The paired data below consists of test scores and hours of preparation for 5 randomly selected students. The equation of the regression line is $\hat { y } = 44.8447 + 3.52427 x$. Find the total variation.
$\begin{array}{c|rrrrr}
\mathrm{x} \text { Hours of preparation } & 5 & 2 & 9 & 6 & 10 \
\hline \mathrm{y} \text { Test score } & 64 & 48 & 72 & 73 & 80
\end{array}$
A) $599.2$
B) $87.4757$
C) $498.103$
D) $511.724$

Question

Quizplus · Accepted Answer

The total variation is calculated by summing the squared differences between each observed value (test score) and the mean of all observed values. Given the test scores (64, 48, 72, 73, 80), the mean test score is $\frac{64 + 48 + 72 + 73 + 80}{5} = 67.4$. The total variation is calculated as: $(64 - 67.4)^2 + (48 - 67.4)^2 + (72 - 67.4)^2 + (73 - 67.4)^2 + (80 - 67.4)^2 = 599.2$.

The Paired Data Below Consists of Test Scores and Hours y^=44.8447+3.52427x\hat { y } = 44.8447 + 3.52427 xy^​=44.8447+3.52427x

The Paired Data Below Consists of Test Scores and Hours $\hat { y } = 44.8447 + 3.52427 x$