, then the Y-intercept of the least-squares regression line is $$\text { If } \bar { Y } = 21 , \bar { X } = 6 \text {, and } b = + 1.5 \text {, }$$ .
A)+30.0
B)-12.0
C)+12.0
D)-30.0

Question

, then the Y-intercept of the least-squares regression line is   $$\text { If } \bar { Y } = 21 , \bar { X } = 6 \text {, and } b = + 1.5 \text {, }$$ .
A)+30.0 
B)-12.0 
C)+12.0 
D)-30.0

Quizplus · Accepted Answer

The equation of the least-squares regression line is $\hat {y} = b \left( x - \bar { x } \right) + \bar { y }$. Substituting the given values, we get $\hat {y} = 1.5 \left( x - 6 \right) + 21$. To find the y-intercept, we set $x$ to $0$ and solve for $\hat {y}$. Therefore, the y-intercept is $\hat { y } = 1.5 \left( 0 - 6 \right) + 21 = \boxed{12}$, so the answer is (C).

, Then the Y-Intercept of the Least-Squares Regression Line Is If Yˉ=21,Xˉ=6, and b=+1.5, \text { If } \bar { Y } = 21 , \bar { X } = 6 \text {, and } b = + 1.5 \text {, } If Yˉ=21,Xˉ=6, and b=+1.5,

, Then the Y-Intercept of the Least-Squares Regression Line Is $\text { If } \bar { Y } = 21 , \bar { X } = 6 \text {, and } b = + 1.5 \text {, }$