Compute the Standard Error of the Estimate
-Find the standard error of estimate, $\mathrm { s } _ { \mathrm { e } }$, for the data below, given that $\hat { \mathrm { y } } = - 2.5 \mathrm { x }$.
$\begin{array}{c|c|c|c|c|}
\mathrm{x} & -1 & -2 & -3 & -4 \
\hline \mathrm{y} & 2 & 6 & 7 & 10
\end{array}$

A) $0.866$
B) $0.675$
C) $0.532$
D) $0.349$

Question

Compute the Standard Error of the Estimate
-Find the standard error of estimate, $\mathrm { s } _ { \mathrm { e } }$, for the data below, given that $\hat { \mathrm { y } } = - 2.5 \mathrm { x }$.
$\begin{array}{c|c|c|c|c|}
\mathrm{x} & -1 & -2 & -3 & -4 \
\hline \mathrm{y} & 2 & 6 & 7 & 10
\end{array}$

A) $0.866$
B) $0.675$
C) $0.532$
D) $0.349$

Quizplus · Accepted Answer

The standard error of the estimate ($s_e$) can be calculated using the formula: $$s_e = \sqrt{\frac{\sum (y_i - \hat{y}_i)^2}{n-2}}$$ where $y_i$ are the actual values, $\hat{y}_i$ are the predicted values from the regression equation, and $n$ is the number of observations. Given $\hat{y} = -2.5x$, we first calculate the predicted values ($\hat{y}_i$) for each $x$:- For $x = -1$, $\hat{y} = -2.5(-1) = 2.5$- For $x = -2$, $\hat{y} = -2.5(-2) = 5$- For $x = -3$, $\hat{y} = -2.5(-3) = 7.5$- For $x = -4$, $\hat{y} = -2.5(-4) = 10$Next, we calculate the squared differences between actual ($y_i$) and predicted values ($\hat{y}_i$):- For $x = -1$, $(2 - 2.5)^2 = 0.25$- For $x = -2$, $(6 - 5)^2 = 1$- For $x = -3$, $(7 - 7.5)^2 = 0.25$- For $x = -4$, $(10 - 10)^2 = 0$Sum of squared differences = $0.25 + 1 + 0.25 + 0 = 1.5$Now, we calculate $s_e$ with $n = 4$:$$s_e = \sqrt{\frac{1.5}{4-2}} = \sqrt{\frac{1.5}{2}} = \sqrt{0.75} = 0.866$$Therefore, the standard error of the estimate is $0.866$.

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 $\mathrm { s } _ { \mathrm { e } }$