Question

Rose drew a regression line for this paired data set.

Answer 1

Answer:

A. $y=1.5x+0.5$

Step-by-step explanation:

We are given that,

The linear regression passes through the points (1,2) and (3,5).

As, the slope of a linear line is given by, $\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$.

We get, the slope of the linear regression is,

Slope = $\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$.

i.e. Slope = $\frac{5-2}{3-1}$.

i.e. Slope = $\frac{3}{2}$.

i.e. Slope = 1.5

As, the linear line is given by 'y=mx+b', where m is the slope and b is the y-intercept.

Substituting the slope and point (1,2) in the general form, we have,

$y=mx+b$ implies $2=1.5\times 1+b$ implies $b=2-1.5$ i.e. b= 0.5

Hence, the equation for the regression line is $y=1.5x+0.5$