Example If q is the acute angle between the two regression lines in the case of two variables x and y show that

with usual meanings. Explain the significance when r = 0 and r = ± 1.

Solution: The slopes of the two regression lines are

If r = q then tan q = ¥ or q = p/2 i.e. there is no relationship between two variables i.e. independent or uncorrelated.

If r = ± 1 then q = 0. The two regression lines are coincident or parallel and the correlation is perfect.

Index

6. 1 Introduction
6. 2 Correlation
6. 3 Types of Correlation
6. 4 Degrees of Correlation
6. 5 Methods of determining correlation
6. 6 Coefficients of Correlation for Bivariate Grouped Data
6. 7 Probable Error
6. 8 Rank Correlation Coefficient
6. 9 Linear Regression