To find the linear correlation coefficient [tex]\( r \)[/tex] for the given data, we first need to understand what it represents. The linear correlation coefficient [tex]\( r \)[/tex] measures the strength and direction of a linear relationship between two variables. Its value ranges from [tex]\( -1 \)[/tex] to [tex]\( 1 \)[/tex], where:
- [tex]\( r = 1 \)[/tex] indicates a perfect positive linear relationship,
- [tex]\( r = -1 \)[/tex] indicates a perfect negative linear relationship,
- [tex]\( r = 0 \)[/tex] indicates no linear relationship.
Given the paired data:
[tex]\[
\begin{array}{c|cccccccc}
\text{Cost (in thousands of dollars)} & 9 & 2 & 3 & 4 & 2 & 5 & 9 & 10 \\
\hline
\text{Number of Products Sold (in thousands)} & 85 & 52 & 55 & 68 & 67 & 86 & 83 & 73
\end{array}
\][/tex]
We aim to determine the correlation coefficient [tex]\( r \)[/tex].
For this data, the correlation coefficient is calculated using statistical methods that take into account the covariance of the variables and the standard deviations of each variable. After careful calculation of these values, the value of the linear correlation coefficient [tex]\( r \)[/tex] is found to be approximately [tex]\( 0.7077213602731203 \)[/tex].
Given the options provided:
- 0.708
- 0.235
- [tex]\( -0.071 \)[/tex]
The value that matches our calculated correlation coefficient is [tex]\( 0.708 \)[/tex].
Therefore, the linear correlation coefficient [tex]\( r \)[/tex] is:
[tex]\[
\boxed{0.708}
\][/tex]
