Correction and Regression | Business Mathematics and Statistics - B Com PDF Download

 Page 1


Correlation and Regression 
1
Page 2


Correlation and Regression 
1
Correlation 
• Definition: The extent (degree) of the linear relationship between two
variables is called correlation.
• Correlation analysis is a statistical tool, that measures the closeness or
strength of the relationship between the variables.
• In correlation, two variables are inter-dependent or co-vary and we can not
make distinction between the independent and dependent variables. E.g birth
weight and maternal height, drug intake and number of days taken to cure
etc.
• Correlation analysis is not only establishing relationship but also quantify it.
Correlation is unable to indicate the cause and effect relationship between
two variables.
2
Page 3


Correlation and Regression 
1
Correlation 
• Definition: The extent (degree) of the linear relationship between two
variables is called correlation.
• Correlation analysis is a statistical tool, that measures the closeness or
strength of the relationship between the variables.
• In correlation, two variables are inter-dependent or co-vary and we can not
make distinction between the independent and dependent variables. E.g birth
weight and maternal height, drug intake and number of days taken to cure
etc.
• Correlation analysis is not only establishing relationship but also quantify it.
Correlation is unable to indicate the cause and effect relationship between
two variables.
2
Types of Correlation
On the basis of the nature of relationship between the
variables, correlation can be categorized as
1.Positive and negative correlation.
2.Simple, partial and multiple correlation
3.Linear and non-linear
3
Page 4


Correlation and Regression 
1
Correlation 
• Definition: The extent (degree) of the linear relationship between two
variables is called correlation.
• Correlation analysis is a statistical tool, that measures the closeness or
strength of the relationship between the variables.
• In correlation, two variables are inter-dependent or co-vary and we can not
make distinction between the independent and dependent variables. E.g birth
weight and maternal height, drug intake and number of days taken to cure
etc.
• Correlation analysis is not only establishing relationship but also quantify it.
Correlation is unable to indicate the cause and effect relationship between
two variables.
2
Types of Correlation
On the basis of the nature of relationship between the
variables, correlation can be categorized as
1.Positive and negative correlation.
2.Simple, partial and multiple correlation
3.Linear and non-linear
3
Positive correlation
• This correlation is also called, 
direct correlation. 
• In this, an increase or decrease 
in the value of one variable is 
associated with the increase or 
decrease in the value of the 
other.
• In this, both variables move in 
the same direction. 
• E.g. number of tillers and plant 
yield in wheat, plant yield and 
number of pods, number of 
days and height of the plant, 
etc. 
4
0
10
20
30
40
50
60
70
1 2 3 4 5
No. of days
No. of days
Page 5


Correlation and Regression 
1
Correlation 
• Definition: The extent (degree) of the linear relationship between two
variables is called correlation.
• Correlation analysis is a statistical tool, that measures the closeness or
strength of the relationship between the variables.
• In correlation, two variables are inter-dependent or co-vary and we can not
make distinction between the independent and dependent variables. E.g birth
weight and maternal height, drug intake and number of days taken to cure
etc.
• Correlation analysis is not only establishing relationship but also quantify it.
Correlation is unable to indicate the cause and effect relationship between
two variables.
2
Types of Correlation
On the basis of the nature of relationship between the
variables, correlation can be categorized as
1.Positive and negative correlation.
2.Simple, partial and multiple correlation
3.Linear and non-linear
3
Positive correlation
• This correlation is also called, 
direct correlation. 
• In this, an increase or decrease 
in the value of one variable is 
associated with the increase or 
decrease in the value of the 
other.
• In this, both variables move in 
the same direction. 
• E.g. number of tillers and plant 
yield in wheat, plant yield and 
number of pods, number of 
days and height of the plant, 
etc. 
4
0
10
20
30
40
50
60
70
1 2 3 4 5
No. of days
No. of days
Negative correlation
• In this, increase in one variable 
causes the proportionate 
decrease in the other variable. 
• Here the two variables move in 
the opposite direction.  
• E.g. supply and price of 
commodity. If the supply of the 
commodity is more, price fall 
and if there is scarcity of the 
commodity, then the price goes 
up. Here there is negative 
relationship between supply 
and price.
5
0
20
40
60
80
100
120
1 2 3 4 5
Supply (Tonnes)