Find the standard error of estimate, se, for the data below, given that y = -2.5x. $$\begin{array} { c | c | c | c | c | }
\mathrm { x } & - 1 & - 2 & - 3 & - 4 \
\hline \mathrm { y } & 2 & 6 & 7 & 10
\end{array}$$
A)0.866
B)0.675
C)0.532
D)0.349

Question

Find the standard error of estimate, se, for the data below, given that y = -2.5x. $$\begin{array} { c | c | c | c | c | } 
\mathrm { x } & - 1 & - 2 & - 3 & - 4 \
\hline \mathrm { y } & 2 & 6 & 7 & 10
\end{array}$$
A)0.866
B)0.675
C)0.532
D)0.349

Quizplus · Accepted Answer

The standard error of estimate, $se$, measures the accuracy of predictions made with a regression line. It's calculated using the formula: $$se = \sqrt{\frac{\sum(y_i - \hat{y}_i)^2}{n-2}}$$ where $y_i$ are the observed values, $\hat{y}_i$ are the predicted values from the regression equation, and $n$ is the number of observations. Given $y = -2.5x$, we first calculate the predicted values ($\hat{y}$) for each $x$, then find the sum of squared differences between observed ($y$) and predicted ($\hat{y}$) values, and finally apply the formula for $se$.1. Calculate $\hat{y}$ for each $x$: For $x = -1, -2, -3, -4$, the predicted $y$ values are $2.5, 5, 7.5, 10$ respectively.2. Calculate the squared differences: $(2-2.5)^2, (6-5)^2, (7-7.5)^2, (10-10)^2$ which are $0.25, 1, 0.25, 0$ respectively.3. Sum the squared differences: $0.25 + 1 + 0.25 + 0 = 1.5$.4. Apply the formula: $se = \sqrt{\frac{1.5}{4-2}} = \sqrt{\frac{1.5}{2}} = \sqrt{0.75} = 0.866$.Therefore, the standard error of estimate, $se$, is 0.866.

Find the Standard Error of Estimate, Se, for the Data x−1−2−3−4y26710\begin{array} { c | c | c | c | c | } \mathrm { x } & - 1 & - 2 & - 3 & - 4 \\\hline \mathrm { y } & 2 & 6 & 7 & 10\end{array}xy​−12​−26​−37​−410​​

Find the Standard Error of Estimate, Se, for the Data $\begin{array} { c | c | c | c | c | } \mathrm { x } & - 1 & - 2 & - 3 & - 4 \\\hline \mathrm { y } & 2 & 6 & 7 & 10\end{array}$