In order for applicants to work for the foreign-service department, they must take a test in the language of the country where they plan to work. The data below shows the relationship between the number of years that
Applicants have studied a particular language and the grades they received on the proficiency exam. Find the
Standard of estimate, $\mathrm { s_e }$ given that ? = 6.91x + 46.26. $$\begin{array} { l | c | c | c | c | c | c | c | c | c | }
\text { Number of years, } x & 3 & 4 & 4 & 5 & 3 & 6 & 2 & 7 & 3 \
\hline \text { Grades on test, } y & 61 & 68 & 75 & 82 & 73 & 90 & 58 & 93 & 72
\end{array}$$
A)4.578
B)3.412
C)5.192
D)6.713

Question

In order for applicants to work for the foreign-service department, they must take a test in the language of the country where they plan to work. The data below shows the relationship between the number of years that
Applicants have studied a particular language and the grades they received on the proficiency exam. Find the
Standard of estimate, $\mathrm { s_e }$ given that ? = 6.91x + 46.26. $$\begin{array} { l | c | c | c | c | c | c | c | c | c | } 
\text { Number of years, } x & 3 & 4 & 4 & 5 & 3 & 6 & 2 & 7 & 3 \
\hline \text { Grades on test, } y & 61 & 68 & 75 & 82 & 73 & 90 & 58 & 93 & 72
\end{array}$$
A)4.578
B)3.412
C)5.192
D)6.713

Quizplus · Accepted Answer

The standard error of the estimate, $s_e$, can be calculated using the formula: $$s_e = \sqrt{\frac{\sum(y - \hat{y})^2}{n-2}}$$ where $y$ is the actual grade, $\hat{y}$ is the predicted grade using the equation $\hat{y} = 6.91x + 46.26$, and $n$ is the number of observations. After calculating the predicted grades for each $x$ value and finding the differences squared between actual grades ($y$) and predicted grades ($\hat{y}$), summing those, and dividing by $n-2$, then taking the square root, the result is approximately 4.578.

In Order for Applicants to Work for the Foreign-Service Department se\mathrm { s_e }se​

In Order for Applicants to Work for the Foreign-Service Department $\mathrm { s_e }$