Compute the Sum of Squared Residuals
-Compute the sum of the squared residuals of the least-squares line for the given data.
$\begin{array}{|c|c|c|c|c|c|c|c|c|c|c|}
\mathrm{x} & -5 & -3 & 4 & 1 & -1 & -2 & 0 & 2 & 3 & -4 \
\hline \mathrm{y} & -10 & -8 & 9 & 1 & -2 & -6 & -1 & 3 & 6 & -8
\end{array}$

A) $7.624$
B) $1.036$
C) $2.097$
D) 0

Question

Compute the Sum of Squared Residuals
-Compute the sum of the squared residuals of the least-squares line for the given data.
$\begin{array}{|c|c|c|c|c|c|c|c|c|c|c|}
\mathrm{x} & -5 & -3 & 4 & 1 & -1 & -2 & 0 & 2 & 3 & -4 \
\hline \mathrm{y} & -10 & -8 & 9 & 1 & -2 & -6 & -1 & 3 & 6 & -8
\end{array}$

A) $7.624$
B) $1.036$
C) $2.097$
D) 0

Quizplus · Accepted Answer

The sum of the squared residuals is the sum of the squared differences between the observed values and the predicted values. The least-squares line for the given data is y = 0.8x - 1.6. The predicted values are:y(-5) = 0.8(-5) - 1.6 = -6.4y(-3) = 0.8(-3) - 1.6 = -4y(4) = 0.8(4) - 1.6 = 1.6y(1) = 0.8(1) - 1.6 = -0.8y(-1) = 0.8(-1) - 1.6 = -2.4y(-2) = 0.8(-2) - 1.6 = -3.2y(0) = 0.8(0) - 1.6 = -1.6y(2) = 0.8(2) - 1.6 = 0y(3) = 0.8(3) - 1.6 = 0.8y(-4) = 0.8(-4) - 1.6 = -4.8The squared residuals are:(-10 - (-6.4))^2 = 12.96(-8 - (-4))^2 = 16(9 - 1.6)^2 = 56.76(1 - (-0.8))^2 = 3.24(-2 - (-2.4))^2 = 0.16(-6 - (-3.2))^2 = 7.84(-1 - (-1.6))^2 = 0.36(3 - 0)^2 = 9(6 - 0.8)^2 = 26.24(-8 - (-4.8))^2 = 10.24The sum of the squared residuals is 12.96 + 16 + 56.76 + 3.24 + 0.16 + 7.84 + 0.36 + 9 + 26.24 + 10.24 = 142.8.

Compute the Sum of Squared Residuals -Compute the Sum of the Squared

Compute the Sum of Squared Residuals
-Compute the Sum of the Squared