SOLUTION: The regression equations are; 7x - 6y + 9 = 0 and 5y - 4x - 3 = 0. Find a. The coefficient of correlation b. Mean value of x c. Mean value of y

Algebra ->  Probability-and-statistics -> SOLUTION: The regression equations are; 7x - 6y + 9 = 0 and 5y - 4x - 3 = 0. Find a. The coefficient of correlation b. Mean value of x c. Mean value of y      Log On


   



Question 1193518: The regression equations are; 7x - 6y + 9 = 0 and 5y - 4x - 3 = 0. Find
a. The coefficient of correlation
b. Mean value of x
c. Mean value of y

Found 2 solutions by ikleyn, Edwin McCravy:
Answer by ikleyn(52832) About Me  (Show Source):
You can put this solution on YOUR website!
.

This is some gibberish raised in degree of 3 . . .


A mixture of pieces from two  (if not more)  different problems.



Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
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.

      

So

matrix%281%2C3%2Cb%5Bxy%5D%2C%22%22=%22%22%2C6%2F7%29 and matrix%281%2C3%2Cb%5Byx%5D%2C%22%22=%22%22%2C4%2F5%29

r%5E2%22%22=%22%22b%5Bxy%5Db%5Byx%5D%22%22=%22%22%286%2F7%29%284%2F5%29%22%22=%22%2224%2F35

r%22%22=%22%22sqrt%2824%2F35%29%22%22=%22%220.8281 <--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%287x+-+6y+%2B+9+=+0%2C+5y+-+4x+-+3+=+0%29

system%287x+-+6y+=+-9+%2C+-4x+%2B+5y+=+3%29

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

system%2835x+-+30y+=+-45+%2C+-24x+%2B+30y+=+18%29

11x=-27

x=-27%2F11  <--mean value of x.


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

system%2828x+-+24y+=+-36+%2C+-28x+%2B+35y+=+21%29

11y=-15

y=-15%2F11  <--mean value of y.


Edwin