1.
Correlation and
Regression
-Aakriti Agarwal
Roll No. 13004
BMS 1A
2.
Correlation
β’
β’
β’
Correlation refers to statistical relationships
involving two random variables or sets of
data
The correlation coefficient is denoted by βrβ
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
β’
β’
β’
β’
β’
β’
β’
4.
Methods to calculate
Correlation
Coefficient
Karl
Pearson
Spearman
5.
Karl Pearson
π=
π
π=0(π₯1
π₯1 β π₯
β π₯ )(π¦1 β π¦)
2
π¦1 β π¦
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
13.
Practical Application
Correlation is used in:
β’ Business
β’ Government
β’ Education
β’ Medicine
β’ Agriculture
14.
Business
β’ Marketing Expenditure and Sales Volume
correlation (to measure the efficiency of
marketing department)
β’ Correlation between prices of two securities
in the stock market.
β’ Price of a commodity to supply(or demand)
correlation.
15.
Government
β’ Year on Year Revenue and Expenditure
Correlation (to forecast revenue based on
expenditure)
β’ Tool in formulating various Economic Policies
by correlating past trends.
β’ Yardstick to measure performance
(Correlation between Planned and Actual
Revenue)
16.
Education Models
β’ Forecasting of student input ο¬ows towards
elementary education (Correlation between
birth rate data and enrollment in
elementary grades)
β’ Forecasting of dropped out student flows at
different levels of education (intermediate,
graduate, post graduate)
17.
Medicine
β’ Finding out after effects of interactions
between different medicines.
β’ Estimating the best treatment where
various methods are applicable
(Correlation between individual
treatmentsβ results and severity of
disease.
18.
Agriculture
β’ Correlation between certain weather
conditions and Productivity.
β’ Correlation between irrigating and
Productivity.
β’ Correlation between price and production
or price and demand, to study demand
supply pattern of crops in different seasons.
19.
Conclusion
β’ Correlation is one of the many effective
ways of forecasting and predicting
possible outcomes based on past
observations.
β’ Though other statistical methods too
need to be implemented to get a
complete picture of the situation.
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