Answer:
A. [tex]y=1.5x+0.5[/tex]
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, [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex].
We get, the slope of the linear regression is,
Slope = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex].
i.e. Slope = [tex]\frac{5-2}{3-1}[/tex].
i.e. Slope = [tex]\frac{3}{2}[/tex].
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,
[tex]y=mx+b[/tex] implies [tex]2=1.5\times 1+b[/tex] implies [tex]b=2-1.5[/tex] i.e. b= 0.5
Hence, the equation for the regression line is [tex]y=1.5x+0.5[/tex]
