Correlation coefficient

• Statistic showing the degree of relation between two variables.
• Value lies between -1 to +1.
• If ,

i) r = 1 : Perfect positive correlation

ii) r = -1 : Perfect negative correlation

iii) r = 0 : No correlation

iv) r = 0.8 , 0.9 , 0.99 : Strong positive correlation

v) r = -0.85 , -0.9 , -0.95 : Strong negative correlation

a) Simple correlation coefficient (r):

• Also called Pearson’s correlation or product moment correlation coefficient.
• Measures nature and strength between two quantitative variables.
• Measures nature and strength between two quantitative variables.
• The sign ‘r’ denotes the nature of Association.
• Value of ‘r’ denotes strength of association.
• Positive sign means increase in one variable Means , increase in another variable and vice-versa ( o to 1).
• Negative sign means increase in one variable , decrease in another variable. ( -1 to 0)
• Value lies between -1 to + 1.

b) Partial correlation:

• Used to study the relationship between the variables taking away the effects of another variable.

Assumptions of partial correlation:

a) One dependent and one independent variable and both measured on continuous scale.

b) One or more control variable.

c) linear relationship between all three variables.

d) Variables must be normally distributed.