Statistical Methods

Unit 9 - Correlation and regression

9.7 Properties of regression lines

• The regression lines intersect at point .
• If the variables are perfectly correlated, the regression lines coincide.
• If the variables are not correlated the regression lines of Y on X and X on Y are perpendicular to each other.

Relation between correlation and regression coefficients
If byx is the regression coefficient in the regression equation of Y on X and b_xy is the regression coefficient in the regression equation of X on Y, then the correlation coefficient r is the square root of the product of b_yx and b_xy.
i.e.,

Test of significance of linearity of regression (significance of regression coefficient)
The significance of the linearity of regression is tested by one of the following methods:

• The method of analysis of variance
• t- test

Let β denote the population regression coefficient. The hypothesis to be tested is
1. H_o : β = 0 (There is no significant linear regression)
2. H₁ : β ≠ 0 (There is significant linear regression)
3. α : 0.05 Say
4. Test statistic is t =

5. Reject H_o if calculated t is more than table t value at (n-2) degrees of freedom, otherwise accept H_o of no significant correlation
Example: Correlation computed between standard length and total length of 38 randomly selected oil sardines is found to be 0.82.Test for significance.