In order for a companyʹs employees to work in a foreign office, they must take a test in the language of thecountry where they plan to work. The data below shows the relationship between the number of years thatemployees have studied a particular language and the grades they received on the proficiency exam. Find theequation of the regression line for the given data. Round the regression line values to the nearest hundredth. $\begin{array}{|l|c|c|c|c|c|c|c|c|c|}
\text { Number of years, } \mathrm{x} & 3 & 4 & 4 & 5 & 3 & 6 & 2 & 7 & 3 \
\hline \text { Grades on test, } \mathrm{y} & 61 & 68 & 75 & 82 & 73 & 90 & 58 & 93 & 72
\end{array}$
A) $\hat {y }= 6.91 x + 46.26$
B) $\hat { y } = 6.91 \mathrm { x } - 46.26$
C) $\hat { y } = 46.26 \mathrm { x } - 6.91$
D) $\hat { y } = 46.26 x + 6.91$

Question

In order for a companyʹs employees to work in a foreign office, they must take a test in the language of thecountry where they plan to work. The data below shows the relationship between the number of years thatemployees have studied a particular language and the grades they received on the proficiency exam. Find theequation of the regression line for the given data. Round the regression line values to the nearest hundredth. $\begin{array}{|l|c|c|c|c|c|c|c|c|c|}
\text { Number of years, } \mathrm{x} & 3 & 4 & 4 & 5 & 3 & 6 & 2 & 7 & 3 \
\hline \text { Grades on test, } \mathrm{y} & 61 & 68 & 75 & 82 & 73 & 90 & 58 & 93 & 72
\end{array}$
A) $\hat {y }= 6.91 x + 46.26$
B) $\hat  { y } = 6.91 \mathrm { x } - 46.26$
C) $\hat  { y } = 46.26 \mathrm { x } - 6.91$
D) $\hat { y } = 46.26 x + 6.91$

Quizplus · Accepted Answer

To find the equation of the regression line, you typically use the formula $\hat{y} = mx + b$, where $m$ is the slope of the line and $b$ is the y-intercept. The calculation of the slope ($m$) and intercept ($b$) requires statistical analysis of the given data points, often involving the use of statistical software or a calculator capable of regression analysis. The correct option, A, $\hat{y} = 6.91x + 46.26$, likely results from such an analysis, providing a linear model that best fits the given data points by minimizing the sum of the squares of the vertical distances of the points from the line.

In Order for a Companyʹs Employees to Work in a Foreign