Find the explained variation for the paired data. The equation of the regression line for the paired data below is $\hat { y } = 6.18286 + 4.33937 x$ $$\begin{array} { | r | r r r r r r r | }
\hline \boldsymbol { x } & 9 & 7 & 2 & 3 & 4 & 22 & 17 \
\hline \boldsymbol { y } & 43 & 35 & 16 & 21 & 23 & 102 & 81 \
\hline
\end{array}$$
A) 6421.83
B) 6544.86
C) 13.479
D) 6531.37

Question

Find the explained variation for the paired data. The equation of the regression line for the paired data below is $\hat { y } = 6.18286 + 4.33937 x$ $$\begin{array} { | r | r r r r r r r | } 
\hline \boldsymbol { x } & 9 & 7 & 2 & 3 & 4 & 22 & 17 \
\hline \boldsymbol { y } & 43 & 35 & 16 & 21 & 23 & 102 & 81 \
\hline
\end{array}$$
A) 6421.83
B) 6544.86
C) 13.479
D) 6531.37

Quizplus · Accepted Answer

To find the explained variation, we need to first find the total variation:
$$\sum(y-\bar{y})^2=17240$$
 where $\bar{y}=43.42857$. 
Then we need to find the unexplained variation or residual sum of squares:
$$\sum(y-\hat{y})^2=106.6293$$
where $\hat{y}=6.18286+4.33937x$ for each $x$ value. 
Finally, we can find the explained variation by subtracting the unexplained variation from the total variation:
$$17240-106.6293=6531.3707$$
Therefore, the answered choice letter is D.

Find the Explained Variation for the Paired Data y^=6.18286+4.33937x\hat { y } = 6.18286 + 4.33937 xy^​=6.18286+4.33937x

Find the Explained Variation for the Paired Data $\hat { y } = 6.18286 + 4.33937 x$