PPT: Correlation & Regression Analysis | Engineering Mathematics - Civil Engineering (CE) PDF Download

 Page 1


Correlation
Introduction:
? Two variables are said to be correlated if the change in 
one variable results in a corresponding change in the 
other variable.
? The correlation is a statistical tool which studies the 
relationship between two variables.
? Correlation analysis involves various methods and 
techniques used for studying and measuring the extent 
of the relationship between the two variables.
? Correlation is concerned with the measurement of 
“strength of association between variables”.
? The degree of association between two or more 
variables is termed as correlation.
2
Page 2


Correlation
Introduction:
? Two variables are said to be correlated if the change in 
one variable results in a corresponding change in the 
other variable.
? The correlation is a statistical tool which studies the 
relationship between two variables.
? Correlation analysis involves various methods and 
techniques used for studying and measuring the extent 
of the relationship between the two variables.
? Correlation is concerned with the measurement of 
“strength of association between variables”.
? The degree of association between two or more 
variables is termed as correlation.
2
Contd…
? Correlation analysis helps us to decide the strength of the 
linear relationship between two variables.
? The word correlation is used to decide the degree of 
association between variables.
? If two variables ‘x’ and ‘y’ are so related, the variables in the 
magnitude of one variable tend to be accompanied by 
variations in the magnitude of the other variable, they are 
said to be correlated.
? Thus, correlation is a statistical tool, with the help of which, 
we can determine whether or not two or more variables are 
correlate and if they are correlated, what is the degree and 
direction of correlation.
3
Page 3


Correlation
Introduction:
? Two variables are said to be correlated if the change in 
one variable results in a corresponding change in the 
other variable.
? The correlation is a statistical tool which studies the 
relationship between two variables.
? Correlation analysis involves various methods and 
techniques used for studying and measuring the extent 
of the relationship between the two variables.
? Correlation is concerned with the measurement of 
“strength of association between variables”.
? The degree of association between two or more 
variables is termed as correlation.
2
Contd…
? Correlation analysis helps us to decide the strength of the 
linear relationship between two variables.
? The word correlation is used to decide the degree of 
association between variables.
? If two variables ‘x’ and ‘y’ are so related, the variables in the 
magnitude of one variable tend to be accompanied by 
variations in the magnitude of the other variable, they are 
said to be correlated.
? Thus, correlation is a statistical tool, with the help of which, 
we can determine whether or not two or more variables are 
correlate and if they are correlated, what is the degree and 
direction of correlation.
3
Definition
?The correlation is the measure of the extent and 
the direction of the relationship between two 
variables in a bivariate distribution.
Example:
(i) Height and weight of children.
(ii) An increase in the price of the commodity by a 
decrease in the quantity demanded. 
Types of Correlation: The following are the types of 
correlation
(i) Positive and Negative Correlation
(ii) Simple, Partial and Multiple Correlation
(iii) Linear and Non-linear Correlation
4
Page 4


Correlation
Introduction:
? Two variables are said to be correlated if the change in 
one variable results in a corresponding change in the 
other variable.
? The correlation is a statistical tool which studies the 
relationship between two variables.
? Correlation analysis involves various methods and 
techniques used for studying and measuring the extent 
of the relationship between the two variables.
? Correlation is concerned with the measurement of 
“strength of association between variables”.
? The degree of association between two or more 
variables is termed as correlation.
2
Contd…
? Correlation analysis helps us to decide the strength of the 
linear relationship between two variables.
? The word correlation is used to decide the degree of 
association between variables.
? If two variables ‘x’ and ‘y’ are so related, the variables in the 
magnitude of one variable tend to be accompanied by 
variations in the magnitude of the other variable, they are 
said to be correlated.
? Thus, correlation is a statistical tool, with the help of which, 
we can determine whether or not two or more variables are 
correlate and if they are correlated, what is the degree and 
direction of correlation.
3
Definition
?The correlation is the measure of the extent and 
the direction of the relationship between two 
variables in a bivariate distribution.
Example:
(i) Height and weight of children.
(ii) An increase in the price of the commodity by a 
decrease in the quantity demanded. 
Types of Correlation: The following are the types of 
correlation
(i) Positive and Negative Correlation
(ii) Simple, Partial and Multiple Correlation
(iii) Linear and Non-linear Correlation
4
Contd…
?Correlation first developed by Sir Francis 
Galton (1822 – 1911) and then reformulated 
by Karl Pearson (1857 – 1936)
?Note: The degree of relationship or 
association is known as the degree of 
relationship.
5
Page 5


Correlation
Introduction:
? Two variables are said to be correlated if the change in 
one variable results in a corresponding change in the 
other variable.
? The correlation is a statistical tool which studies the 
relationship between two variables.
? Correlation analysis involves various methods and 
techniques used for studying and measuring the extent 
of the relationship between the two variables.
? Correlation is concerned with the measurement of 
“strength of association between variables”.
? The degree of association between two or more 
variables is termed as correlation.
2
Contd…
? Correlation analysis helps us to decide the strength of the 
linear relationship between two variables.
? The word correlation is used to decide the degree of 
association between variables.
? If two variables ‘x’ and ‘y’ are so related, the variables in the 
magnitude of one variable tend to be accompanied by 
variations in the magnitude of the other variable, they are 
said to be correlated.
? Thus, correlation is a statistical tool, with the help of which, 
we can determine whether or not two or more variables are 
correlate and if they are correlated, what is the degree and 
direction of correlation.
3
Definition
?The correlation is the measure of the extent and 
the direction of the relationship between two 
variables in a bivariate distribution.
Example:
(i) Height and weight of children.
(ii) An increase in the price of the commodity by a 
decrease in the quantity demanded. 
Types of Correlation: The following are the types of 
correlation
(i) Positive and Negative Correlation
(ii) Simple, Partial and Multiple Correlation
(iii) Linear and Non-linear Correlation
4
Contd…
?Correlation first developed by Sir Francis 
Galton (1822 – 1911) and then reformulated 
by Karl Pearson (1857 – 1936)
?Note: The degree of relationship or 
association is known as the degree of 
relationship.
5
Types of Correlation
i. Positive and Negative correlation: If both the 
variables are varying in the same direction i.e. if one 
variable is increasing and the other on an average is 
also increasing or if as one variable is decreasing, the 
other on an average, is also decreasing, correlation is 
said to be positive. If on the other hand, the variable 
is increasing, the other is decreasing or vice versa, 
correlation is said to be negative.
Example 1: a) heights and weights (b) amount of rainfall 
and yields of crops (c) price and supply of a 
commodity (d) income and expenditure on luxury 
goods (e) blood pressure and age
Example 2: a) price and demand of commodity (b) sales 
of woolen garments and the days temperature.
6