Question

given the data points (1, 3), (2, 5), and (3, 7), what is the equation of the line of regression (best - fit line)?
○ y = 3x - 1
○ y = 2x + 1
○ y = 2x - 1
○ y = x + 2

Explanation:

Step1: Calculate $\bar{x}$ and $\bar{y}$

$\bar{x} = \frac{1+2+3}{3} = 2$
$\bar{y} = \frac{3+5+7}{3} = 5$

Step2: Compute slope $m$

First calculate numerator: $\sum(x_i-\bar{x})(y_i-\bar{y}) = (1-2)(3-5)+(2-2)(5-5)+(3-2)(7-5) = (-1)(-2)+0+1(2) = 4$
Denominator: $\sum(x_i-\bar{x})^2 = (1-2)^2+(2-2)^2+(3-2)^2 = 1+0+1 = 2$
$m = \frac{4}{2} = 2$

Step3: Find intercept $b$

Use $\bar{y}=m\bar{x}+b$: $5 = 2*2 + b$
$b = 5-4 = 1$

Step4: Form regression equation

$y = mx + b$

Answer:

B. y=2x+1