Question

For two given sets of data it is known that x bar is 10 and y bar is 4,the gradient of the regression line y on x is 0.6 .Find the equation of the regression line and estimate y when x = 2

Answer 1

$$\bar{y}=a+b\bar{x}$$

$b=0.6$

Given that $\bar{y}=4, \bar{x}=10$. Then

$$4=a+0.6(10)$$

Solve for $a$

$$a=4-6$$ $$a=-2$$

The equation of the regression line 

$$\bar{y}=-2+0.6\cdot\bar{x}$$

Estimate $y$ when $x=2$

$$y=-2+0.6\cdot2$$ $$y=-0.8$$