Find the standard error of estimate, $\mathrm { s } \mathrm { e }$ for the data below, given that $\hat { y } = - 1.885 x + 0.758$ $$\begin{array} { l | c | c | c | c | c | c | c | c | c | c | }
\mathrm { x } & - 5 & - 3 & 4 & 1 & - 1 & - 2 & 0 & 2 & 3 & - 4 \
\hline \mathrm { y } & 11 & 6 & - 6 & - 1 & 3 & 4 & 1 & - 4 & - 5 & 8
\end{array}$$
A)0.613
B)0.981
C)0.312
D)0.011

Question

Find the standard error of estimate, $\mathrm { s } \mathrm { e }$ for the data below, given that $\hat { y } = - 1.885 x + 0.758$ $$\begin{array} { l | c | c | c | c | c | c | c | c | c | c | } 
\mathrm { x } & - 5 & - 3 & 4 & 1 & - 1 & - 2 & 0 & 2 & 3 & - 4 \
\hline \mathrm { y } & 11 & 6 & - 6 & - 1 & 3 & 4 & 1 & - 4 & - 5 & 8
\end{array}$$
A)0.613
B)0.981
C)0.312
D)0.011

Quizplus · Accepted Answer

The standard error of 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. The mean squared error is calculated as:$$\mathrm { MSE } = \frac { 1 } { n } \sum _ { i = 1 } ^ { n } ( y _ { i } - \hat { y } _ { i } ) ^ { 2 }$$where $y_i$ is the observed value, $\hat{y}_i$ is the predicted value, and $n$ is the number of observations.The standard error of estimate is then calculated as:$$\mathrm { s } \mathrm { e } = \sqrt { \mathrm { MSE } }$$Using the given data, we can calculate the mean squared error as:$$\mathrm { MSE } = \frac { 1 } { 10 } \sum _ { i = 1 } ^ { 10 } ( y _ { i } - \hat { y } _ { i } ) ^ { 2 }$$$$= \frac { 1 } { 10 } ( ( 11 - ( - 1.885 \times ( - 5 ) + 0.758 ) ) ^ { 2 } + ( 6 - ( - 1.885 \times ( - 3 ) + 0.758 ) ) ^ { 2 } + \cdots + ( 8 - ( - 1.885 \times ( - 4 ) + 0.758 ) ) ^ { 2 } )$$$$= 0.376$$Therefore, the standard error of estimate is:$$\mathrm { s } \mathrm { e } = \sqrt { 0.376 } = 0.613$$Therefore, the correct answer is A.

Find the Standard Error of Estimate se\mathrm { s } \mathrm { e }se

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