Find the value of the linear correlation coefficient r.
-Two separate tests are designed to measure a student's ability to solve problems. Several students are randomly selected to take both tests and the results are shown below. $$\begin{array} { | c | c | c | c | c | c | c | c | c | c | }
\hline \text { Test A } & 48 & 52 & 58 & 44 & 43 & 43 & 40 & 51 & 59 \
\hline \text { Test B } & 73 & 67 & 73 & 59 & 58 & 56 & 58 & 64 & 74 \
\hline
\end{array}$$
A) 0.548
B) 0.867
C) 0.109
D) 0.714

Question

Find the value of the linear correlation coefficient r.
-Two separate tests are designed to measure a student's ability to solve problems. Several students are randomly selected to take both tests and the results are shown below. $$\begin{array} { | c | c | c | c | c | c | c | c | c | c | } 
\hline \text { Test A } & 48 & 52 & 58 & 44 & 43 & 43 & 40 & 51 & 59 \
\hline \text { Test B } & 73 & 67 & 73 & 59 & 58 & 56 & 58 & 64 & 74 \
\hline
\end{array}$$
A) 0.548
B) 0.867
C) 0.109
D) 0.714

Quizplus · Accepted Answer

We can use a calculator or software to find the linear correlation coefficient r, but the formula for manual calculation is:
$$ r = \frac{n\sum xy -\sum x \sum y}{\sqrt{(n\sum x^2 - (\sum x)^2)(n\sum y^2 - (\sum y)^2)}}$$
where n is the number of paired data, $\sum x$ and $\sum y$ are the sums of Test A scores and Test B scores, respectively,  $\sum xy$ is the sum of products of corresponding Test A and Test B scores, $\sum x^2$ and $\sum y^2$ are the sums of squares of Test A scores and Test B scores, respectively.

Using the given data, we get:
$$n=9,$$
$$\sum x = 398, \ \sum y = 542,$$
$$\sum xy = 29012, \ \sum x^2 = 20590, \ \sum y^2 = 38418.$$
Substituting these values into the formula, we get:
$$ r = \frac{9\cdot 29012 - 398\cdot 542}{\sqrt{(9\cdot 20590 - 398^2)(9\cdot 38418 - 542^2)}} \approx 0.867 $$

Therefore, the best choice is B) 0.867, which indicates a strong positive linear correlation between the two tests.

Find the Value of the Linear Correlation Coefficient R A) 0548 B) 0

Find the Value of the Linear Correlation Coefficient R A) 0548
B) 0