finding a linear regression model\nfind a linear function that models the data in the table.\nf(x) = x +…

Explanation:

Step1: Recall linear - function form

A linear function is of the form $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept.

Step2: Calculate the slope $m$

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let's take two points, say $(x_1,y_1)=(0,1)$ and $(x_2,y_2)=(2,4)$. Then $m=\frac{4 - 1}{2-0}=\frac{3}{2}$.

Step3: Find the y - intercept $b$

We know that when $x = 0$, $y=b$ in the equation $y=mx + b$. From the table, when $x = 0$, $y = 1$, so $b = 1$.

Answer:

$\frac{3}{2}x+1$