Question

use linear regression to find a function that fits the following points. (5, 2.4) (10, 8.9) ?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, $x_1 = 5,y_1=2.4,x_2 = 10,y_2 = 8.9$. So $m=\frac{8.9 - 2.4}{10 - 5}=\frac{6.5}{5}=1.3$.

Step2: Calculate the y - intercept

We use the point - slope form $y=mx + b$ and substitute one of the points, say $(x_1,y_1)=(5,2.4)$ and $m = 1.3$. Then $2.4=1.3\times5 + b$. Solving for $b$, we get $b=2.4-1.3\times5=2.4 - 6.5=-4.1$.

Answer:

$1.3x-4.1$