Correlation and Regression
· Correlation: The
correlation is the measure of extent and direction
of relationship between two variables in two bivariate
distribution. Two variables are said to have correlation when they are so related that the change in the value of one
variable is accompanied by the change in the
value of other.
· Positive
and negative correlation: If two variables vary in the same
direction, i.e. if increase or decrease in the values of one variable
corresponds to increase or decrease in another variable then the correlation is
considered to be positive correlation.
On the other hand
if two variables very in the opposite direction, i.e. if one variable increase
or decreases corresponds to the second variable decrease or increase then the two
variables are considered to have negative correlation.
· Linear
and non-linear correlation
A linear correlation coefficient
is a measure of linear relationship between the two variables X and Y. If all
the points in the scatter diagram seem to lie near a line, then the correlation
is called linear. If the points seems to lie near to some curve, then the
correlation is called non-linear.
Simple and Multiple or partial correlation
Correlation between two variable - simple
Correlation
coefficient between more than two variables - multiple or partial
· Scatter
diagram: Scatter diagram is a simple and attractive method of
diagrammatic representation of bivariate distribution for ascertaining the
nature of correlation between two variables.
· Coefficient of correlation: The
coefficient of correlation is a number which indicates to what extent two
variables are related, to what extent variations in one go with the variations
in the other. The coefficient of correlation lies between –1 and 1 inclusive.
· Karl Pearson's Coefficient of
Correlation: One of the widely used mathematical methods of calculating
the correlations coefficient between two variable is Karl Pearson's correlation
coefficient. It is denoted by rxy or
simply r and is defined by
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