical Application
Correlation is used in:
• Business
• Government
• Education
• Medicine
• Agriculture

14. Business
• Marketing Expenditure and Sales Volume
correlation (to measure the efficiency of
marketing department)
• Correlation between prices of two securities
in the stock market.
• Price of a commodity to supply(or demand)
correlation.

15. Government
• Year on Year Revenue and Expenditure
Correlation (to forecast revenue based on
expenditure)
• Tool in formulating various Economic Policies
by correlating past trends.
• Yardstick to measure performance
(Correlation between Planned and Actual
Revenue)

16. Education Models
• Forecasting of student input flows towards
elementary education (Correlation between
birth rate data and enrollment in
elementary grades)
• Forecasting of dropped out student flows at
different levels of education (intermediate,
graduate, post graduate)

17. Medicine
• Finding out after effects of interactions
between different medicines.
• Estimating the best treatment where
various methods are applicable
(Correlation between individual
treatments’ results and severity of
disease.

18. Agriculture
• Correlation between certain weather
conditions and Productivity.
• Correlation between irrigating and
Productivity.
• Correlation between price and production
or price and demand, to study demand
supply pattern of crops in different seasons.

19. Conclusion
• Correlation is one of the many effective
ways of forecasting and predicting
possible outcomes based on past
observations.
• Though other statistical methods too
need to be implemented to get a
complete picture of the situation.

20. Thank You