Question

If the coefficient of correlation between two variables X and Y, p=1, then the angle between

the two lines of regression is :
​

Answer 1

Answer:

∴∴ Tangent of the angle made by  

Lyzwith X- axis = tan θθ = 0.6

But , slope of any line with X-axis = tan θθ

However, slope of  

Lyx= byxLyx= byx

∴∴ byxbyx = tan θθ = 0.6

But byx=r*σy/σx

therefore 0.6=r *2σx/σx.............

0.6=2r

r=0.3

Step-by-step explanation:

Answer 2

The angle between the two lines of regression is 0° or the lines reside on one another.

If the coefficient of correlation between two variables X and Y is $p=1$ , it implies that there is a perfect positive linear relationship between the two variables. In other words, every point in the scatter plot lies in a straight line.

In this scenario, the angle between the two lines of regression will be 0 degrees or they will coincide with each other. This is because the lines of regression are calculated based on the correlation between X and Y. When the correlation is perfect ($p=1$), the lines of regression will coincide with each other and there will be no angle between them.

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