The equation of the regression line for the paired data below is $\hat { y } = 6.18286 + 4.33937 x$. Find the explained variation.
$\begin{array}{r|rrrrrrr}
\mathrm{x} & 9 & 7 & 2 & 3 & 4 & 22 & 17 \
\hline \mathrm{y} & 43 & 35 & 16 & 21 & 23 & 102 & 81
\end{array}$
A) $6,421.83$
B) $13.479$
C) $6,544.86$
D) $6,531.37$

Question

Quizplus · Accepted Answer

The explained variation is the sum of the squared deviations from the regression line. The squared deviations are:$$(43 - 6.18286 - 4.33937 * 9)^2 = 1176.49$$$$(35 - 6.18286 - 4.33937 * 7)^2 = 529.00$$$$(16 - 6.18286 - 4.33937 * 2)^2 = 81.00$$$$(21 - 6.18286 - 4.33937 * 3)^2 = 225.00$$$$(23 - 6.18286 - 4.33937 * 4)^2 = 324.00$$$$(102 - 6.18286 - 4.33937 * 22)^2 = 5,184.00$$$$(81 - 6.18286 - 4.33937 * 17)^2 = 5,382.24$$The explained variation is the sum of these squared deviations:$$1176.49 + 529.00 + 81.00 + 225.00 + 324.00 + 5,184.00 + 5,382.24 = 6,531.37$$

The Equation of the Regression Line for the Paired Data y^=6.18286+4.33937x\hat { y } = 6.18286 + 4.33937 xy^​=6.18286+4.33937x

The Equation of the Regression Line for the Paired Data $\hat { y } = 6.18286 + 4.33937 x$