Understanding Simple Linear Correlation in Commerce: Lecture Compilation by Dr. Parminder Kaur

Ch – 10 SIMPLE LINEAR CORRELATION
 
 
Lecture compiled by
  
Dr. Parminder Kaur
  
Assistant Professor
  
Department of Commerce
 
 
For B.Com(Prog) II Sem Sec A
SIMPLE LINEAR CORRELATION
 
DEFINITION OF CORRELATION
“If two or more quantities vary in sympathy so
that movements in one tend to be
accompanied by corresponding movements in
other(s) then they are said to be correlated.”
     
Or
“Correlation is an analysis of co-variation
between two or more variables.”
TYPES OF CORRELATION
 
The following are different types of
correlation:
Positive and Negative Correlation
Simple, Partial and Multiple Correlation
Linear and Non-linear Correlation
 Positive and Negative Correlation
 
The correlation between two variables is said
to be 
positive or direct
 if an increase (or a
decrease) in one variable corresponds to an
increase (or a decrease) in the other.
The correlation between two variables is said
to be 
negative or inverse
 if an increase (or a
decrease) corresponds to a decrease (or an
increase) in the other.
Simple, Partial and Multiple Correlation
 
Simple Correlation: 
It involves the study of only two variables. For
example, when we study the correlation between the price and
demand of a product, it is a problem of simple correlation.
Partial Correlation: 
It involves the study of three or more variables,
but considers only two variables to be influencing each other. For
example, if we consider three variables, namely yield of wheat,
amount of rainfall and amount of fertilizers and limit our correlation
analysis to yield and rainfall, with the effect of fertilizers removed, it
becomes a problem relating to partial correlation only.
Multiple Correlation: 
It involves the study of three or more
variables simultaneously. For example, if we study the relationship
between the yield of wheat per acre and both amount of rainfall
and the amount of fertilizers used, it becomes a problem relating to
multiple correlation.
Linear and Non-linear Correlation
 
Linear Correlation: 
The correlation between two
variables is said to be 
linear 
if the amount of
change in one variable tends to bear a constant
ratio to the amount of change in other variable.
Non-linear (or Curvilinear): 
The correlation
between two variables is said to be 
non-linear or
curvilinear
 if the amount of change in one
variable does not bear a constant ratio to the
amount of change in other variable.
METHODS OF STUDYING
CORRELATION
 
Scatter Diagram Method
Karl Pearson’s Coefficient of
Correlation, and
Rank Correlation  Method
Scatter Diagram Method
 
A scatter diagram of the data helps in having a
visual idea about the nature of association
between two variables. If the points cluster
along a straight line, the association between
two variables is linear. Further, if the points
cluster along a curve, the corresponding
association is non-linear or curvilinear. Finally,
if the points neither cluster along a straight
line nor along a curve, there is absence of any
association between the variables.
Covariance
 
The covariance between X and Y, is denoted by Cov (X, Y)
 
 
Thankyou
 
Lecture sourced from
Book “Business Mathematics and Statistics” by R. S. Bhardwaj
Book “Business Mathematics and Statistics” by Dr. J. K. Thukral
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Correlation analysis is essential in understanding the co-variation between two or more variables. This lecture compiled by Dr. Parminder Kaur, an Assistant Professor in the Department of Commerce, delves into the definition of correlation, types of correlation such as positive/negative, simple/partial/multiple, and linear/non-linear correlations. It explores methods of studying correlation including scatter diagram and Karl Pearson's Coefficient of Correlation. Gain insights into how variables relate and influence each other in the realm of commerce.


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  1. Ch 10 SIMPLE LINEAR CORRELATION Lecture compiled by Dr. Parminder Kaur Assistant Professor Department of Commerce For B.Com(Prog) II Sem Sec A

  2. SIMPLE LINEAR CORRELATION DEFINITION OF CORRELATION If two or more quantities vary in sympathy so that movements in accompanied by corresponding movements in other(s) then they are said to be correlated. Or Correlation is an analysis of co-variation between two or more variables. one tend to be

  3. TYPES OF CORRELATION The correlation: Positive and Negative Correlation Simple, Partial and Multiple Correlation Linear and Non-linear Correlation following are different types of

  4. Positive and Negative Correlation The correlation between two variables is said to be positive or direct if an increase (or a decrease) in one variable corresponds to an increase (or a decrease) in the other. The correlation between two variables is said to be negative or inverse if an increase (or a decrease) corresponds to a decrease (or an increase) in the other.

  5. Simple, Partial and Multiple Correlation Simple Correlation: It involves the study of only two variables. For example, when we study the correlation between the price and demand of a product, it is a problem of simple correlation. Partial Correlation: It involves the study of three or more variables, but considers only two variables to be influencing each other. For example, if we consider three variables, namely yield of wheat, amount of rainfall and amount of fertilizers and limit our correlation analysis to yield and rainfall, with the effect of fertilizers removed, it becomes a problem relating to partial correlation only. Multiple Correlation: It involves the study of three or more variables simultaneously. For example, if we study the relationship between the yield of wheat per acre and both amount of rainfall and the amount of fertilizers used, it becomes a problem relating to multiple correlation.

  6. Linear and Non-linear Correlation Linear Correlation: The correlation between two variables is said to be linear if the amount of change in one variable tends to bear a constant ratio to the amount of change in other variable. Non-linear (or Curvilinear): The correlation between two variables is said to be non-linear or curvilinear if the amount of change in one variable does not bear a constant ratio to the amount of change in other variable.

  7. METHODS OF STUDYING CORRELATION Scatter Diagram Method Karl Pearson s Coefficient of Correlation, and Rank Correlation Method

  8. Scatter Diagram Method A scatter diagram of the data helps in having a visual idea about the nature of association between two variables. If the points cluster along a straight line, the association between two variables is linear. Further, if the points cluster along a curve, the corresponding association is non-linear or curvilinear. Finally, if the points neither cluster along a straight line nor along a curve, there is absence of any association between the variables.

  9. Covariance The covariance between X and Y, is denoted by Cov (X, Y)

  10. Thankyou Lecture sourced from Book Business Mathematics and Statistics by R. S. Bhardwaj Book Business Mathematics and Statistics by Dr. J. K. Thukral

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