'Correlation' studies and measures the direction and intensity of relationship among variables. "Scatter diagram" is a useful technique of visual presentation of the relationship between the two variables, say X and Y. Correlation is commonly classified into negative and positive correlation. Correlation is positive when the variable X rises, variable Y will also rise and vice-versa. This means both X and Y move in the same direction. Correlation is negative when the two variables X and Y move in the opposite directions, i.e., when X rises, Y falls and vice-versa.
The value of co-efficient of correlation (r) lies between minus 1 and plus 1,\(-1 \leq r \leq 1\).
(i) If r = 0, the two variables are uncorrelated. There is no linear relation between them.
(ii) If r = \(\pm 1\), the correlation is perfect with exact linear relation.
(iii) A high value of r indicates strong linear relationship.
(iv) A low value of r (close to zero) indicates a weak linear relation.
(a) Define a 'Scatter Diagram'.
(b) Answer the following q~estions:
(i) Does zero correlation mean independence?
(ii) Does r = ±l indicate perfect correlation between the given two variables? (iii) Does a high value of r indicate a weak linear relation?