Question

use linear regression to find a function that fits the following points. (-2, -1) (3, 9) ?x +

Explanation:

Step1: Find the slope

The slope $m$ of a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $m=\frac{y_2 - y_1}{x_2 - x_1}$. Here, $x_1=-2,y_1 = - 1,x_2=3,y_2 = 9$. So $m=\frac{9-(-1)}{3-(-2)}=\frac{9 + 1}{3+2}=\frac{10}{5}=2$.

Step2: Find the y - intercept

The equation of a line is $y=mx + b$. We know $m = 2$, and we can use one of the points, say $(x = - 2,y=-1)$. Substitute into the equation: $-1=2\times(-2)+b$. Then $-1=-4 + b$. Solving for $b$, we get $b=-1 + 4=3$.

Answer:

$2x+3$