use linear regression to find a function that fits the following points. (-2, -1) (3, 9) ?x +
use linear regression to find a function that fits the following points. (-2, -1) (3, 9) ?x +
Answer
Explanation:
Step1: Calculate the slope
The slope $m$ of the 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: Calculate the y - intercept
Use the point - slope form $y - y_1=m(x - x_1)$ and then convert to slope - intercept form $y=mx + b$. Let's use the point $(x_1,y_1)=(-2,-1)$ and $m = 2$. Substitute into $y - y_1=m(x - x_1)$: $y-(-1)=2(x - (-2))$, which simplifies to $y + 1=2(x + 2)$. Expand the right side: $y+1=2x + 4$. Then solve for $y$: $y=2x+3$. So the y - intercept $b = 3$.
Answer:
$2x + 3$