The equation of the regression line for the paired data below is $\hat { y } = 3 x$. Find the standard error of estimate.
$\begin{array}{r|rrrr}
\mathrm{x} & 2 & 4 & 5 & 6 \
\hline \mathrm{y} & 7 & 11 & 13 & 20
\end{array}$
A) $2.2361$
B) $4.1892$
C) $5.00$
D) $6.2750$

Question

Quizplus · Accepted Answer

The standard error of estimate (SEE) measures the accuracy of predictions made with a regression line. It's calculated using the formula $\sqrt{\frac{\sum(y - \hat{y})^2}{n-2}}$, where $y$ is the actual value, $\hat{y}$ is the predicted value from the regression equation, and $n$ is the number of data points. Given the regression equation $\hat{y} = 3x$, we calculate the predicted values for each $x$ and then the differences ($y - \hat{y}$) squared. Summing these and dividing by $n-2$ (4 data points, so $n-2 = 2$), then taking the square root gives the SEE. Calculating with the given data, the SEE is found to be approximately $2.2361$.

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 $\hat { y } = 3 x$