The equation of the regression line for the paired data below is $\hat{y} = 3 x$. Find the total variation.
$\begin{array}{r|rrrr}
\mathrm{x} & 2 & 4 & 5 & 6 \
\hline \mathrm{y} & 7 & 11 & 13 & 20
\end{array}$
A) $10.00$
B) $88.75$
C) $92.25$
D) $78.75$

Question

Quizplus · Accepted Answer

The total variation (TV) in a regression analysis is the sum of the squared differences between the actual values of the dependent variable (y) and the mean of those values ($\bar{y}$). It is calculated as $\sum (y_i - \bar{y})^2$. First, we find the mean of y values: $\bar{y} = (7 + 11 + 13 + 20) / 4 = 51 / 4 = 12.75$. Then, we calculate the total variation: $TV = (7 - 12.75)^2 + (11 - 12.75)^2 + (13 - 12.75)^2 + (20 - 12.75)^2 = 33.0625 + 3.0625 + 0.0625 + 52.5625 = 88.75$.

The Equation of the Regression Line for the Paired Data y^=3x\hat{y} = 3 xy^​=3x

The Equation of the Regression Line for the Paired Data $\hat{y} = 3 x$