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. Calculatethe linear correlation coefficient. $$\begin{array} { l | c | c | c | c | c | c | c | c | c | }
\text { Number of years, } x & 7 & 8 & 8 & 9 & 7 & 10 & 6 & 11 & 7 \
\hline \text { Grades on test, } y & 62 & 69 & 76 & 83 & 74 & 91 & 59 & 94 & 73
\end{array}$$
A) 0.934
B) 0.911
C) 0.891
D) 0.902

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. Calculatethe linear correlation coefficient. $$\begin{array} { l | c | c | c | c | c | c | c | c | c | } 
\text { Number of years, } x & 7 & 8 & 8 & 9 & 7 & 10 & 6 & 11 & 7 \
\hline \text { Grades on test, } y & 62 & 69 & 76 & 83 & 74 & 91 & 59 & 94 & 73
\end{array}$$
A) 0.934
B) 0.911
C) 0.891
D) 0.902

Quizplus · Accepted Answer

The linear correlation coefficient (Pearson's r) measures the strength and direction of a linear relationship between two variables. Calculating it for the given data set involves using the formula for Pearson's r, which requires summing the products of the deviations of each variable from its mean, and then dividing by the square root of the product of the sums of the squares of the deviations of each variable. The calculation based on the provided data results in a correlation coefficient of 0.934, indicating a strong positive linear relationship between the number of years studied and the grades on the proficiency exam.

In Order for a Companyʹs Employees to Work in a Foreign