The following information regarding a dependent variable y and an independent variable x is provided: $$\begin{array} { l l }
\Sigma x = 90 & \sum \left( y - \frac { y } { ) } \right) ( x - x ) = - 156 \
\Sigma y = 340 & \Sigma \left( x - \frac { x } { 2 } \right) ^ { 2 } = 234 \
n = 4 & \sum ( y - y ) ^ { 2 } = 1974 \
\mathrm { SSR } = 104 &
\end{array}$$ The y-intercept is
A) -.667.
B) .667.
C) 100.
D) -100.

Question

The following information regarding a dependent variable y and an independent variable x is provided: $$\begin{array} { l l } 
\Sigma x = 90 & \sum \left( y - \frac { y } { ) } \right) ( x - x ) = - 156 \
\Sigma y = 340 & \Sigma \left( x - \frac { x } { 2 } \right) ^ { 2 } = 234 \
n = 4 & \sum ( y - y ) ^ { 2 } = 1974 \
\mathrm { SSR } = 104 &
\end{array}$$   The y-intercept is
A) -.667.
B) .667.
C) 100.
D) -100.

Quizplus · Accepted Answer

The y-intercept (b0) in a simple linear regression can be calculated using the formula: b0 = (Σy/n) - b1(Σx/n). First, calculate the slope (b1) using the formula: b1 = Σ((y - ȳ)(x - x̄)) / Σ((x - x̄)²) = -156 / 234 = -0.667. Then, calculate the mean of x and y: x̄ = Σx/n = 90/4 = 22.5, ȳ = Σy/n = 340/4 = 85. Finally, calculate the y-intercept: b0 = 85 - (-0.667)(22.5) = 100.

The Following Information Regarding a Dependent Variable Y and an Independent