Question

the regression line are 9x+y=15and 4x+y=5 correlation r(xy)

Answer 1

Answer:

I didn't know about this lecture notes mang

Answer 2

Concept:

A regression line is a line that is used to represent how a set of data behaves. The link between a predictor variable and the response is described by regression coefficients.

Given:

The given regression lines are $9x+y=15$ and $4x+y=5$.

Find:

The coefficient of correlation (r).

Solution:

The given lines of regression are:

$9x+y=15$                      ...... eq (1)

$4x+y=5$                        ...... eq (2)

From eq (1) the regression line of x on y

$9x+y=15$

⇒ $x=\frac{15-y}{9}$

⇒ $x=\frac{15}{9} -\frac{1}{9} y$

∴ $b_{xy} =-\frac{1}{9}$

From eq (2) the regression line of y on x

$4x+y=5$

⇒ $y=5-4x$

∴ $b_{yx} =-4$

Calculate the coefficient of correlation (r)

$r=\sqrt{b_{xy}*b_{yx}}$

$r=\sqrt{(-\frac{1}{9})*(-4) }$

$r=\sqrt{\frac{4}{9}}$

$r=\frac{2}{3}$

$r=0.66$

The coefficient of correlation is 0.66.