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=(1-0)/(8-6) \\ m=(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=(1)/(2)*6+b \\ 0=3+b \\ b=-3 \end{gathered}`

thus,

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

`y=(1)/(2)x-3`