Compute the Standard Error of the Estimate
-Find the standard error of estimate, $\mathrm { s } _ { \mathrm { e } }$, for the data below, given that $\hat { y } = - 1.885 \mathrm { x } + 0.758$.
$\begin{array}{l|c|c|c|c|c|c|c|c|c|c|}
\mathrm{x} & -5 & -3 & 4 & 1 & -1 & -2 & 0 & 2 & 3 & -4 \
\hline \mathrm{y} & 11 & 6 & -6 & -1 & 3 & 4 & 1 & -4 & -5 & 8
\end{array}$

A) $0.613$
B) $0.981$
C) $0.312$
D) $0.011$

Question

Compute the Standard Error of the Estimate
-Find the standard error of estimate, $\mathrm { s } _ { \mathrm { e } }$, for the data below, given that $\hat  { y } = - 1.885 \mathrm { x } + 0.758$.
$\begin{array}{l|c|c|c|c|c|c|c|c|c|c|}
\mathrm{x} & -5 & -3 & 4 & 1 & -1 & -2 & 0 & 2 & 3 & -4 \
\hline \mathrm{y} & 11 & 6 & -6 & -1 & 3 & 4 & 1 & -4 & -5 & 8
\end{array}$

A) $0.613$
B) $0.981$
C) $0.312$
D) $0.011$

Quizplus · Accepted Answer

The standard error of the estimate is the square root of the mean squared error, which is the average of the squared differences between the observed values and the predicted values. In this case, the observed values are the y-values, the predicted values are the $\hat  { y }$ values, and the mean squared error is:$$\mathrm { MSE } = \frac { 1 } { n } \sum _ { i = 1 } ^ { n } ( y _ { i } - \hat { y } _ { i } ) ^ { 2 }$$where n is the number of data points.Plugging in the values from the table, we get:$$\mathrm { MSE } = \frac { 1 } { 10 } \sum _ { i = 1 } ^ { 10 } ( y _ { i } - ( - 1.885 x _ { i } + 0.758 ) ) ^ { 2 } = 0.375$$Therefore, the standard error of the estimate is:$$\mathrm { s } _ { \mathrm { e } } = \sqrt { \mathrm { MSE } } = \sqrt { 0.375 } = 0.613$$So the correct answer is A.

Compute the Standard Error of the Estimate -Find the Standard se\mathrm { s } _ { \mathrm { e } }se​

Compute the Standard Error of the Estimate
-Find the Standard $\mathrm { s } _ { \mathrm { e } }$