Find the explained variation for the paired data.
-The equation of the regression line for the paired data below is $$\hat { y } = 3 x$$ x. Find the explained variation. $$\begin{array} { r | r r r r }
x & 2 & 4 & 5 & 6 \
\hline y & 7 & 11 & 13 & 20
\end{array}$$
A) 88.75
B) 10.00
C) 78.75
D) 72.45

Question

Find the explained variation for the paired data.
-The equation of the regression line for the paired data below is $$\hat { y } = 3 x$$ x. Find the explained variation. $$\begin{array} { r | r r r r } 
x & 2 & 4 & 5 & 6 \
\hline y & 7 & 11 & 13 & 20
\end{array}$$
A) 88.75
B) 10.00
C) 78.75
D) 72.45

Quizplus · Accepted Answer

The first step is to find the mean of x and y, which are $\bar {x} = 4.25$ and $\bar {y} = 12.75$. Then, we can find the total sum of squares (SST) by summing the squared differences between each y value and the mean of y:

$SST = (7-12.75)^2 + (11-12.75)^2 + (13-12.75)^2 + (20-12.75)^2 = 70.75$

Next, we can find the sum of squared errors (SSE) by summing the squared differences between each y value and its predicted value from the regression line:

$SSE = (7-6)^2 + (11-12)^2 + (13-15)^2 + (20-18)^2 = 16$

Finally, we can find the explained variation (SSR) by subtracting SSE from SST:

$SSR = SST - SSE = 70.75 - 16 = 54.75$

Therefore, the explained variation is 54.75, which corresponds to answer choice C.

Find the Explained Variation for the Paired Data y^=3x\hat { y } = 3 xy^​=3x

Find the Explained Variation for the Paired Data $\hat { y } = 3 x$