Find the value of the linear correlation coefficient $$ r $$ using the paired data below. x 75359516356516 y 165146136177195157115 0.109 -0.078 -0.086 0.214

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We are given seven paired observations. Reading the numbers in groups we have

$$
\begin{array}{ccccccc}
x: & 75, & 35, & 95, & 16, & 35, & 65, \; 16 \quad (\text{but note there are 7 values})\[1mm]
y: & 165, & 146, & 136, & 177, & 195, & 157, & 115
\end{array}
$$

A clear way to see the data is to write the seven pairs as

$$
(75, 165),\; (35, 146),\; (95, 136),\; (16, 177),\; (35, 195),\; (65, 157),\; (16, 115).
$$

We wish to find the linear correlation coefficient

$$
r = \frac{S_{xy}}{\sqrt{S_{xx}\,S_{yy}}},
$$

where

$$
S_{xy} =
To find the linear correlation coefficient $$ r $$, we need to calculate $$ S_{xy} $$, $$ S_{xx} $$, and $$ S_{yy} $$ using the given paired data. After computing these values, we can plug them into the formula: \[ r = \frac{S_{xy}}{\sqrt{S_{xx} \times S_{yy}}} $$ Once all calculations are done, the value of $$ r $$ will be determined based on the computed values.

Find the value of the linear correlation coefficient \( r \) using the paired data below. x 75359516356516 y 165146136177195157115 0.109 -0.078 -0.086 0.214

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