Question 1193518
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Forgive Ikleyn, she doesn't understand regression and correlation. And
she loves to run people down.

Solve one equation for x and the other for y, so that the product of
the coefficients of variables on the right are less than 1.  So we
solve the first one for x and the second one for y.

{{{matrix(3,3,
7x - 6y + 9,""="",0,  
7x,""="",6y-9,
x,""="",expr(6/7)y-9/7)}}}      {{{matrix(3,3,
5y - 4x - 3,""="",0,  
5y,""="",4x+3,
y,""="",expr(4/5)x+3/5)}}}

So

{{{matrix(1,3,b[xy],""="",6/7)}}} and {{{matrix(1,3,b[yx],""="",4/5)}}}

{{{r^2}}}{{{""=""}}}{{{b[xy]b[yx]}}}{{{""=""}}}{{{(6/7)(4/5)}}}{{{""=""}}}{{{24/35}}}

{{{r}}}{{{""=""}}}{{{sqrt(24/35)}}}{{{""=""}}}{{{0.8281}}} <--correlation coefficient

The point whose coordinates are the means is the point of
intersection of the two regression lines.

To find the mean value for x and y, solve the system

{{{system(7x - 6y + 9 = 0, 5y - 4x - 3 = 0)}}}

{{{system(7x - 6y = -9 , -4x + 5y = 3)}}}

Eliminate y by multiplying the first by 5 and the second by 6

{{{system(35x - 30y = -45 , -24x + 30y = 18)}}}

{{{11x=-27}}}

{{{x=-27/11}}}  <--mean value of x.


Eliminate x by multiplying the first by 4 and the second by 7

{{{system(28x - 24y = -36 , -28x + 35y = 21)}}}

{{{11y=-15}}}

{{{y=-15/11}}}  <--mean value of y.


Edwin</pre>