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
Equation of the regression line for the given data. $$\begin{array} { l | c | c | c | c | c | c | c | c | c | }
\text { Number of years, } \mathrm { x } & 3 & 4 & 4 & 5 & 3 & 6 & 2 & 7 & 3 \
\hline \text { Grades on test, } \mathrm { y } & 61 & 68 & 75 & 82 & 73 & 90 & 58 & 93 & 72
\end{array}$$
A) $\hat { \hat { y } }$ = 6.910x + 46.261
B) $\hat { \mathrm { y } }$ = 6.910x - 46.261
C) $\hat { \mathrm { y } }$ = 46.261x - 6.910
D) $\hat { \mathbf { y } }$ = 46.261x + 6.910

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
Equation of the regression line for the given data. $$\begin{array} { l | c | c | c | c | c | c | c | c | c | } 
\text { Number of years, } \mathrm { x } & 3 & 4 & 4 & 5 & 3 & 6 & 2 & 7 & 3 \
\hline \text { Grades on test, } \mathrm { y } & 61 & 68 & 75 & 82 & 73 & 90 & 58 & 93 & 72
\end{array}$$
A) $\hat { \hat { y } }$ = 6.910x + 46.261
B) $\hat { \mathrm { y } }$ = 6.910x - 46.261
C) $\hat { \mathrm { y } }$ = 46.261x - 6.910
D) $\hat { \mathbf { y } }$ = 46.261x + 6.910

Quizplus · Accepted Answer

To find the equation of the regression line, we typically use the formula $\hat{y} = mx + b$, where $m$ is the slope and $b$ is the y-intercept. The correct choice, A, represents a linear relationship where for each additional year of study, the grade on the test increases by 6.910 points, starting from a base of 46.261 when x equals 0. This choice correctly formats the equation of a line with $m$ as the coefficient of $x$ and $b$ as the constant term.

In Order for Applicants to Work for the Foreign-Service Department