Course Outlines

Correlation – Pearson's correlation,

 Rank correlation,

 Probable error and properties of correlation.

Regression – Equation of regression,

 Angle between regression lines,

 Properties, Standard error of estimate.


Introduction 

·   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.

·   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


·     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.

·     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.

·     Interpretation of correlation coefficient:

i) When r = +1, there is perfect positive correlation between the variables.

ii) When r = –1, there is perfect negative correlation between the variables.    iii)   When r = 0, there is no correlation between the variables.

iv) When r lies between 0.7 to 0.999 (or – 0.7 to – 0.999), there is a high degree of positive (or negative) correlation between the variables.

v)   When r lies between 0.5 to 0.699 )or - 0.5 to – 0.699) there is a moderate degree of positive (or negative) correlation between the variables.

vi)  When r is less than 0.5 there is low degree of correlation.