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

Algebra.Com's Answer #825618 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "
\r\n" );
document.write( "Forgive Ikleyn, she doesn't understand regression and correlation. And\r\n" );
document.write( "she loves to run people down.\r\n" );
document.write( "\r\n" );
document.write( "Solve one equation for x and the other for y, so that the product of\r\n" );
document.write( "the coefficients of variables on the right are less than 1.  So we\r\n" );
document.write( "solve the first one for x and the second one for y.\r\n" );
document.write( "\r\n" );
document.write( "      \r\n" );
document.write( "\r\n" );
document.write( "So\r\n" );
document.write( "\r\n" );
document.write( "\"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\n" );
document.write( "\r\n" );
document.write( "\"r%5E2\"\"%22%22=%22%22\"\"b%5Bxy%5Db%5Byx%5D\"\"%22%22=%22%22\"\"%286%2F7%29%284%2F5%29\"\"%22%22=%22%22\"\"24%2F35\"\r\n" );
document.write( "\r\n" );
document.write( "\"r\"\"%22%22=%22%22\"\"sqrt%2824%2F35%29\"\"%22%22=%22%22\"\"0.8281\" <--correlation coefficient\r\n" );
document.write( "\r\n" );
document.write( "The point whose coordinates are the means is the point of\r\n" );
document.write( "intersection of the two regression lines.\r\n" );
document.write( "\r\n" );
document.write( "To find the mean value for x and y, solve the system\r\n" );
document.write( "\r\n" );
document.write( "\"system%287x+-+6y+%2B+9+=+0%2C+5y+-+4x+-+3+=+0%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"system%287x+-+6y+=+-9+%2C+-4x+%2B+5y+=+3%29\"\r\n" );
document.write( "\r\n" );
document.write( "Eliminate y by multiplying the first by 5 and the second by 6\r\n" );
document.write( "\r\n" );
document.write( "\"system%2835x+-+30y+=+-45+%2C+-24x+%2B+30y+=+18%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"11x=-27\"\r\n" );
document.write( "\r\n" );
document.write( "\"x=-27%2F11\"  <--mean value of x.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Eliminate x by multiplying the first by 4 and the second by 7\r\n" );
document.write( "\r\n" );
document.write( "\"system%2828x+-+24y+=+-36+%2C+-28x+%2B+35y+=+21%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"11y=-15\"\r\n" );
document.write( "\r\n" );
document.write( "\"y=-15%2F11\"  <--mean value of y.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );