Question

use linear regression to find a function that fits the following points. (-2, -4) (8, 1) ?x +

Explanation:

Step1: Calculate the slope

The formula for the slope $m$ of a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Here, $x_1=-2,y_1 = - 4,x_2=8,y_2 = 1$. So $m=\frac{1-(-4)}{8-(-2)}=\frac{1 + 4}{8 + 2}=\frac{5}{10}=0.5$.

Step2: Calculate the y - intercept

The equation of a line is $y=mx + b$. We can substitute one of the points and the slope into this equation to find $b$. Let's use the point $(8,1)$ and $m = 0.5$. Then $1=0.5\times8 + b$. Simplify the right - hand side: $1 = 4 + b$. Solve for $b$: $b=1 - 4=-3$.

Answer:

$0.5x-3$