Find the unexplained variation for the paired data.
-The paired data below consists of heights and weights of 6 randomly selected adults. The equation of the regression line is $\hat { \mathrm { y } } = - 181.342 + 144.46 \mathrm { x }$. Find the unexplained variation.
$\begin{array}{c|rrrrrr}
\text { x Height (meters) } & 1.61 & 1.72 & 1.78 & 1.80 & 1.67 & 1.88 \
\hline \text { y Weight }(\mathrm{kg}) & 54 & 62 & 70 & 84 & 61 & 92
\end{array}$

A) $100.06$
B) $119.3$
C) $979.44$
D) $1079.5$

Question

Find the unexplained variation for the paired data.
-The paired data below consists of heights and weights of 6 randomly selected adults. The equation of the regression line is $\hat { \mathrm { y } } = - 181.342 + 144.46 \mathrm { x }$. Find the unexplained variation.
$\begin{array}{c|rrrrrr}
\text { x Height (meters) } & 1.61 & 1.72 & 1.78 & 1.80 & 1.67 & 1.88 \
\hline \text { y Weight }(\mathrm{kg}) & 54 & 62 & 70 & 84 & 61 & 92
\end{array}$

A) $100.06$
B) $119.3$
C) $979.44$
D) $1079.5$

Quizplus · Accepted Answer

The unexplained variation is the sum of the squared residuals. The residual for each data point is the difference between the observed value and the predicted value. The squared residual is the square of the residual. The sum of the squared residuals is the unexplained variation.The predicted values for the data points are:$\hat { \mathrm { y } } = - 181.342 + 144.46 \mathrm { x }$$\hat { \mathrm { y } } = - 181.342 + 144.46 ( 1.61 ) = 53.98$$\hat { \mathrm { y } } = - 181.342 + 144.46 ( 1.72 ) = 63.02$$\hat { \mathrm { y } } = - 181.342 + 144.46 ( 1.78 ) = 72.06$$\hat { \mathrm { y } } = - 181.342 + 144.46 ( 1.80 ) = 74.10$$\hat { \mathrm { y } } = - 181.342 + 144.46 ( 1.67 ) = 60.94$$\hat { \mathrm { y } } = - 181.342 + 144.46 ( 1.88 ) = 83.08$The residuals are:$54 - 53.98 = 0.02$$62 - 63.02 = -1.02$$70 - 72.06 = -2.06$$84 - 74.10 = 9.90$$61 - 60.94 = 0.06$$92 - 83.08 = 8.92$The squared residuals are:$0.02^2 = 0.0004$$(-1.02)^2 = 1.0404$$(-2.06)^2 = 4.2436$$9.90^2 = 98.01$$0.06^2 = 0.0036$$8.92^2 = 79.5824$The sum of the squared residuals is the unexplained variation:$0.0004 + 1.0404 + 4.2436 + 98.01 + 0.0036 + 79.5824 = 182.8804$The unexplained variation is 182.8804.

Find the Unexplained Variation for the Paired Data y^=−181.342+144.46x\hat { \mathrm { y } } = - 181.342 + 144.46 \mathrm { x }y^​=−181.342+144.46x

Find the Unexplained Variation for the Paired Data $\hat { \mathrm { y } } = - 181.342 + 144.46 \mathrm { x }$