Theta is the acute angle between these regression lines.

The equation of the line of regression of y on x is 3x +2y -26 =0 and that of the line of regression of x on y is 6x + y - 31 =0. Find the angle theta between these two regression lines with the help of correlation coefficient and it's square.I have calculated it with the help of slope formula but when i calculated taking r and it's square, both the answers are different. I think i am somewhere wrong. Help from any member of this forum is appreciated.

Re: Theta is the acute angle between these regression lines.

I don't know why you would need the correlation coefficient. Have you started by graphing the two lines? Do you know that the gradient of a line can be found by $\displaystyle \displaystyle \begin{align*} m = \tan{(\theta)} \end{align*}$, where $\displaystyle \displaystyle \begin{align*} \theta \end{align*}$ is the angle measured in the anticlockwise direction of the positive x-axis? If you have the gradients of the lines (which you should be able to get quite easily), you can evaluate the angles made with the x-axis, and with a diagram you should then be able to use basic geometry to evaluate the angle between your two lines.

You always need to TRY some things BEFORE asking for help, and you should post WHAT you have done so that we know WHERE you are stuck and need the specific help.

Re: Theta is the acute angle between these regression lines.

Hi,Thanks for your reply.I calculated the angle between these two regression lines by both methods. Both the answers are same and correct. I was misled by the wrong formula calculation inadvertently made by the author of book.Author put product of two regression coefficients ( correlation coefficient) instead of sum of two regression coefficients in the denominator part of formula.ANSWER: 24.2277 IN DEGREES