Question

What is the equation for the linear model in the scatterplot obtained by choosing the two points closest to the line

Answer 1

consider two points closest to the line. say ,

$\begin{gathered} (x_1,y_1)=(6,0) \\ (x_2_{}_{}_{},y_2)=(8,1) \end{gathered}$

let us find the slope, m by the formula

$m=\frac{y_2-y_1}{x_2_{}_{}-x_1}$

subsitute the points in the formula,

$\begin{gathered} m=\frac{1-0}{8-6} \\ m=\frac{1}{2} \end{gathered}$

let us find the y - intercept.

$y=mx+b\ldots(1)$

subsitute the one of the point (6,0) in the above equation.

$\begin{gathered} 0=\frac{1}{2}\times6+b \\ 0=3+b \\ b=-3 \end{gathered}$

thus,

subsitute m= 1/2 and b = - 3 in the equation (1),

$y=\frac{1}{2}x-3$