Question

obtain the regression line (y=a+bx) from the following data

x: 5 9 1 10 5

y:7 10 3 8 2

Answer 1

$\overline{x}=\frac{30}{5}=6,\:\:\overline{y}=\frac{30}{5}=6$

$\overline{x}=6\:and\:\overline{y}=6$

$b_{yx}=\frac{n\sum xy-\sum x\sum y}{n\sum x^2-\left(\sum x^2\right)}=\frac{5\left(218\right)-\left(30\times 30\right)}{5\left(232\right)-232}$

$\:b_{yx}=\frac{1090-900}{1160-232}=\frac{190}{928}=\frac{95}{464}$

Regression line $y$ on $x$

$\:y-\overline{y}=b_{yx}\left(x-\overline{x}\right)$

$y-6=\frac{95}{464}\left(x-6\right)$

$464y-2784=95x-570$

$464y=95x+2214$

$464y=95x+2214$

$\:\:y=\frac{2214}{464}+\frac{95}{464}x$