Question

Find the equation of the regression line when x is 77,50, 71,52, 81,94, 96,99, 67 while y is, 82,66, 78, 34,47, 85,99, 99,68

Answer 1

To find the regression line, the method of least squares is applied. The regression line is given by, $y(hat)= k*x+m$ where, $k$ is the slope coefficient and $m$ is the intercept. In order to find the regression equation we first estimate $k$ and $m$ using the formula below,

$k=(n*summation(xy)-summation(x)*summation(y))/(n*summation(x^2)-(summation(x))^2)$

$m=mean(y)-k*mean(x)$

The above data can be summarized as follows,

$n=9, summation(x)=687, summation(y)=658, summation(x^2)=55077, summation(y^2)=51980, summation(x*y)=52578, mean(y)=summation(y)/n=76.333333, mean(x)=summation(x)/n=73.111111$

$k=((9*52578)-(687*658))/((9*55077)-(687)^2) =0.8918(4 decimal places), m=76.333333-(0.8918*73.1111111) =5.0405(4 decimal places)$

Therefore, equation of the regression line is given as,

$y(hat)=0.8918*x+5.0405.$