Question

what is the equation for the linear model in the scatter plot obtained by choosing the two points closest to the line? variable x variable y 22 12 22 21 10 36 13 22 6 30 35 3 20 33

Explanation:

Step1: Select two points on the line

Let's choose two points on the line from the scatter - plot. For example, we can choose $(x_1,y_1)=(10,36)$ and $(x_2,y_2)=(20,33)$.

Step2: Calculate the slope $m$

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Substituting the values, we get $m=\frac{33 - 36}{20 - 10}=\frac{- 3}{10}=-0.3$.

Step3: Use the point - slope form $y - y_1=m(x - x_1)$

Using the point $(x_1,y_1)=(10,36)$ and $m = - 0.3$, we have $y-36=-0.3(x - 10)$.

Step4: Simplify the equation

$y-36=-0.3x + 3$. Then $y=-0.3x+39$.

Answer:

$y=-0.3x + 39$